Tax horsepower

In Belgium, the tax power depended on the cubic capacity of the engine in cubic centimeters at the rate of 1 tax horse power for every 200 cm³ (12 cu in).

The Cheval Fiscal, often abbreviated to CV from "chevaux-vapeur" (literally "steam horses") in tax law, is used for the issuing of French registration certificates known as "cartes grises" ("grey cards"). It is an administrative unit originally calculated partly from the power of the engine and used to calculate the amount of tax that may be due at the time of registration.

The Citroën 2CV (two tax horsepower) was the car that kept such a name for the longest time.

Its use in France dates from 1 January 1913. It was updated in 1956, with further revisions in 1978 and a new emission-based system introduced in 1998.

It was originally defined using the following formula:

${\displaystyle CV=n\times D^{2}\times L\times \omega \times K}$

where:

${\displaystyle n}$ is the number of cylinders,

${\displaystyle D}$ is the cylinder bore in centimeters,

${\displaystyle L}$ is the stroke in centimeters,

${\displaystyle \omega }$ is the engine speed in revolutions per second,

${\displaystyle K}$ is a coefficient depending on the number of cylinders (single-cylinder engine : 0.00020; two-cylinder engine : 0.00017; four-cylinder engine: 0.00015; six-or-more-cylinder engine: 0.00013)

In a circular issued on 28 December 1956, the chevaux fiscaux was defined as:

${\displaystyle P={K\times n\times D^{2}\times L\times w}}$

where:

${\displaystyle P}$ = puissance administrative,

${\displaystyle K}$ = constant of 0.00015,

${\displaystyle n}$ = number of cylinders,

${\displaystyle D}$ = bore in centimeters,

${\displaystyle L}$ = stroke in centimeters,

${\displaystyle w}$ = speed of rotation in revolutions per second

The result is multiplied by 0.7 for a diesel engine.

1978 Engine Speed Parameter Formulas

For calculating ${\displaystyle K}$, k1, k2... kn represent the theoretical speed in km/h of the vehicle with the engine running at 1000 rpm in 1st, 2nd... nth forward gears. ${\displaystyle K}$ is a representation of the average speed across the forward gears, with various adjustments added for various transmission types.
Forward speeds	Manual transmissions	Forward speeds	Automatic transmissions[lower-alpha 1]
3 speeds (or fewer)	${\displaystyle K={\frac {k1+k2+k3}{3}}}$	2-speed	${\displaystyle K={\frac {k1+k2}{2.7}}}$
4 speeds	${\displaystyle K={\frac {k1+k2+k3+k4}{4}}}$	3-speed	${\displaystyle K={\frac {k1+k2+k3}{3.48}}}$
5 speeds	k5 ≤ 1.25*k4: ${\displaystyle K={\frac {k1+k2+k3+k5}{4}}}$	4-speed[lower-alpha 2][13]	k4 ≤ 1.4*k3: ${\displaystyle K={\frac {k1+k2+k4}{3.48}}}$
	k5 > 1.25*k4: ${\displaystyle K={\frac {k1+k2+k3+1.25\ k4}{4}}}$		k4 > 1.4*k3: ${\displaystyle K={\frac {k1+k2+1.4\ k3}{3.48}}}$
Manual w/ Overdrive	For transmissions with one or more overdrive speeds, the over- drive ratio is only applied to the fourth (top) gear. The calculations are administered as for a five-speed transmission.	CVT	${\displaystyle K={\frac {km+kM}{2.3}}}$ km and kM represent the velocity at 1000 rpm reached in the lowest and highest available ratios
"Automatics" include semi-automatic transmissions. The provision for four-speed automatics was added on 15 May 1983.

A new system was announced on 23 December 1977[13] to come into force on 1 January 1978 calculated by the following formula:

${\displaystyle P=m\left(0.0458\ {\frac {C}{K}}\right)^{1.48}}$

where:

${\displaystyle P}$ = puissance administrative,

${\displaystyle m}$ = coefficient of 1 for petrol or 0.7 for diesel,

${\displaystyle C}$ = engine capacity in cubic centimeters,

${\displaystyle K}$ = parameter calculated from a weighted arithmetic average speed in kilometers per hour theoretically reached by the vehicle at an engine speed of 1000 revolutions per minute in each gearbox ratio (see dropdown table to the right for more details).

From 1998 until January 2020,[14] the fiscal tax depended on a standardised value of carbon dioxide CO₂ emissions in grams per kilometer (g/km) and the maximum engine power in kilowatts (kW). If C is the amount of CO₂ released and P the engine power, then:

${\displaystyle P_{A}={\frac {C}{45}}+\left({\frac {P}{40}}\right)^{1.6}}$

${\displaystyle P_{A}}$ is expressed in horsepower, rounded to the nearest integer. The official emission rate of CO₂ included in the calculation is taken from the European certificate of conformity.

