List of conversion factors
This article gives a list of conversion factors for several physical quantities. A number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10−6 metre). Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted.
The following quantities are considered: length, area, volume, plane angle, solid angle, mass, density, time, frequency, velocity, volumetric flow rate, acceleration, force, pressure (or mechanical stress), torque (or moment of force), energy, power (or heat flow rate), action, dynamic viscosity, kinematic viscosity, electric current, electric charge, electric dipole, electromotive force (or electric potential difference), electrical resistance, capacitance, magnetic flux, magnetic flux density, inductance, temperature, information entropy, luminous intensity, luminance, luminous flux, illuminance, radiation.
| Symbol | Definition |
|---|---|
| ≡ | exactly equal |
| ≈ | approximately equal to |
| ≘ | (exactly) corresponds to (different types of quantity describing the same phenomenon) |
| digits | indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...) |
| (H) | of chiefly historical interest |
Length
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| ångström | Å | ≡ 1×10−10 m | ≡ 0.1 nm |
| astronomical unit | au | ≡ 149597870700 m ≈ Distance from Earth to Sun |
≡ 149597870700 m [1] |
| attometre | am | ≡ 1×10−18 m | ≡ 1×10−18 m |
| barleycorn (H) | = 1⁄3 in (see note above about rounding) | = 8.46×10−3 m | |
| bohr, atomic unit of length | a0 | = Bohr radius of hydrogen | ≈ 5.2917721092(17)×10−11 m[2] |
| cable length (imperial) | ≡ 608 ft | ≈ 185.3184 m | |
| cable length (International) | ≡ 1⁄10 nmi | ≡ 185.2 m | |
| cable length (US) | ≡ 720 ft | = 219.456 m | |
| chain (Gunter's; Surveyor's) | ch | ≡ 66 ft (US) ≡ 4 rods[3] | ≈ 20.11684 m |
| cubit (H) | ≡ Distance from fingers to elbow ≈ 18 in | ≈ 0.5 m | |
| ell (H) | ell | ≡ 45 in [4] (In England usually) | = 1.143 m |
| fathom | ftm | ≡ 6 ft [4] | = 1.8288 m |
| femtometre | fm | ≡ 1×10−15 m | ≡ 1×10−15 m |
| fermi | fm | ≡ 1×10−15 m[4] | ≡ 1×10−15 m |
| finger | ≡ 7⁄8 in | = 0.022225 m | |
| finger (cloth) | ≡ 4+1⁄2 in | = 0.1143 m | |
| foot (Benoît) (H) | ft (Ben) | ≈ 0.304799735 m | |
| foot (Cape) (H) | Legally defined as 1.033 English feet in 1859 | ≈ 0.314858 m | |
| foot (Clarke's) (H) | ft (Cla) | ≈ 0.3047972654 m | |
| foot (Indian) (H) | ft Ind | ≈ 0.304799514 m | |
| foot, metric | mf | ≡ 300 mm | ≡ 0.3 m |
| foot, metric (Mesures usuelles) (H) | ≡ 1⁄3 m | ≡ 0.3 m | |
| foot (International) | ft | ≡ 0.3048 m ≡ 1⁄3 yd ≡ 12 inches | ≡ 0.3048 m |
| foot (Sear's) (H) | ft (Sear) | ≈ 0.30479947 m | |
| foot (US Survey) | ft (US) | ≡ 1200⁄3937 m [5] | ≈ 0.304800610 m |
| french; charriere | F | ≡ 1⁄3 mm | = 0.3×10−3 m |
| furlong | fur | ≡ 10 chains = 660 ft = 220 yd [4] | = 201.168 m |
| hand | ≡ 4 in [4] | ≡ 0.1016 m | |
| inch (International) | in | ≡ 2.54 cm ≡ 1⁄36 yd ≡ 1⁄12 ft | ≡ 0.0254 m |
| league (land) | lea | ≈ 1 hour walk, Currently defined in US as 3 Statute miles,[3] but historically varied from 2 to 9 km | ≈ 4828 m |
| light-day | ≡ 24 light-hours | ≡ 2.59020683712×1013 m | |
| light-hour | ≡ 60 light-minutes | ≡ 1.0792528488×1012 m | |
| light-minute | ≡ 60 light-seconds | ≡ 1.798754748×1010 m | |
| light-second | ≡ Distance light travels in one second in vacuum | ≡ 299792458 m | |
| light-year | ly | ≡ Distance light travels in vacuum in 365.25 days [6] | ≡ 9.4607304725808×1015 m |
| line | ln | ≡ 1⁄12 in [7] | = 0.002116 m |
| link (Gunter's; Surveyor's) | lnk | ≡ 1⁄100 ch [4] ≡ 0.66 ft (US) ≡ 7.92 in | ≈ 0.2011684 m |
| link (Ramsden's; Engineer's) | lnk | ≡ 1 ft [4] | = 0.3048 m |
| metre (SI base unit) (meter) | m | ≡ Distance light travels in 1⁄299792458 of a second in vacuum.[8] | (SI base unit) |
| mickey | ≡ 1⁄200 in | = 1.27×10−4 m | |
| micrometre (old: micron) | μ; μm | ≡ 1×10−6 m | ≡ 1×10−6 m |
| mil; thou | mil | ≡ 1×10−3 in | = 2.54×10−5 m |
| mil (Sweden and Norway) | mil | ≡ 10 km | = 10000 m |
| mile (geographical) (H) | ≡ 6082 ft | = 1853.7936 m | |
| mile (international) | mi | ≡ 80 chains ≡ 5280 ft ≡ 1760 yd | ≡ 1609.344 m |
| mile (tactical or data) | ≡ 6000 ft | ≡ 1828.8 m | |
| mile (telegraph) (H) | mi | ≡ 6087 ft | = 1855.3176 m |
| mile (US Survey) | mi | ≡ 5280 US Survey feet ≡ (5280 × 1200⁄3937) m | ≈ 1609.347219 m |
| nail (cloth) | ≡ 2+1⁄4 in [4] | = 0.05715 m | |
| nanometre | nm | ≡ 1×10−9 m | ≡ 1×10−9 m |
| nautical league | NL; nl | ≡ 3 nmi [4] | = 5556 m |
| nautical mile (Admiralty) | NM (Adm); nmi (Adm) | = 6080 ft | = 1853.184 m |
| nautical mile (international) | NM; nmi | ≡ 1852 m[9] | ≡ 1852 m |
| nautical mile (US pre 1954) | ≡ 1853.248 m | ≡ 1853.248 m | |
| pace | ≡ 2.5 ft [4] | = 0.762 m | |
| palm | ≡ 3 in [4] | = 0.0762 m | |
| parsec | pc | Distant point with a parallax shift of one arc second from a base of one astronomical unit. ≡ 648000/π au[10][11] |
≈ 30856775814913700 m[12] |
| pica | ≡ 12 points | Dependent on point measures. | |
| picometre | pm | ≡ 1×10−12 m | ≡ 1×10−12 m |
| point (American, English)[13][14] | pt | ≡ 1⁄72.272 in | ≈ 0.000351450 m |
| point (Didot; European) [14][15] | pt | ≡ 1⁄12 × 1⁄72 of pied du roi; After 1878: ≡ 5⁄133 cm |
≈ 0.00037597 m; After 1878: ≈ 0.00037593985 m |
| point (PostScript) [13] | pt | ≡ 1⁄72 in | = 0.0003527 m |
| point (TeX) [13] | pt | ≡ 1⁄72.27 in | = 0.0003514598 m |
| quarter | ≡ 1⁄4 yd | = 0.2286 m | |
| rod; pole; perch (H) | rd | ≡ 16+1⁄2 ft | = 5.0292 m |
| rope (H) | rope | ≡ 20 ft [4] | = 6.096 m |
| shaku (Japan) | ≡ 10/33 m | ≈ 0.303 0303 m | |
