Torque is force, horsepower is force times speed
Torque is a twisting effort: a force applied at a distance from the centre of rotation. Four hundred pound-feet means the crankshaft is being twisted as hard as a 400 lb weight hung on a one-foot lever. It says nothing about how fast anything is moving.
Power is the rate at which that twisting does work. Spin the same 400 lb-ft twice as fast and you do twice as much work per minute, so you have twice the power. That is the entire relationship: power = torque × rotational speed. Everything else is unit bookkeeping.
The distinction matters because torque and power answer different questions. Torque at the wheels, after gearing, is what accelerates the car at that instant. Power is what determines how much torque you can have after gearing at a given road speed — because a gearbox trades speed for torque at constant power. Two engines with identical peak torque but different peak power will not accelerate the same way, because the one that makes its torque higher up can be geared shorter and multiply it further. This is why power to weight, not torque to weight, is the number that predicts lap times and quarter-mile trap speeds.
Neither figure is meaningful without the speed it was measured at. A dyno sheet quoting “500 lb-ft” with no rpm is not a specification.
Where 5,252 comes from
James Watt defined one horsepower as 33,000 foot-pounds of work per minute. To convert a rotating shaft's output into that unit you need to turn revolutions into linear distance.
One revolution carries a point on a one-foot lever arm through a circle of circumference 2π feet. So a torque of T lb-ft turning at N revolutions per minute does T × 2πN foot-pounds of work every minute. Divide by 33,000 to express that in horsepower:
HP = T × 2πN ÷ 33,000 = T × N ÷ (33,000 ÷ 2π) = T × N ÷ 5252.113.
That is the whole derivation. The constant is not an empirical fudge; it is 33,000 divided by 2π, and it is exact to as many decimals as you care to carry. The commonly quoted 5,252 is that number rounded, and using it introduces an error of about 0.002% — irrelevant for engines, but this calculator carries the exact value anyway.
The metric version follows the same logic. One watt is one newton-metre per second, so kilowatts equal torque in N·m times rpm divided by 9549.297, which is 30,000 ÷ π. And because one mechanical horsepower is 745.6999 W while one metric PS is 735.49875 W, a PS figure is always about 1.4% larger than the same power quoted in hp. That difference alone explains most of the apparent disagreements between European and American spec sheets.
The famous consequence of the constant: horsepower and torque curves plotted in hp and lb-ft on the same axes always cross at 5,252 rpm, because that is the speed at which the multiplier N ÷ 5252.113 equals one. Below that speed the lb-ft number is the larger of the two; above it, the hp number is. This tells you nothing about the engine — it is a property of the units.
Worked example: 500 lb-ft at 3,000 rpm, then the same engine at 5,500
A diesel pickup measures 500 lb-ft at 3,000 rpm on the dyno.
- Multiply torque by speed. 500 × 3,000 = 1,500,000 lb-ft·rpm.
- Divide by the constant. 1,500,000 ÷ 5252.113 = 285.60 hp.
- Convert to kilowatts. 285.60 × 0.7456999 = 212.97 kW.
- Convert to PS. 212.97 ÷ 0.73549875 = 289.56 PS.
- Check the torque in metric. 500 × 1.3558179 = 677.91 N·m, and 677.91 × 3,000 ÷ 9549.297 = 212.97 kW, which agrees with step 3 exactly.
Now suppose a petrol engine makes less torque — 400 lb-ft — but does it at 5,500 rpm. 400 × 5,500 ÷ 5252.113 = 418.88 hp. The petrol engine makes 20% less torque and 47% more power, purely because it makes its torque at a higher speed. Gear it appropriately and it will out-accelerate the diesel despite the smaller number on the spec sheet.
Working backwards is just as common. A manufacturer claims 400 hp at 6,000 rpm but publishes no torque figure. Rearranged: T = 400 × 5252.113 ÷ 6,000 = 350.14 lb-ft at that speed. Note that this is torque at the power peak, which is always lower than peak torque, because torque has already begun falling by the time power peaks.
Reading a dyno sheet properly
First, check which power the number is. Flywheel (brake) horsepower is measured on an engine dyno with the engine bolted to the brake; wheel horsepower comes off a chassis dyno and is lower by whatever the drivetrain absorbs. Rules of thumb for drivetrain loss vary by layout and are only rules of thumb: manual rear-drive cars are commonly quoted around 15%, automatics and all-wheel-drive higher. Never compare a wheel figure to a manufacturer's flywheel claim without saying so.
