The tax horsepower or taxable horsepower was an early system by which taxation rates for automobiles were reckoned in some European countries, such as Britain, Belgium, Germany, France, and Italy; some US states like Illinois charged license plate purchase and renewal fees for passenger automobiles based on taxable horsepower. The tax horsepower rating was computed not from actual engine power but by a simple mathematical formula based on cylinder dimensions. At the beginning of the twentieth century tax power was reasonably close to real power; as the internal combustion engine developed, real power became larger than nominal taxable power by a factor of ten or more.
The so-called RAC horse-power formula was concocted in 1910 by the RAC at the invitation of the British government. The British RAC horsepower rating was calculated from total piston surface area (i.e. "bore" only). To minimise tax ratings British designers developed engines of a given swept volume (capacity) with very long stroke and low piston surface area. Another effect was the multiplicity of models: Sevens, Eights, Nines, Tens, Elevens, Twelves, Fourteens, Sixteens etc. each to fit with a taxation class. Larger more lightly stressed engines may have been equally economical to run yet, in less variety, produced much more economically.
British cars and cars in other countries applying the same approach to automobile taxation continued to feature these long thin cylinders in their engine blocks even in the 1950s and 1960s, after auto-taxation had ceased to be based on piston diameters, partly because limited funds meant that investment in new models often involved new bodies while under the hood/bonnet engines lurked from earlier decades with only minor upgrades such as (typically) higher compression ratios as higher octane fuels slowly returned to European service stations.
The RAC (British) formula for calculating tax horsepower:
- D is the diameter (or bore) of the cylinder in inches
- n is the number of cylinders 
The distortive effects on engine design were seen to reduce the saleability of British vehicles in export markets. While the system had protected the home market from the import of large engined low priced (because produced in such high volumes) American vehicles the need for roomy generously proportioned cars for export was now paramount and the British government abandoned the tax horsepower system with effect from 1 January 1947 replacing it at first with a tax on cubic capacity itself in turn replaced by a flat tax applying from 1 January 1948.
Although tax horsepower was computed on a similar basis in several other European countries during the two or three decades before the Second World War, continental cylinder dimensions were already quoted in millimeters, reflecting the metric measurement system. As a result of roundings when converting the formula between the two measurement systems, a British tax horse-power unit ended up being worth 1.014 continental (i.e. French) tax horse-power units.
Before World War II, France was the leading European producer of powerful luxury automobiles.  Brands such as Bugatti, Delage, Delahaye, and Talbot-Lago made vehicles that are still collectible today. 
After World War II, the government of France decided to end this situation. Since that time, the dirigiste approach of the French government uses puissance fiscale tax regulations to encourage manufacturers to build cars with small engines, and French motorists to buy them. 
French-made vehicles have very small engines relative to vehicle size, sometimes comically small. The 1948-1990 Citroën 2CV model for example was launched with a 425 cc two-cylinder engine that weighs only 100 pounds (45 kg), essentially a motorcycle with 4 wheels. Since many export markets do not have this same constraint, the French automobile industry has become less relevant as an export power.
In France, fiscal horsepower survives. However, in 1956 it was redefined: the formula became more complicated but now it took account of cylinder stroke and of cylinder bore, so that there was no longer any fiscal advantage in producing engines with thin cylinders. The 1956 French fiscal horsepower formula also took account of engine speed, measured in rpm. The government modified the fiscal horsepower formula again in 1978 and in 1998. Since 1998 the taxable horsepower is calculated from the sum of a CO2 emission figure (over 45), and the maximum power output of the engine in kilowatts (over 40) to the power of 1.6.
Diesel engines have long been favoured by French fiscal horsepower calculations. First, since 1956, diesel engines have had a .7 coefficient applied to the calculated value, thus lowering the fiscal horsepower. Secondly, diesel powered vehicles generally produce less CO2 than equivalent gasoline powered models, which in turn reduces the calculated fiscal horsepower using the post 1998 formulas.
Tax horse-power (Steuer-PS) was introduced in Germany on 3 June 1906. It was based on the number of cylinders in the car's engine multiplied by the cylinder bore (or diameter) multiplied by the length of the piston stroke in the cylinder stroke. It therefore took account of the overall engine displacement from the beginning. This was in contrast to the British tax horsepower formula which used the cylinder bore (or diameter) but ignored the length of the piston stroke in the cylinder and so encouraged manufacturers to design engines with implausibly long thin cylinders.
The German formula applied a higher tax horse-power factor to two stroke engined cars than to four stroke engined cars based on the contention that a two stroke engine, wherein each cylinder produces explosive power every time the piston moves down, works harder than a four stroke engine wherein each cylinder produces explosive power only during one downward movement in every two.