| span (H) | ≡ 9 in [4] | = 0.2286 m | |
| spat[16] | ≡ 1×1012 m | ||
| stick (H) | ≡ 2 in | = 0.0508 m | |
| toise (French, post 1667) (H) | T | ≡ 27000/13853 m | ≈ 1.949 0363 m |
| twip | twp | ≡ 1⁄1440 in | = 1.7638×10−5 m |
| x unit; siegbahn | xu | ≈ 1.0021×10−13 m [4] | |
| yard (International) | yd | ≡ 0.9144 m [5] ≡ 3 ft ≡ 36 in | ≡ 0.9144 m |
| yoctometre | ym | ≡ 1×10−24 m | ≡ 1×10−24 m |
| zeptometre | zm | ≡ 1×10−21 m | ≡ 1×10−21 m |
Area
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| acre (international) | ac | ≡ 1 ch × 10 ch = 4840 sq yd | ≡ 4046.8564224 m2 |
| acre (US survey) | ac | ≡ 10 sq ch = 4840 sq yd, also 43560 sq ft | ≈ 4046.873 m2[17] |
| are | a | ≡ 100 m2 | ≡ 100 m2 |
| barn | b | ≡ 10−28 m2 | ≡ 10−28 m2 |
| barony | ≡ 4000 ac | ≡ 1.61874256896×107 m2 | |
| board | bd | ≡ 1 in × 1 ft | ≡ 7.74192×10−3 m2 |
| boiler horsepower equivalent direct radiation | bhp EDR | ≡ 1 ft2 × 1 bhp / (240 BTUIT/h) | ≈ 12.958174 m2 |
| circular inch | circ in | ≡ π⁄4 sq in | ≈ 5.067075×10−4 m2 |
| circular mil; circular thou | circ mil | ≡ π⁄4 mil2 | ≈ 5.067075×10−10 m2 |
| cord | ≡ 192 bd | ≡ 1.48644864 m2 | |
| cuerda (PR Survey) | cda | ≡ 1 cda x 1 cda = 0.971222 acre | ≡ 3930.395625 m2 |
| dunam | ≡ 1000 m2 | ≡ 1000 m2 | |
| guntha (India) | ≡ 121 sq yd | ≈ 101.17 m2 | |
| hectare | ha | ≡ 10000 m2 | ≡ 10000 m2 |
| hide | ≈ 120 ac (variable) | ≈ 5×105 m2 | |
| rood | ro | ≡ 1⁄4 ac | = 1011.7141056 m2 |
| ping | ≡ 20⁄11 m × 20⁄11 m | ≈ 3.306 m2 | |
| section | ≡ 1 mi × 1 mi | = 2.589988110336×106 m2 | |
| shed | ≡ 10−52 m2 | = 10−52 m2 | |
| square (roofing) | ≡ 10 ft × 10 ft | = 9.290304 m2 | |
| square chain (international) | sq ch | ≡ 66 ft × 66 ft = 1⁄10 ac | ≡ 404.68564224 m2 |
| square chain (US Survey) | sq ch | ≡ 66 ft (US) × 66 ft (US) = 1⁄10 US survey acre | ≈ 404.6873 m2 |
| square foot | sq ft | ≡ 1 ft × 1 ft | ≡ 9.290304×10−2 m2 |
| square foot (US Survey) | sq ft | ≡ 1 ft (US) × 1 ft (US) | ≈ 9.2903411613275×10−2 m2 |
| square inch | sq in | ≡ 1 in × 1 in | ≡ 6.4516×10−4 m2 |
| square kilometre | km2 | ≡ 1 km × 1 km | = 106 m2 |
| square link (Gunter's)(International) | sq lnk | ≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft | = 4.0468564224×10−2 m2 |
| square link (Gunter's)(US Survey) | sq lnk | ≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US) | ≈ 4.046872×10−2 m2 |
| square link (Ramsden's) | sq lnk | ≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft | = 0.09290304 m2 |
| square metre (SI unit) | m2 | ≡ 1 m × 1 m | = 1 m2 |
| square mil; square thou | sq mil | ≡ 1 mil × 1 mil | = 6.4516×10−10 m2 |
| square mile | sq mi | ≡ 1 mi × 1 mi | ≡ 2.589988110336×106 m2 |
| square mile (US Survey) | sq mi | ≡ 1 mi (US) × 1 mi (US) | ≈ 2.58999847×106 m2 |
| square rod/pole/perch | sq rd | ≡ 1 rd × 1 rd | = 25.29285264 m2 |
| square yard (International) | sq yd | ≡ 1 yd × 1 yd | ≡ 0.83612736 m2 |
| stremma | ≡ 1000 m2 | = 1000 m2 | |
| township | ≡ 36 sq mi (US) | ≈ 9.323994×107 m2 | |
| yardland | ≈ 30 ac | ≈ 1.2×105 m2 |
Volume
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| acre-foot | ac ft | ≡ 1 ac x 1 ft = 43560 cu ft | = 1233.48183754752 m3 |
| acre-inch | ≡ 1 ac × 1 in | = 102.79015312896 m3 | |
| barrel (imperial) | bl (imp) | ≡ 36 gal (imp) | = 0.16365924 m3 |
| barrel (petroleum); archaic blue-barrel | bl; bbl | ≡ 42 gal (US) | ≡ 0.158987294928 m3 |
| barrel (US dry) | bl (US) | ≡ 105 qt (US) = 105/32 bu (US lvl) | = 0.115628198985075 m3 |
| barrel (US fluid) | fl bl (US) | ≡ 31+1⁄2 gal (US) | = 0.119240471196 m3 |
| board-foot | bdft | ≡ 144 cu in | ≡ 2.359737216×10−3 m3 |
| bucket (imperial) | bkt | ≡ 4 gal (imp) | = 0.01818436 m3 |
| bushel (imperial) | bu (imp) | ≡ 8 gal (imp) | = 0.03636872 m3 |
| bushel (US dry heaped) | bu (US) | ≡ 1+1⁄4 bu (US lvl) | = 0.0440488377086 m3 |
| bushel (US dry level) | bu (US lvl) | ≡ 2150.42 cu in | = 0.03523907016688 m3 |
| butt, pipe | ≡ 126 gal (US) (wine) | = 0.476961884784 m3 | |
| coomb | ≡ 4 bu (imp) | = 0.14547488 m3 | |
| cord (firewood) | ≡ 8 ft × 4 ft × 4 ft | = 3.624556363776 m3 | |
| cord-foot | ≡ 16 cu ft | = 0.453069545472 m3 | |
| cubic fathom | cu fm | ≡ 1 fm × 1 fm × 1 fm | = 6.116438863872 m3 |
| cubic foot | ft3 | ≡ 1 ft × 1 ft × 1 ft | ≡ 0.028316846592 m3 |
| cubic inch | in3 | ≡ 1 in × 1 in × 1 in | ≡ 16.387064×10−6 m3 |
| cubic metre (SI unit) | m3 | ≡ 1 m × 1 m × 1 m | ≡ 1 m3 |
| cubic mile | cu mi | ≡ 1 mi × 1 mi × 1 mi | ≡ 4168181825.440579584 m3 |
| cubic yard | yd3 | ≡ 27 cu ft | ≡ 0.764554857984 m3 |
| cup (breakfast) | ≡ 10 fl oz (imp) | = 284.130625×10−6 m3 | |
| cup (Canadian) | c (CA) | ≡ 8 fl oz (imp) | = 227.3045×10−6 m3 |
| cup (metric) | c | ≡ 250.0×10−6 m3 | ≡ 250.0×10−6 m3 |
| cup (US customary) | c (US) | ≡ 8 US fl oz ≡ 1⁄16 gal (US) | = 236.5882365×10−6 m3 |
| cup (US food nutrition labeling) | c (US) | ≡ 240 mL[18] | = 2.4×10−4 m3 |
| dash (imperial) | ≡ 1⁄384 gi (imp) = 1⁄2 pinch (imp) | = 369.961751302083×10−9 m3 | |
| dash (US) | ≡ 1⁄96 US fl oz = 1⁄2 US pinch | = 308.057599609375×10−9 m3 | |
| dessertspoon (imperial) | ≡ 1⁄12 gi (imp) | = 11.8387760416×10−6 m3 | |
| drop (imperial) | gtt | ≡ 1⁄288 fl oz (imp) | = 98.6564670138×10−9 m3 |
| drop (imperial) (alt) | gtt | ≡ 1⁄1824 gi (imp) | ≈ 77.886684×10−9 m3 |
| drop (medical) | ≡ 1⁄12 mL | = 83.3×10−9 m3 | |
| drop (metric) | ≡ 1⁄20 mL | = 50.0×10−9 m3 | |
| drop (US) | gtt | ≡ 1⁄360 US fl oz | = 82.14869322916×10−9 m3 |
| drop (US) (alt) | gtt | ≡ 1⁄456 US fl oz | ≈ 64.85423149671×10−9 m3 |
| drop (US) (alt) | gtt | ≡ 1⁄576 US fl oz | ≈ 51.34293326823×10−9 m3 |