Tax horse-power (Steuer-PS) was introduced in Germany on 3 June 1906 however in contrast to many regions, i.e. British and French tax horsepower formulae above, it was calculated based on the overall engine displacement from its implementation.

The German formula applied a higher tax horse-power factor to two stroke engine cars than to four-stroke engined cars based on the fact each cylinder in a two-stroke engine fires (has a power stroke) every revolution whereas an Otto cycle or four-stroke cylinder only fires every second revolution .[15]

The formulae for calculating units of tax horsepower (Steuer-PS) were as follows:

four-stroke engined cars = ${\displaystyle 0.30\times i\times d^{2}\times s}$

two-stroke engined cars = ${\displaystyle 0.45\times i\times d^{2}\times s}$

where:

${\displaystyle i}$ = the number of cylinders

${\displaystyle d}$ = the diameter (or bore) of each cylinder

${\displaystyle s}$ = the stroke length of each cylinder

Incomplete fractions were rounded up to the nearest whole number so a four-stroke engined car of 1,000 cc (61 cu in) would end up designated as a 4 PS (or four horsepower) car for car tax purposes.

After April 1928, recognizing the logic of the linear relationship between tax horsepower and engine capacity, the authorities simply set car tax rates according to engine size for passenger cars. (For commercial vehicles vehicle tax became a function of vehicle weight.) Attempts to correlate new tax horsepower values with old ones result in small differences due to roundings used in the new formula which are, for most purposes, unimportant.

In 1933 the Hitler government came into power and identified the promotion of the auto industry as key to economic recovery: new cars purchased after April 1933 were no longer burdened by an annual car tax charge[16] and German passenger car production surged from 41,727 in 1932 to 276,804 in 1938. Thereafter war and military defeat led to a change in car tax policy and after 1945 tax horse-power returned in West Germany, applying the 1928 formula, as a determinant of annual car tax on new cars purchased in or after 1945. However, the introduction of tax on road fuel in 1951 and progressive increases in fuel tax thereafter reduced the importance of annual car tax so that today far more of the tax on car ownership is collected via fuel taxes than via annual car tax.[17]

Fiscal horsepower is still used in Italy for insurance purposes; it was formerly used also for car property taxation and it is based on engine displacement. Following the 1973 oil crisis up until the 1990s, it was heavily imposed on vehicles with engines larger than 2,000 cc,[18][19][20] prompting Italian car makers to fit turbochargers for extra power without enlarging the displacement.[21][22]

Fiscal horsepower also lives on in Spain, but is defined simply in terms of overall engine capacity. It therefore encourages small engines, but does not influence the ratio of cylinder bore to stroke. The current Spanish definition does, however, add a factor that varies in order to favour four-stroke engines over two-stroke engines.

${\displaystyle P_{f}=T\left({0.785\cdot D^{2}\cdot R}\right)^{0.6}\cdot n}$

where:

${\displaystyle P_{f}}$ = Tax Horsepower (Potencia fiscal),

${\displaystyle T}$ = 0.08 for four-stroke engines, 0.11 for two-stroke engines,

${\displaystyle D}$ = cylinder bore in centimeters,

${\displaystyle R}$ = stroke length in centimeters,

${\displaystyle n}$ = Number of cylinders

The 26 cantons of Switzerland used (and use) a variety of different taxation methods. Originally, all of Switzerland used the tax horsepower, calculated as follows:

${\displaystyle {\text{CV/PS}}=0.4\times i\times d^{2}\times S}$

where:

${\displaystyle i}$ = the number of cylinders,

${\displaystyle d}$ = the diameter (or bore) of the cylinder in cm,

${\displaystyle S}$ = the piston stroke in cm[23]

or 1.6/π = 0.51 times engine displacement in cc

The limits between the horsepower denominations were drawn at either 0.49, 0.50, or 0.51 in different cantons. Thus, the eight horsepower category would cover cars of about 7.5–8.5 CV. In 1973 Berne switched to a taxation system based on vehicle weight, and a few other cantons followed. In 1986 Ticino switched to a system based on a calculation including engine size and weight.[23] Nonetheless, the tax horsepower system remained in effect for seven cantons as of 2007. However, as of 2022, although quite likely earlier, Geneva is the only canton to still base road tax purely on tax horsepower.[24] The plethora of different taxation systems has contributed to there always being an uncommonly wide variety of different cars marketed in Switzerland.