Second, check the correction factor. SAE J1349 corrects measured power to a standard inlet condition so that a dyno pull in Denver in August can be compared with one in Detroit in January. An uncorrected number from a hot, high day can read several percent low. Different correction standards — SAE J1349, DIN 70020, ECE R85, JIS — give slightly different answers on the same engine, so the standard should be printed on the sheet.
Third, check whether the number is a peak or a curve. Peak power is one point; the area under the curve between shift points is what actually moves the car. An engine with a broad, flat torque plateau will beat a peaky engine with a higher headline number in most real driving, because it spends more of its time near its best output.
If you want an independent sanity check on a power claim, run it against the car's quarter-mile trap speed. Trap speed is set by power and weight, and it is very hard to fake.
Power per 100 lb-ft of torque, by engine speed
| Engine speed (rpm) | Power (hp) | Power (kW) |
|---|---|---|
| 1,000 | 19.04 | 14.20 |
| 2,000 | 38.08 | 28.40 |
| 3,000 | 57.12 | 42.59 |
| 4,000 | 76.16 | 56.79 |
| 5,000 | 95.20 | 70.99 |
| 5,252 | 100.00 | 74.57 |
| 6,000 | 114.24 | 85.19 |
| 7,000 | 133.28 | 99.39 |
| 8,000 | 152.32 | 113.58 |
Each row is 100 × rpm ÷ 5252.113, then × 0.7456999 for kilowatts. The 5,252 rpm row is where the hp and lb-ft numbers coincide.
Mistakes that make the conversion wrong
- Mixing units in one formula. The 5,252 constant works only with lb-ft and hp. Feed it newton-metres and the answer is 36% off. Use 9549.297 for N·m and kW.
- Confusing hp with PS. Metric PS is 735.5 W and mechanical hp is 745.7 W, so a 400 PS car is 394.5 hp. European brochures quote PS; American ones quote hp.
- Using torque at the power peak as peak torque. They occur at different engine speeds. The reverse solve here gives torque at the speed you entered, nothing else.
- Comparing wheel horsepower to a manufacturer figure. Manufacturers quote flywheel power measured to a stated standard. Chassis dynos measure at the tyre.
- Treating the 5,252 crossover as significant. It is a unit artefact. In kW and N·m the curves cross at 9,549 rpm instead, and nothing about the engine has changed.
- Quoting torque without an engine speed. Torque alone is not a power specification and cannot be converted without the rpm it was made at.
Key terms
- Brake horsepower (bhp)
- Power measured at the crankshaft on a dynamometer brake, before any drivetrain losses.
- PS (Pferdestärke)
- Metric horsepower, defined as 75 kgf·m per second = 735.49875 W. About 1.4% smaller than mechanical hp.
- SAE J1349
- The SAE test code that specifies how engine power is measured and corrected to standard atmospheric conditions.
- Brake mean effective pressure
- Torque normalised by displacement — the average pressure that would produce the measured torque. It lets engines of different sizes be compared directly.
What to do with the number once you have it
Power on its own predicts nothing. Power divided by mass predicts acceleration, which is why every racing class and every road test converges on pounds per horsepower or kilowatts per tonne rather than on raw output. A 400 hp car weighing 4,200 lb and a 250 hp car weighing 2,600 lb are within a whisker of each other on paper.
Between the crankshaft and the road there is a gearbox and a final drive, and their job is to convert power into whatever combination of torque and speed the situation needs. That is why axle ratio and speed at a given rpm belong in the same conversation as horsepower: gearing decides where on the power curve the engine sits at any road speed, and therefore how much of the engine's capability you are actually using.
If you are chasing more power rather than measuring what you have, the causal chain runs backwards through airflow. Torque is set by how much air the engine traps and how efficiently it burns it, so more torque means more air — from displacement, from better breathing, or from boost. Once you have decided how much power you want, injector sizing follows from it directly, because fuel flow is proportional to power rather than to displacement.
One last piece of context on the constant. Because horsepower is a defined unit rather than a physical constant, several definitions coexist: mechanical horsepower at 745.6999 W, metric PS at 735.49875 W, and electrical horsepower at exactly 746 W. Automotive work uses mechanical hp in the United States and either kW or PS elsewhere. When a figure looks 1.4% off from what you expected, this is almost always why.