| fifth | ≡ 1⁄5 US gal | = 757.0823568×10−6 m3 | |
| firkin | ≡ 9 gal (imp) | = 0.04091481 m3 | |
| fluid drachm (imperial) | fl dr | ≡ 1⁄8 fl oz (imp) | = 3.5516328125×10−6 m3 |
| fluid dram (US); US fluidram | fl dr | ≡ 1⁄8 US fl oz | = 3.6966911953125×10−6 m3 |
| fluid scruple (imperial) | fl s | ≡ 1⁄24 fl oz (imp) | = 1.18387760416×10−6 m3 |
| gallon (beer) | beer gal | ≡ 282 cu in | = 4.621152048×10−3 m3 |
| gallon (imperial) | gal (imp) | ≡ 4.54609 L | ≡ 4.54609×10−3 m3 |
| gallon (US dry) | gal (US) | ≡ 1⁄8 bu (US lvl) | = 4.40488377086×10−3 m3 |
| gallon (US fluid; Wine) | gal (US) | ≡ 231 cu in | ≡ 3.785411784×10−3 m3 |
| gill (imperial); Noggin | gi (imp); nog | ≡ 5 fl oz (imp) | = 142.0653125×10−6 m3 |
| gill (US) | gi (US) | ≡ 4 US fl oz | = 118.29411825×10−6 m3 |
| hogshead (imperial) | hhd (imp) | ≡ 2 bl (imp) | = 0.32731848 m3 |
| hogshead (US) | hhd (US) | ≡ 2 fl bl (US) | = 0.238480942392 m3 |
| jigger (bartending) | ≡ 1+1⁄2 US fl oz | ≈ 44.36×10−6 m3 | |
| kilderkin | ≡ 18 gal (imp) | = 0.08182962 m3 | |
| lambda | λ | ≡ 1 mm3 | = 1×10−9 m3 |
| last | ≡ 80 bu (imp) | = 2.9094976 m3 | |
| litre (liter) | L or l | ≡ 1 dm3 [19] | ≡ 0.001 m3 |
| load | ≡ 50 cu ft | = 1.4158423296 m3 | |
| minim (imperial) | min | ≡ 1⁄480 fl oz (imp) = 1/60 fl dr (imp) | = 59.1938802083×10−9 m3 |
| minim (US) | min | ≡ 1⁄480 US fl oz = 1⁄60 US fl dr | = 61.611519921875×10−9 m3 |
| ounce (fluid imperial) | fl oz (imp) | ≡ 1⁄160 gal (imp) | ≡ 28.4130625×10−6 m3 |
| ounce (fluid US customary) | US fl oz | ≡ 1⁄128 gal (US) | ≡ 29.5735295625×10−6 m3 |
| ounce (fluid US food nutrition labeling) | US fl oz | ≡ 30 mL[18] | ≡ 3×10−5 m3 |
| peck (imperial) | pk | ≡ 2 gal (imp) | = 9.09218×10−3 m3 |
| peck (US dry) | pk | ≡ 1⁄4 US lvl bu | = 8.80976754172×10−3 m3 |
| perch | per | ≡ 16+1⁄2 ft × 1+1⁄2 ft × 1 ft | = 0.700841953152 m3 |
| pinch (imperial) | ≡ 1⁄192 gi (imp) = 1/16 tsp (imp) | = 739.92350260416×10−9 m3 | |
| pinch (US) | ≡ 1⁄48 US fl oz = 1/16 US tsp | = 616.11519921875×10−9 m3 | |
| pint (imperial) | pt (imp) | ≡ 1⁄8 gal (imp) | = 568.26125×10−6 m3 |
| pint (US dry) | pt (US dry) | ≡ 1⁄64 bu (US lvl) ≡ 1⁄8 gal (US dry) | = 550.6104713575×10−6 m3 |
| pint (US fluid) | pt (US fl) | ≡ 1⁄8 gal (US) | = 473.176473×10−6 m3 |
| pony | ≡ 3⁄4 US fl oz | = 22.180147171875×10−6 m3 | |
| pottle; quartern | ≡ 1⁄2 gal (imp) = 80 fl oz (imp) | = 2.273045×10−3 m3 | |
| quart (imperial) | qt (imp) | ≡ 1⁄4 gal (imp) | = 1.1365225×10−3 m3 |
| quart (US dry) | qt (US) | ≡ 1⁄32 bu (US lvl) = 1⁄4 gal (US dry) | = 1.101220942715×10−3 m3 |
| quart (US fluid) | qt (US) | ≡ 1⁄4 gal (US fl) | = 946.352946×10−6 m3 |
| quarter; pail | ≡ 8 bu (imp) | = 0.29094976 m3 | |
| register ton | ≡ 100 cu ft | = 2.8316846592 m3 | |
| sack (US) | ≡ 3 bu (US lvl) | = 0.10571721050064 m3 | |
| seam | ≡ 8 bu [16] | = 0.29095 m3 | |
| shot (US) | usually 1.5 US fl oz[16] | ≈ 44.4×10−6 m3 | |
| strike (imperial) | ≡ 2 bu (imp) | = 0.07273744 m3 | |
| strike (US) | ≡ 2 bu (US lvl) | = 0.07047814033376 m3 | |
| tablespoon (Australian metric) | ≡ 20.0×10−6 m3 | ||
| tablespoon (Canadian) | tbsp | ≡ 1⁄2 fl oz (imp) | = 14.20653125×10−6 m3 |
| tablespoon (imperial) | tbsp | ≡ 5⁄8 fl oz (imp) | = 17.7581640625×10−6 m3 |
| tablespoon (metric) | ≡ 15×10−6 m3 | ||
| tablespoon (US customary) | tbsp | ≡ 1⁄2 US fl oz | = 14.78676478125×10−6 m3 |
| tablespoon (US food nutrition labeling) | tbsp | ≡ 15 mL[18] | = 15×10−6 m3 |
| teaspoon (Canadian) | tsp | ≡ 1⁄6 fl oz (imp) | = 4.735510416×10−6 m3 |
| teaspoon (imperial) | tsp | ≡ 1⁄24 gi (imp) | = 5.91938802083×10−6 m3 |
| teaspoon (metric) | ≡ 5.0×10−6 m3 | ≡ 5.0×10−6 m3 | |
| teaspoon (US customary) | tsp | ≡ 1⁄6 US fl oz | = 4.92892159375×10−6 m3 |
| teaspoon (US food nutrition labeling) | tsp | ≡ 5 mL[18] | = 5×10−6 m3 |
| timber foot | ≡ 1 cu ft | = 0.028316846592 m3 | |
| ton (displacement) | ≡ 35 cu ft | = 0.99108963072 m3 | |
| ton (freight) | ≡ 40 cu ft | = 1.13267386368 m3 | |
| ton (water) | ≡ 28 bu (imp) | = 1.01832416 m3 | |
| tun | ≡ 252 gal (wine) | = 0.953923769568 m3 | |
| wey (US) | ≡ 40 bu (US lvl) | = 1.4095628066752 m3 |
Plane angle
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| NATO mil | (various) | ≡ 2π⁄6400 rad | ≈ 0.981748×10−3 rad |
| Swedish streck | ≡ 2π⁄6300 rad | ≈ 0.997302×10−3 rad | |
| milliradian | mrad | ≡ 1⁄1000 rad | ≈ 1×10−3 rad |
| Warsaw Pact mil | ≡ 2π⁄6000 rad | ≈ 1.047167×10−3 rad | |
| arcminute; MOA | ' | ≡ 1°⁄60 | ≈ 0.290888×10−3 rad |
| arcsecond | " | ≡ 1°⁄3600 | ≈ 4.848137×10−6 rad |
| centesimal minute of arc | ' | ≡ 1⁄100 grad | ≈ 0.157080×10−3 rad |
| centesimal second of arc | " | ≡ 1⁄10000 grad | ≈ 1.570796×10−6 rad |
| degree (of arc) | ° | ≡ 1⁄360 of a revolution ≡ π⁄180 rad | ≈ 17.453293×10−3 rad |
| grad; gradian; gon | grad | ≡ 1⁄400 of a revolution ≡ π⁄200 rad ≡ 0.9° | ≈ 15.707963×10−3 rad |
| octant | ≡ 45° | ≈ 0.785398 rad | |
| quadrant | ≡ 90° | ≈ 1.570796 rad | |
| radian (SI unit) | rad | The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians. |
= 1 rad |
| sextant | ≡ 60° | ≈ 1.047198 rad | |
| sign | ≡ 30° | ≈ 0.523599 rad |
Solid angle
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| spat | ≡ 4π sr[16] – The solid angle subtended by a sphere at its centre. | ≈ 12.56637 sr | |
| square degree | deg2; sq.deg.; (°)2 | ≡ (π⁄180)2 sr | ≈ 0.30462×10−3 sr |
| steradian (SI unit) | sr | The solid angle subtended at the center of a sphere of radius r by a portion of the sphere having an area r2. A sphere subtends 4π sr.[16] |
= 1 sr |
Mass
Notes:
- See Weight for detail of mass/weight distinction and conversion.