The formula for tax horsepower was as follows:
- 1 unit of tax horse-power (Steuer-PS) for four-stroke engined cars = 0.30·i·d2·s
- 1 unit of tax horse-power (Steuer-PS) for two-stroke engined cars = 0.45·i·d2·s
In these formulae:
- i = the number of cylinders
- d = the diameter (or bore) of each cylinder
- s = the stroke length of each cylinder
Because the formula took account of both the bore and the stroke of each cylinder there was a direct linear relationship between a car's engine size and its tax horsepower according to the German formula. Using the engine size data it was possible to determine the tax horsepower using the following data:
- 1 unit of tax horse-power (Steuer-PS) (for four-stroke engined cars) = 261.8 cc
- 1 unit of tax horse-power (Steuer-PS) (for two-stroke engined cars) = 175.5 cc
Incomplete fractions were rounded up to the nearest whole number so a four stroke engined car of 1,000cc would end up designated as a 4PS (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 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 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.
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:
- i is the number of cylinders,
- d is the diameter (or bore) of the cylinder in cm
- S is the piston stroke in cm
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. As of 1966, thirteen cantons changed to a taxation system based on displacement (with certain minor differences). 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. Nonetheless, the tax horsepower system remains in effect for seven cantons as of 2007[update]. The plethora of different taxation systems has contributed to there always being an uncommonly wide variety of different cars marketed in Switzerland.
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.
Impact on engine design and on auto-industry development
The fiscal benefits of reduced cylinder diameters (bore) in favor of longer cylinders (stroke) may have been a factor in encouraging the proliferation of relatively small six-cylinder-engined models appearing in Europe in the 1930s, as the market began to open up for faster middle-weight models. The system clearly perpetuated side-valve engines in countries where the taxation system encouraged these engine designs, and delayed the adoption of ohv engines because the small cylinder diameter reduced the space available for overhead valves and the lengthy combustion chamber in any case reduced their potential for improving combustion efficiency.
Another effect was to make it very expensive to run cars imported from countries where there was no fiscal incentive to minimise cylinder diameters: this may have limited car imports from the USA to Europe during a period when western governments were employing naked protectionist policies in response to economic depression, and thereby encouraged US auto-makers wishing to exploit the European auto-markets to set up their own dedicated subsidiary plants in the larger European markets.
Taxation can modify incentives and tax horsepower is no exception. Large capacity (displacement) engines are penalized, so engineers working where engine capacity is taxed are encouraged to minimize capacity. This rarely happened in the USA, where license plate fees, even adjusted for horsepower ratings, were comparatively much lower than European car taxes.
Naming and classification of individual car models
The tax horsepower rating was often used as the car model name. For example, the Morris Eight got its name from its horsepower rating of eight; not from the number of cylinders of the engine. British cars of the 1920s and 1930s were frequently named using a combination of tax horsepower and actual horsepower - for example, the Talbot 14-45 had an actual power of 45 hp and a tax horsepower of only 14 hp. The Citroën 2CV (French deux chevaux vapeur [fiscaux], two tax horsepowers) was the car that kept such a name for the longest time.
- "The Horse-power story". Milestones, the journal of the IAM. 23rd year of publication: pages 20–22. Spring 1968.
- Motor-Car Taxation. Effects of Different Methods on Design. Models for Home Use and Export. The Times, Saturday, Feb 16, 1946; pg. 5; Issue 50378
- Richard Hodgson. "The RAC HP (horsepower) Rating - Was there any technical basis?". wolfhound.org.uk. Retrieved 2007-08-11.
- Change In Motor Tax On January 1. The Times, Wednesday, Feb 13, 1946
- The New Car Tax. The Times, Wednesday, Jun 18, 1947
- Oswald, Werner (2001). Deutsche Autos 1920-1945, volume 2 (in German). Motorbuch Verlag. p. 532. ISBN 3-613-02170-6.
- Claus Jacobi (managing editor), Rudolf Augstein (proprietor & former managing editor) (8 May 1967). "AUTOMOBILE / ABSATZKRISE ... Durch Reichsgesetz befreite Adolf Hitler im Frühjahr 1933 alle Volksgenossen, die ein Automobil kauften, von der Kraftfahrzeugsteuer. Binnen zwei Jahren stieg der Auto-Absatz auf das Doppelte.". 20/1967. SPIEGEL-ONLINE. p. 27. Retrieved 2013-05-18.
- Oswald, Werner (2001). Deutsche Autos 1920-1945, volume 2 (in German). Motorbuch Verlag. p. 533. ISBN 3-613-02170-6.
- Büschi, Hans-Ulrich, ed. (5 March 1987). Automobil Revue 1987 (in German/French) 82. Berne, Switzerland: Hallwag AG. pp. 96–97. ISBN 3-444-00458-3.