- Avoirdupois is a system of mass based on a pound of 16 ounces, while Troy weight is the system of mass where 12 troy ounces equals one troy pound.
- The symbol g0 is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atomic mass unit, unified | u; AMU | Same as dalton (see below) | ≈ 1.660539040(20)×10−27 kg[3] |
| atomic unit of mass, electron rest mass | me | ≈ 9.10938291(40)×10−31 kg[20] | |
| bag (coffee) | ≡ 60 kg | = 60 kg | |
| bag (Portland cement) | ≡ 94 lb av | = 42.63768278 kg | |
| barge | ≡ 22+1⁄2 short ton | = 20411.65665 kg | |
| carat | kt | ≡ 3+1⁄6 gr | = 205.1965483 mg |
| carat (metric) | ct | ≡ 200 mg | = 200 mg |
| clove | ≡ 8 lb av | = 3.62873896 kg | |
| crith | ≡ mass of 1 L of hydrogen gas at STP | ≈ 89.9349 mg | |
| dalton | Da | 1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest | ≈ 1.660538921(73)×10−27 kg[3] |
| dram (apothecary; troy) | dr t | ≡ 60 gr | = 3.8879346 g |
| dram (avoirdupois) | dr av | ≡ 27+11⁄32 gr | = 1.7718451953125 g |
| electronvolt mass-equivalent | eV/c2 | ≡ 1 eV / c2 | = 1.78266184(45)×10−36 kg[3] |
| gamma | γ | ≡ 1 μg | = 1 μg |
| grain | gr | ≡ 1⁄7000 lb av | ≡ 64.79891 mg |
| grave | gv | grave was the original name of the kilogram | ≡ 1 kg |
| hundredweight (long) | long cwt or cwt | ≡ 112 lb av | = 50.80234544 kg |
| hundredweight (short); cental | sh cwt | ≡ 100 lb av | = 45.359237 kg |
| hyl; metric slug | ≡ 1 kgf / 1 m/s2 | = 9.80665 kg | |
| kilogram (kilogramme) | kg | ≈ mass of the prototype near Paris ≈ mass of 1 litre of water |
(SI base unit)[8] |
| kip | kip | ≡ 1000 lb av | = 453.59237 kg |
| mark | ≡ 8 oz t | = 248.8278144 g | |
| mite | ≡ 1⁄20 gr | = 3.2399455 mg | |
| mite (metric) | ≡ 1⁄20 g | = 50 mg | |
| ounce (apothecary; troy) | oz t | ≡ 1⁄12 lb t | = 31.1034768 g |
| ounce (avoirdupois) | oz av | ≡ 1⁄16 lb | = 28.349523125 g |
| ounce (US food nutrition labelling) | oz | ≡ 28 g[18] | = 28 g |
| pennyweight | dwt; pwt | ≡ 1⁄20 oz t | = 1.55517384 g |
| point | ≡ 1⁄100 ct | = 2 mg | |
| pound (avoirdupois) | lb av | ≡ 0.45359237 kg = 7000 grains | ≡ 0.45359237 kg |
| pound (metric) | ≡ 500 g | = 500 g | |
| pound (troy) | lb t | ≡ 5760 grains | = 0.3732417216 kg |
| quarter (imperial) | ≡ 1⁄4 long cwt = 2 st = 28 lb av | = 12.70058636 kg | |
| quarter (informal) | ≡ 1⁄4 short ton | = 226.796185 kg | |
| quarter, long (informal) | ≡ 1⁄4 long ton | = 254.0117272 kg | |
| quintal (metric) | q | ≡ 100 kg | = 100 kg |
| scruple (apothecary) | s ap | ≡ 20 gr | = 1.2959782 g |
| sheet | ≡ 1⁄700 lb av | = 647.9891 mg | |
| slug; geepound | slug | ≡ g0 × 1 lb av × 1 s2/ft | ≈ 14.593903 kg |
| stone | st | ≡ 14 lb av | = 6.35029318 kg |
| ton, assay (long) | AT | ≡ 1 mg × 1 long ton ÷ 1 oz t | = 32.6 g |
| ton, assay (short) | AT | ≡ 1 mg × 1 short ton ÷ 1 oz t | = 29.16 g |
| ton, long | long tn or ton | ≡ 2240 lb | = 1016.0469088 kg |
| ton, short | sh tn | ≡ 2000 lb | = 907.18474 kg |
| tonne (mts unit) | t | ≡ 1000 kg | = 1000 kg |
| wey | ≡ 252 lb = 18 st | = 114.30527724 kg (variants exist) | |
| zentner | Ztr. | Definitions vary.[16][21] |
Density
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| gram per millilitre | g/mL | ≡ g/mL | = 1000 kg/m3 |
| kilogram per cubic metre (SI unit) | kg/m3 | ≡ kg/m3 | = 1 kg/m3 |
| kilogram per litre | kg/L | ≡ kg/L | = 1000 kg/m3 |
| ounce (avoirdupois) per cubic foot | oz/ft3 | ≡ oz/ft3 | ≈ 1.001153961 kg/m3 |
| ounce (avoirdupois) per cubic inch | oz/in3 | ≡ oz/in3 | ≈ 1.729994044×103 kg/m3 |
| ounce (avoirdupois) per gallon (imperial) | oz/gal | ≡ oz/gal | ≈ 6.236023291 kg/m3 |
| ounce (avoirdupois) per gallon (US fluid) | oz/gal | ≡ oz/gal | ≈ 7.489151707 kg/m3 |
| pound (avoirdupois) per cubic foot | lb/ft3 | ≡ lb/ft3 | ≈ 16.01846337 kg/m3 |
| pound (avoirdupois) per cubic inch | lb/in3 | ≡ lb/in3 | ≈ 2.767990471×104 kg/m3 |
| pound (avoirdupois) per gallon (imperial) | lb/gal | ≡ lb/gal | ≈ 99.77637266 kg/m3 |
| pound (avoirdupois) per gallon (US fluid) | lb/gal | ≡ lb/gal | ≈ 119.8264273 kg/m3 |
| slug per cubic foot | slug/ft3 | ≡ slug/ft3 | ≈ 515.3788184 kg/m3 |
Time
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atomic unit of time | a.u. | ≡ a0/(α⋅c) | ≈ 2.418884254×10−17 s |
| Callippic cycle | ≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d | = 2.396736 Gs or 2.3983776 Gs[note 1] | |
| century | c | ≡ 100 years (100 a) | = 3.1556952 Gs[note 2][note 3] |
| day | d | = 24 h = 1440 min | = 86.4 ks[note 3] |
| day (sidereal) | d | ≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame) | ≈ 86.1641 ks |
| decade | dec | ≡ 10 years (10 a) | = 315.569520 Ms[note 2][note 3] |
| fortnight | fn | ≡ 2 wk | = 1.2096 Ms[note 3] |
| helek | ≡ 1⁄1080 h | = 3.3 s | |
| Hipparchic cycle | ≡ 4 Callippic cycles - 1 d | = 9.593424 Gs | |
| hour | h | ≡ 60 min | = 3.6 ks[note 3] |
| jiffy | j | ≡ 1⁄60 s | = 16.6 ms |
| jiffy (alternative) | ja | ≡ 1⁄100 s | = 10 ms |
| kè (quarter of an hour) | ≡ 1⁄4 h = 1⁄96 d = 15 min | = 900 s | |
| kè (traditional) | ≡ 1⁄100 d = 14.4 min | = 864 s | |
| lustre; lūstrum | ≡ 5 a of 365 d[note 4] | = 157.68 Ms | |
| Metonic cycle; enneadecaeteris | ≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a | = 599.616 Ms | |
| millennium | ≡ 1000 years (1000 a) | = 31.556952 Gs[note 2][note 3] | |
| milliday | md | ≡ 1⁄1000 d | = 86.4 s |
| minute | min | ≡ 60 s, due to leap seconds sometimes 59 s or 61 s, | = 60 s[note 3] |
| moment | ≡ 90 s | = 90 s | |
| month (full) | mo | ≡ 30 d[22] | = 2.592×106 s[note 3] |
| month (Greg. av.) | mo | = 30.436875 d | ≈ 2.6297 Ms[note 3] |
| month (hollow) | mo | ≡ 29 d[22] | = 2.5056 Ms[note 3] |
| Month (synodic) | mo | Cycle time of moon phases ≈ 29.530589 d (average) | ≈ 2.551 Ms |
| octaeteris | = 48 mo (full) + 48 mo (hollow) + 3 mo (full)[23][24] = 8 a of 365.25 d = 2922 d | = 252.4608 Ms[note 3] | |
| Planck time | ≡ (Gℏ⁄c5)1⁄2 | ≈ 5.39116×10−44 s[25] | |
| second (SI base unit) | s | ≡ Time of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0 K[8] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792458 metres. | (SI base unit) |
| shake | ≡ 10−8 s | = 10 ns | |
| sigma | ≡ 10−6 s | = 1 μs | |
| Sothic cycle | ≡ 1461 a of 365 d | = 46.074096 Gs | |
| svedberg | S | ≡ 10−13 s | = 100 fs |
| week | wk | ≡ 7 d = 168 h = 10080 min | = 604.8 ks[note 3] |
| year (common) | a, y, or yr | 365 d | = 31.536 Ms[note 3][26] |
| year (Gregorian) | a, y, or yr | = 365.2425 d average, calculated from common years (365 d) plus leap years (366 d) on most years divisible by 4. See leap year for details. | = 31.556952 Ms[note 3] |
| year (Julian) | a, y, or yr | = 365.25 d average, calculated from common years (365 d) plus one leap year (366 d) every four years | = 31.5576 Ms |
| year (leap) | a, y, or yr | 366 d | = 31.6224 Ms[note 3][26] |
| year (mean tropical) | a, y, or yr | Conceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [Converter 1] approximately 365.24219 d, each day being 86400 SI seconds[27] | ≈ 31.556925 Ms |
| year (sidereal) | a, y, or yr | ≡ Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately 365.256363 d | ≈ 31.5581497632 Ms |
Notes:
| |||
Frequency
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| actions per minute | APM | ≡ 1/60 Hz | ≈ 0.0167 Hz |
| cycle per second | cps | ≡ 1 Hz | = 1 cps = 1 Hz |
| degree per second | deg/s | ≡ 1 °/s ≡ 1/360 Hz | = 0.0027 Hz |
| hertz (SI unit) | Hz | ≡ One cycle per second | = 1 Hz = 1/s |
| radian per second | rad/s | ≡ 1/(2π) Hz | ≈ 0.159155 Hz |
| revolution per minute | rpm | ≡ One rpm equals one rotation completed around a fixed axis in one minute of time. | ≈ 0.104719755 rad/s |
Speed or velocity
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| foot per hour | fph | ≡ 1 ft/h | = 8.46×10−5 m/s |
| foot per minute | fpm | ≡ 1 ft/min | = 5.08×10−3 m/s |
| foot per second | fps | ≡ 1 ft/s | = 3.048×10−1 m/s |
| furlong per fortnight | ≡ furlong/fortnight | ≈ 1.663095×10−4 m/s | |
| inch per hour | iph | ≡ 1 in/h | = 7.05×10−6 m/s |
| inch per minute | ipm | ≡ 1 in/min | = 4.23×10−4 m/s |
| inch per second | ips | ≡ 1 in/s | = 2.54×10−2 m/s |
| kilometre per hour | km/h | ≡ 1 km/h | = 2.7×10−1 m/s |
| knot | kn | ≡ 1 nmi/h = 1.852 km/h | = 0.514 m/s |
| knot (Admiralty) | kn | ≡ 1 NM (Adm)/h = 1.853184 km/h[28] | = 0.514773 m/s |
| mach number | M | Ratio of the speed to the speed of sound[note 1] in the medium (unitless). | ≈ 340 m/s in air at sea level ≈ 295 m/s in air at jet altitudes |
| metre per second (SI unit) | m/s | ≡ 1 m/s | = 1 m/s |
| mile per hour | mph | ≡ 1 mi/h | = 0.44704 m/s |
| mile per minute | mpm | ≡ 1 mi/min | = 26.8224 m/s |
| mile per second | mps | ≡ 1 mi/s | = 1609.344 m/s |
| speed of light in vacuum | c | ≡ 299792458 m/s | = 299792458 m/s |
| speed of sound in air | s | 1225 to 1062 km/h (761–660 mph or 661–574 kn)[note 1] | ≈ 340 to 295 m/s |
| |||
A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.
Flow (volume)
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| cubic foot per minute | CFM | ≡ 1 ft3/min | = 4.719474432×10−4 m3/s |
| cubic foot per second | ft3/s | ≡ 1 ft3/s | = 0.028316846592 m3/s |
| cubic inch per minute | in3/min | ≡ 1 in3/min | = 2.7311773×10−7 m3/s |
| cubic inch per second | in3/s | ≡ 1 in3/s | = 1.6387064×10−5 m3/s |
| cubic metre per second (SI unit) | m3/s | ≡ 1 m3/s | = 1 m3/s |
| gallon (US fluid) per day | GPD | ≡ 1 gal/d | = 4.381263638×10−8 m3/s |
| gallon (US fluid) per hour | GPH | ≡ 1 gal/h | = 1.051503273×10−6 m3/s |
| gallon (US fluid) per minute | GPM | ≡ 1 gal/min | = 6.30901964×10−5 m3/s |
| litre per minute | l/min or L/min | ≡ 1 L/min | = 1.6×10−5 m3/s |
Acceleration
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| foot per hour per second | fph/s | ≡ 1 ft/(h⋅s) | = 8.46×10−5 m/s2 |
| foot per minute per second | fpm/s | ≡ 1 ft/(min⋅s) | = 5.08×10−3 m/s2 |
| foot per second squared | fps2 | ≡ 1 ft/s2 | = 3.048×10−1 m/s2 |
| gal; galileo | Gal | ≡ 1 cm/s2 | = 10−2 m/s2 |
| inch per minute per second | ipm/s | ≡ 1 in/(min⋅s) | = 4.23×10−4 m/s2 |
| inch per second squared | ips2 | ≡ 1 in/s2 | = 2.54×10−2 m/s2 |
| knot per second | kn/s | ≡ 1 kn/s | ≈ 5.14×10−1 m/s2 |
| metre per second squared (SI unit) | m/s2 | ≡ 1 m/s2 | = 1 m/s2 |
| mile per hour per second | mph/s | ≡ 1 mi/(h⋅s) | = 4.4704×10−1 m/s2 |
| mile per minute per second | mpm/s | ≡ 1 mi/(min⋅s) | = 26.8224 m/s2 |
| mile per second squared | mps2 | ≡ 1 mi/s2 | = 1.609344×103 m/s2 |
| standard gravity | g0 | ≡ 9.80665 m/s2 | = 9.80665 m/s2 |
Force
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atomic unit of force | ≡ me⋅α2⋅c2⁄a0 | ≈ 8.23872206×10−8 N[30] | |
| dyne (CGS unit) | dyn | ≡ g⋅cm/s2 | = 10−5 N |
| kilogram-force; kilopond; grave-force | kgf; kp; gvf | ≡ g0 × 1 kg | = 9.80665 N |
| kip; kip-force | kip; kipf; klbf | ≡ g0 × 1000 lb | = 4.4482216152605×103 N |
| milligrave-force, gravet-force | mgvf; gvtf | ≡ g0 × 1 g | = 9.80665 mN |
| long ton-force | tnf | ≡ g0 × 1 long ton | = 9.96401641818352×103 N |
| newton (SI unit) | N | A force capable of giving a mass of one kilogram an acceleration of one metre per second per second.[31] | = 1 N = 1 kg⋅m/s2 |
| ounce-force | ozf | ≡ g0 × 1 oz | = 0.27801385095378125 N |
| pound-force | lbf | ≡ g0 × 1 lb | = 4.4482216152605 N |
| poundal | pdl | ≡ 1 lb⋅ft/s2 | = 0.138254954376 N |
| short ton-force | tnf | ≡ g0 × 1 short ton | = 8.896443230521×103 N |
| sthene (mts unit) | sn | ≡ 1 t⋅m/s2 | = 103 N |
Pressure or mechanical stress
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atmosphere (standard) | atm | ≡ 101325 Pa[32] | |
| atmosphere (technical) | at | ≡ 1 kgf/cm2 | = 9.80665×104 Pa[32] |
| bar | bar | ≡ 100000 Pa | ≡ 105 Pa |
| barye (CGS unit) | ≡ 1 dyn/cm2 | = 0.1 Pa | |
| centimetre of mercury | cmHg | ≡ 13595.1 kg/m3 × 1 cm × g0 | ≈ 1.33322×103 Pa[32] |
| centimetre of water (4 °C) | cmH2O | ≈ 999.972 kg/m3 × 1 cm × g0 | ≈ 98.0638 Pa[32] |
| foot of mercury (conventional) | ftHg | ≡ 13595.1 kg/m3 × 1 ft × g0 | ≈ 4.063666×104 Pa[32] |
| foot of water (39.2 °F) | ftH2O | ≈ 999.972 kg/m3 × 1 ft × g0 | ≈ 2.98898×103 Pa[32] |
| inch of mercury (conventional) | inHg | ≡ 13595.1 kg/m3 × 1 in × g0 | ≈ 3.386389×103 Pa[32] |
| inch of water (39.2 °F) | inH2O | ≈ 999.972 kg/m3 × 1 in × g0 | ≈ 249.082 Pa[32] |
| kilogram-force per square millimetre | kgf/mm2 | ≡ 1 kgf/mm2 | = 9.80665×106 Pa[32] |
| kip per square inch | ksi | ≡ 1 kipf/sq in | ≈ 6.894757×106 Pa[32] |
| long ton per square foot | ≡ 1 long ton × g0 / 1 sq ft | ≈ 1.0725178011595×105 Pa | |
| micrometre of mercury | μmHg | ≡ 13595.1 kg/m3 × 1 μm × g0 ≈ 0.001 torr | ≈ 0.1333224 Pa[32] |
| millimetre of mercury | mmHg | ≡ 13595.1 kg/m3 × 1 mm × g0 ≈ 1 torr | ≈ 133.3224 Pa[32] |
| millimetre of water (3.98 °C) | mmH2O | ≈ 999.972 kg/m3 × 1 mm × g0 = 0.999972 kgf/m2 | = 9.80638 Pa |
| pascal (SI unit) | Pa | ≡ N/m2 = kg/(m⋅s2) | = 1 Pa[33] |
| pièze (mts unit) | pz | ≡ 1000 kg/m⋅s2 | = 103 Pa = 1 kPa |
| pound per square foot | psf | ≡ 1 lbf/ft2 | ≈ 47.88026 Pa[32] |
| pound per square inch | psi | ≡ 1 lbf/in2 | ≈ 6.894757×103 Pa[32] |
| poundal per square foot | pdl/sq ft | ≡ 1 pdl/sq ft | ≈ 1.488164 Pa[32] |
| short ton per square foot | ≡ 1 short ton × g0 / 1 sq ft | ≈ 9.5760518×104 Pa | |
| torr | torr | ≡ 101325⁄760 Pa | ≈ 133.3224 Pa[32] |
Torque or moment of force
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| pound-force-foot | lbf⋅ft | ≡ g0 × 1 lb × 1 ft | = 1.3558179483314004 N⋅m |
| poundal-ft | pdl⋅ft | ≡ 1 lb⋅ft2/s2 | = 4.21401100938048×10−2 N⋅m |
| pound force-inch | lbf⋅in | ≡ g0 × 1 lb × 1 in | = 0.1129848290276167 N⋅m |
| kilogram force-meter | kgf⋅m | ≡ g0 × N × m | = 9.80665 N⋅m |
| newton-metre (SI unit) | N⋅m | ≡ N × m = kg⋅m2/s2 | = 1 N⋅m |
Energy
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| barrel of oil equivalent | boe | ≈ 5.8×106 BTU59 °F | ≈ 6.12×109 J |
| British thermal unit (ISO) | BTUISO | ≡ 1.0545×103 J | = 1.0545×103 J |
| British thermal unit (International Table) | BTUIT | = 1.05505585262×103 J | |
| British thermal unit (mean) | BTUmean | ≈ 1.05587×103 J | |
| British thermal unit (thermochemical) | BTUth | ≈ 1.054350×103 J | |
| British thermal unit (39 °F) | BTU39 °F | ≈ 1.05967×103 J | |
| British thermal unit (59 °F) | BTU59 °F | ≡ 1.054804×103 J | = 1.054804×103 J |
| British thermal unit (60 °F) | BTU60 °F | ≈ 1.05468×103 J | |
| British thermal unit (63 °F) | BTU63 °F | ≈ 1.0546×103 J | |
| calorie (International Table) | calIT | ≡ 4.1868 J | = 4.1868 J |
| calorie (mean) | calmean | 1⁄100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm | ≈ 4.19002 J |
| calorie (thermochemical) | calth | ≡ 4.184 J | = 4.184 J |
| Calorie (US; FDA) | Cal | ≡ 1 kcal = 1000 cal | = 4184 J |
| calorie (3.98 °C) | cal3.98 °C | ≈ 4.2045 J | |
| calorie (15 °C) | cal15 °C | ≡ 4.1855 J | = 4.1855 J |
| calorie (20 °C) | cal20 °C | ≈ 4.1819 J | |
| Celsius heat unit (International Table) | CHUIT | ≡ 1 BTUIT × 1 K/°R | = 1.899100534716×103 J |
| cubic centimetre of atmosphere; standard cubic centimetre | cc atm; scc | ≡ 1 atm × 1 cm3 | = 0.101325 J |
| cubic foot of atmosphere; standard cubic foot | cu ft atm; scf | ≡ 1 atm × 1 ft3 | = 2.8692044809344×103 J |
| cubic foot of natural gas | ≡ 1000 BTUIT | = 1.05505585262×106 J | |
| cubic yard of atmosphere; standard cubic yard | cu yd atm; scy | ≡ 1 atm × 1 yd3 | = 77.4685209852288×103 J |
| electronvolt | eV | ≡ e × 1 V | ≡ 1.602176634×10−19 J |
| erg (CGS unit) | erg | ≡ 1 g⋅cm2/s2 | = 10−7 J |
| foot-pound force | ft lbf | ≡ g0 × 1 lb × 1 ft | = 1.3558179483314004 J |
| foot-poundal | ft pdl | ≡ 1 lb⋅ft2/s2 | = 4.21401100938048×10−2 J |
| gallon-atmosphere (imperial) | imp gal atm | ≡ 1 atm × 1 gal (imp) | = 460.63256925 J |
| gallon-atmosphere (US) | US gal atm | ≡ 1 atm × 1 gal (US) | = 383.5568490138 J |
| hartree, atomic unit of energy | Eh | ≡ me⋅α2⋅c2 (= 2 Ry) | ≈ 4.359744×10−18 J |
| horsepower-hour | hp⋅h | ≡ 1 hp × 1 h | = 2.684519537696172792×106 J |
| inch-pound force | in lbf | ≡ g0 × 1 lb × 1 in | = 0.1129848290276167 J |
| joule (SI unit) | J | The work done when a force of one newton moves the point of its application a distance of one metre in the direction of the force.[31] | = 1 J = 1 m⋅N = 1 kg⋅m2/s2 = 1 C⋅V = 1 W⋅s |
| kilocalorie; large calorie | kcal; Cal | ≡ 1000 calIT | = 4.1868×103 J |
| kilowatt-hour; Board of Trade Unit | kW⋅h; B.O.T.U. | ≡ 1 kW × 1 h | = 3.6×106 J |
| litre-atmosphere | l atm; sl | ≡ 1 atm × 1 L | = 101.325 J |
| quad | ≡ 1015 BTUIT | = 1.05505585262×1018 J | |
| rydberg | Ry | ≡ R∞⋅ℎ⋅c | ≈ 2.179872×10−18 J |
| therm (E.C.) | ≡ 100000 BTUIT | = 105.505585262×106 J | |
| therm (US) | ≡ 100000 BTU59 °F | = 105.4804×106 J | |
| thermie | th | ≡ 1 McalIT | = 4.1868×106 J |
| tonne of coal equivalent | TCE | ≡ 7 Gcalth | = 29.288×109 J |
| tonne of oil equivalent | toe | ≡ 10 GcalIT | = 41.868×109 J |
| ton of TNT | tTNT | ≡ 1 Gcalth | = 4.184×109 J |
| watt-hour | W⋅h | ≡ 1 W × 1 h | = 3.6×103 J |
| watt-second | W⋅s | ≡ 1 J | = 1×100 J |
Power or heat flow rate
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atmosphere-cubic centimetre per minute | atm ccm | ≡ 1 atm × 1 cm3/min | = 1.68875×10−3 W |
| atmosphere-cubic centimetre per second | atm ccs | ≡ 1 atm × 1 cm3/s | = 0.101325 W |
| atmosphere-cubic foot per hour | atm cfh | ≡ 1 atm × 1 cu ft/h | = 0.79700124704 W |
| atmosphere-cubic foot per minute | atm cfm | ≡ 1 atm × 1 cu ft/min | = 47.82007468224 W |
| atmosphere-cubic foot per second | atm cfs | ≡ 1 atm × 1 cu ft/s | = 2.8692044809344×103 W |
| BTU (International Table) per hour | BTUIT/h | ≡ 1 BTUIT/h | ≈ 0.293071 W |
| BTU (International Table) per minute | BTUIT/min | ≡ 1 BTUIT/min | ≈ 17.584264 W |
| BTU (International Table) per second | BTUIT/s | ≡ 1 BTUIT/s | = 1.05505585262×103 W |
| calorie (International Table) per second | calIT/s | ≡ 1 calIT/s | = 4.1868 W |
| erg per second | erg/s | ≡ 1 erg/s | = 10−7 W |
| foot-pound-force per hour | ft⋅lbf/h | ≡ 1 ft lbf/h | ≈ 3.766161×10−4 W |
| foot-pound-force per minute | ft⋅lbf/min | ≡ 1 ft lbf/min | = 2.259696580552334×10−2 W |
| foot-pound-force per second | ft⋅lbf/s | ≡ 1 ft lbf/s | = 1.3558179483314004 W |
| horsepower (boiler) | hp | ≈ 34.5 lb/h × 970.3 BTUIT/lb | ≈ 9809.5 W[34] |
| horsepower (European electrical) | hp | ≡ 75 kp⋅m/s | = 736 W |
| horsepower (electrical) | hp | ≡ 746 W | = 746 W[34] |
| horsepower (mechanical) | hp | ≡ 550 ft⋅lbf/s[34] | = 745.69987158227022 W |
| horsepower (metric) | hp or PS | ≡ 75 m⋅kgf/s | = 735.49875 W[34] |
| litre-atmosphere per minute | L·atm/min | ≡ 1 atm × 1 L/min | = 1.68875 W |
| litre-atmosphere per second | L·atm/s | ≡ 1 atm × 1 L/s | = 101.325 W |
| lusec | lusec | ≡ 1 L·µmHg/s [16] | ≈ 1.333×10−4 W |
| poncelet | p | ≡ 100 m⋅kgf/s | = 980.665 W |
| square foot equivalent direct radiation | sq ft EDR | ≡ 240 BTUIT/h | ≈ 70.337057 W |
| ton of air conditioning | ≡ 2000 lb of ice melted / 24 h | ≈ 3504 W | |
| ton of refrigeration (imperial) | ≡ 2240 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F | ≈ 3.938875×103 W | |
| ton of refrigeration (IT) | ≡ 2000 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F | ≈ 3.516853×103 W | |
| watt (SI unit) | W | The power which in one second of time gives rise to one joule of energy.[31] | = 1 W = 1 J/s = 1 N⋅m/s = 1 kg⋅m2/s3 |
Action
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atomic unit of action | au | ≡ ℏ ≡ ℎ⁄2π | ≈ 1.05457168×10−34 J⋅s[35] |
Dynamic viscosity
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| pascal second (SI unit) | Pa⋅s | ≡ N⋅s/m2, kg/(m⋅s) | = 1 Pa⋅s |
| poise (CGS unit) | P | ≡ 1 barye⋅s | = 0.1 Pa⋅s |
| pound per foot hour | lb/(ft⋅h) | ≡ 1 lb/(ft⋅h) | ≈ 4.133789×10−4 Pa⋅s |
| pound per foot second | lb/(ft⋅s) | ≡ 1 lb/(ft⋅s) | ≈ 1.488164 Pa⋅s |
| pound-force second per square foot | lbf⋅s/ft2 | ≡ 1 lbf⋅s/ft2 | ≈ 47.88026 Pa⋅s |
| pound-force second per square inch | lbf⋅s/in2 | ≡ 1 lbf⋅s/in2 | ≈ 6894.757 Pa⋅s |
Kinematic viscosity
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| square foot per second | ft2/s | ≡ 1 ft2/s | = 0.09290304 m2/s |
| square metre per second (SI unit) | m2/s | ≡ 1 m2/s | = 1 m2/s |
| stokes (CGS unit) | St | ≡ 1 cm2/s | = 10−4 m2/s |
Electric current
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| ampere (SI base unit) | A | ≡ one coulomb of charge going past a given point per second.[36] | (SI base unit) |
| electromagnetic unit; abampere (CGS unit) | abamp | ≘ 10 A | = 10 A |
| esu per second; statampere (CGS unit) | esu/s | ≘ (10 A⋅cm/s) / c | ≈ 3.335641×10−10 A |
Electric charge
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| abcoulomb; electromagnetic unit (CGS unit) | abC; emu | ≘ 10 C | = 10 C |
| atomic unit of charge | au | ≡ e | = 1.602176634×10−19 C |
| coulomb | C | ≡ charge of exactly 1/(1.602176634×10−19) elementary charges[36] | = 1 C = 1 A⋅s |
| faraday | F | ≡ 1 mol × NA⋅e | ≈ 96485.3383 C |
| milliampere hour | mA⋅h | ≡ 0.001 A × 1 h | = 3.6 C |
| statcoulomb; franklin; electrostatic unit (CGS unit) | statC; Fr; esu | ≘ (10 A⋅cm) / c | ≈ 3.335641×10−10 C |
Electric dipole
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| atomic unit of electric dipole moment | ea0 | ≈ 8.47835281×10−30 C⋅m[37] | |
| coulomb-meter | C⋅m | = 1 C⋅m | |
| debye | D | ≡ 10−10 esu⋅Å | ≘ 3.33564095×10−30 C⋅m[38] |
Electromotive force, electric potential difference
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| abvolt (CGS unit) | abV | ≘ 10−8 V | = 10−8 V |
| statvolt (CGS unit) | statV | ≘ c⋅(1 μJ/A⋅m) | = 299.792458 V |
| volt (SI unit) | V | The difference in electric potential across two points along a conducting wire carrying one ampere of constant current when the power dissipated between the points equals one watt.[31] | = 1 V = 1 W/A = 1 kg⋅m2/(A⋅s3) = 1 J/C |
Electrical resistance
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| ohm (SI unit) | Ω | The resistance between two points in a conductor when one volt of electric potential difference, applied to these points, produces one ampere of current in the conductor.[31] | = 1 Ω = 1 V/A = 1 kg⋅m2/(A2⋅s3) |
Capacitance
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| farad (SI unit) | F | The capacitance between two parallel plates that results in one volt of potential difference when charged by one coulomb of electricity.[31] | = 1 F = 1 C/V = 1 A2⋅s4/(kg⋅m2) |
Magnetic flux
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| maxwell (CGS unit) | Mx | ≘ 10−8 Wb[34] | = 10−8 Wb |
| weber (SI unit) | Wb | Magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.[31] | = 1 Wb = 1 V⋅s = 1 kg⋅m2/(A⋅s2) |
Magnetic flux density
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| gauss (CGS unit) | G | ≡ Mx/cm2 ≘ 10−4 T | = 10−4 T [39] |
| tesla (SI unit) | T | ≡ Wb/m2 | = 1 T = 1 Wb/m2 = 1 kg/(A⋅s2) |
Inductance
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| henry (SI unit) | H | The inductance of a closed circuit that produces one volt of electromotive force when the current in the circuit varies at a uniform rate of one ampere per second.[31] | = 1 H = 1 Wb/A = 1 kg⋅m2/(A⋅s)2 |
Temperature
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| degree Celsius | °C | [°C] ≡ [K] − 273.15 | [K] ≡ [°C] + 273.15 |
| degree Delisle | °De | [K] = 373.15 − [°De] × 2⁄3 | |
| degree Fahrenheit | °F | [°F] ≡ [°C] × 9⁄5 + 32 | [K] ≡ ([°F] + 459.67) × 5⁄9 |
| degree Newton | °N | [K] = [°N] × 100⁄33 + 273.15 | |
| degree Rankine | °R; | [°R] ≡ [K] × 9⁄5 | [K] ≡ [°R] × 5/9 |
| degree Réaumur | °Ré | [K] = [°Ré] × 5⁄4 + 273.15 | |
| degree Rømer | °Rø | [K] = ([°Rø] − 7.5) × 40⁄21 + 273.15 | |
| Regulo Gas Mark | GM | [°F] ≡ [GM] × 25 + 250 | [K] ≡ [GM] × 125⁄9 + 394.26 |
| kelvin (SI base unit) | K | ≡ change in the thermodynamic temperature T that results in a change of thermal energy kT by 1.380 649 × 10−23 J.[40] | (SI base unit) |
Information entropy
| Name of unit | Symbol | Definition | Relation to SI units | Relation to bits |
|---|---|---|---|---|
| natural unit of information; nit; nepit | nat | |||
| shannon | Sh | ≡ ln(2) × nat | ≈ 0.693147 nat | = 1 bit |
| hartley; ban | Hart; ban | ≡ ln(10) × nat | ≈ 2.302585 nat | |
| bit | bit; b | = 1 bit | ||
| nibble | ≡ 4 bits | = 22 bit | ||
| byte | B | ≡ 8 bits | = 23 bit | |
| kilobyte (decimal) | kB | ≡ 1000 B | = 8000 bit | |
| kibibyte (kilobyte) | KiB | ≡ 1024 B | = 213 bit = 8192 bit |
Modern standards (such as ISO 80000) prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the (discrete) storage space of digital devices is measured in bits. Thus, uncompressed redundant data occupy more than one bit of storage per shannon of information entropy. The multiples of a bit listed above are usually used with this meaning.
Luminous intensity
The candela is the preferred nomenclature for the SI unit.
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| candela (SI base unit) | cd | The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.[36] | (SI base unit) |
| candlepower (new) | cp | ≡ cd The use of candlepower as a unit is discouraged due to its ambiguity. | = 1 cd |
| candlepower (old, pre-1948) | cp | Varies and is poorly reproducible.[41] Approximately 0.981 cd.[16] | ≈ 0.981 cd |
Luminance
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| candela per square foot | cd/ft2 | ≡ cd/ft2 | ≈ 10.763910417 cd/m2 |
| candela per square inch | cd/in2 | ≡ cd/in2 | ≈ 1550.0031 cd/m2 |
| candela per square metre (SI unit); nit (deprecated[16]) | cd/m2 | ≡ cd/m2 | = 1 cd/m2 |
| footlambert | fL | ≡ (1/π) cd/ft2 | ≈ 3.4262590996 cd/m2 |
| lambert | L | ≡ (104/π) cd/m2 | ≈ 3183.0988618 cd/m2 |
| stilb (CGS unit) | sb | ≡ 104 cd/m2 | = 104 cd/m2 |
Luminous flux
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| lumen (SI unit) | lm | The luminous flux of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant flux of 1/683 watt.[36] | = 1 lm = 1 cd⋅sr |
Illuminance
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| footcandle; lumen per square foot | fc | ≡ lm/ft2 | = 10.763910417 lx |
| lumen per square inch | lm/in2 | ≡ lm/in2 | ≈ 1550.0031 lx |
| lux (SI unit) | lx | ≡ lm/m2 | = 1 lx = 1 lm/m2 |
| phot (CGS unit) | ph | ≡ lm/cm2 | = 104 lx |
Radiation
Radiation – source activity
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| becquerel (SI unit) | Bq | ≡ Number of disintegrations per second | = 1 Bq = 1/s |
| curie | Ci | ≡ 3.7×1010 Bq[42] | = 3.7×1010 Bq |
| rutherford (H) | Rd | ≡ 1 MBq | = 106 Bq |
Although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (s−1), Hz is used only for periodic phenomena (i.e. repetitions at regular intervals), and Bq is only used for stochastic processes (i.e. at random intervals) associated with radioactivity.[43]
Radiation – exposure
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| roentgen | R | 1 R ≡ 2.58×10−4 C/kg[34] | = 2.58×10−4 C/kg |
The roentgen is not an SI unit and the NIST strongly discourages its continued use.[44]
Radiation – absorbed dose
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| gray (SI unit) | Gy | ≡ 1 J/kg[45] | = 1 Gy = 1 J/kg = 1 m2⋅s2 |
| rad | rad | ≡ 0.01 Gy[34] | = 0.01 Gy |
Radiation – equivalent dose
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| Röntgen equivalent man | rem | ≡ 0.01 Sv | = 0.01 Sv |
| sievert (SI unit) | Sv | ≡ 1 J/kg[43] | = 1 Sv = 1 J/kg = 1 m2⋅s2 |
Although the definitions for sievert (Sv) and gray (Gy) would seem to indicate that they measure the same quantities, this is not the case. The effect of receiving a certain dose of radiation (given as Gy) is variable and depends on many factors, thus a new unit was needed to denote the biological effectiveness of that dose on the body; this is known as the equivalent dose and is shown in Sv. The general relationship between absorbed dose and equivalent dose can be represented as
- H = Q ⋅ D
where H is the equivalent dose, D is the absorbed dose, and Q is a dimensionless quality factor. Thus, for any quantity of D measured in Gy, the numerical value for H measured in Sv may be different.[46]
Notes
- The technical definition of tropical year is the period of time for the ecliptic longitude of the Sun to increase 360 degrees. (Urban & Seidelmann 2013, Glossary, s.v. year, tropical)
References
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