Torque to HP Converter
Our free force pressure & torque converter handles torqueto hp conversions. See tables, ratios, and examples for quick reference.
Torque to HP Converter
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Formula: HP = (Torque x RPM) / 5252
Worked example โ 400 lb-ft at 4000 RPM = 304.65 HP (227.14 kW)
Formula
HP = (Torque x RPM) / 5252
Horsepower equals torque (in lb-ft) multiplied by RPM, divided by 5252. The constant 5252 is derived from 33,000 ft-lb/min (the definition of 1 HP) divided by 2 times pi. This formula links the static rotational force (torque) with the rate of rotation (RPM) to produce a measure of power output.
Worked Examples
Example 1: V8 Engine at Peak Torque
Problem:A V8 engine produces 400 lb-ft of torque at 4000 RPM. What is the horsepower?
Solution:HP = (Torque x RPM) / 5252 HP = (400 x 4000) / 5252 HP = 1,600,000 / 5252 HP = 304.65 kW = 304.65 x 0.7457 = 227.14 kW
Result:400 lb-ft at 4000 RPM = 304.65 HP (227.14 kW)
Example 2: Electric Motor in Nm
Problem:An electric motor produces 350 Nm at 6000 RPM. Convert to horsepower.
Solution:Convert to lb-ft: 350 x 0.7376 = 258.16 lb-ft HP = (258.16 x 6000) / 5252 HP = 1,548,960 / 5252 HP = 294.93 HP
Result:350 Nm at 6000 RPM = 294.93 HP (219.90 kW)
Frequently Asked Questions
How do you convert torque to horsepower?
The formula to convert torque to horsepower is HP = (Torque x RPM) / 5252, where torque is in pound-feet. The constant 5252 comes from the definition of horsepower (33,000 ft-lb/min) divided by 2 times pi. This means horsepower is directly proportional to both torque and RPM, so an engine making 250 lb-ft at 5000 RPM produces about 238 HP. At exactly 5252 RPM, the horsepower and torque values in lb-ft are equal.
What is the difference between horsepower and torque?
Torque is a rotational force measured at an instant, while horsepower is a rate of doing work over time. Torque tells you how much twisting force the engine produces, and horsepower tells you how quickly that force can do work. In practical terms, torque determines how strongly a vehicle accelerates at low speeds and how well it handles loads, while horsepower determines top speed and sustained high-speed performance. An engine with high torque but low RPM can still have modest horsepower.
Why do torque and HP curves cross at 5252 RPM?
The crossover at 5252 RPM is a mathematical certainty when both are plotted in their standard units (lb-ft and HP). Since HP = (Torque x RPM) / 5252, when RPM equals 5252, HP equals Torque numerically. This is not a physical phenomenon but a consequence of the units chosen. Below 5252 RPM the torque number is higher than HP, and above 5252 RPM the HP number exceeds torque. This relationship holds for every internal combustion engine.
What is the difference between HP and PS (metric horsepower)?
Mechanical horsepower (HP) equals 550 foot-pounds per second or about 745.7 watts, while metric horsepower (PS, from the German Pferdestarke) equals 75 kilogram-force meters per second or about 735.5 watts. One HP equals approximately 1.01387 PS. The difference is small but can matter for precise engineering specifications. European car manufacturers traditionally quote power in PS or kW, while American manufacturers use HP.
How do you convert newton-metres of torque into pound-feet first?
One pound-foot equals 1.35582 N-m, so a torque in N-m multiplied by 0.73756 gives lb-ft. The 5252 constant only works with torque in lb-ft, so metric torque figures must be converted before the division. A 340 N-m engine therefore supplies 340 x 0.73756 = 250.8 lb-ft, and at 5000 rpm that is (250.8 x 5000) / 5252 = 238.7 hp. Skipping the unit step inflates the answer by about 36 percent.
What is the metric equivalent of the 5252 constant?
Working directly in SI, power in kilowatts equals torque in newton-metres times rpm divided by 9549. That constant comes from the same physics: angular velocity in radians per second is rpm x 2 x pi / 60, and power equals torque times angular velocity, so 9549 is simply 60,000 divided by 2 pi. Use 9549 with N-m and 5252 with lb-ft, and never mix the two pairings.
Why do the torque and horsepower curves always cross at the same engine speed?
Because horsepower is a derived quantity, not an independent one. Since hp equals torque times rpm divided by 5252, the two numeric values must be equal at the speed where the divisor cancels, which is 5252 rpm. Below that speed the lb-ft figure is numerically larger; above it the hp figure is larger. The crossing point is an artefact of the imperial unit definitions rather than an engine characteristic.
What is the difference between brake horsepower and wheel horsepower?
Brake horsepower is measured at the crankshaft on an engine dynamometer, before any drivetrain. Wheel horsepower comes from a chassis dyno and already has clutch, gearbox, differential and tyre losses subtracted. The gap depends on the driveline layout and its parasitic drag, so the same engine reports a lower number at the wheels. Always establish which measurement point a torque and rpm pair came from before comparing two engines.
How does gearing multiply torque without creating extra horsepower?
A reduction gear multiplies output torque by the gear ratio while dividing output speed by the same ratio. In the hp equation the two changes cancel, so shaft power stays the same apart from friction losses in the gearset. This is why a low first gear delivers large wheel torque yet no more power, and why peak acceleration occurs near the rpm where the engine makes peak horsepower rather than peak torque.
What is the difference between hp, PS and kilowatts in engine ratings?
Mechanical horsepower is defined as 33,000 ft-lb per minute, which equals 745.7 watts. PS, the metric horsepower used across much of Europe, is defined as 75 kgf-m per second, or 735.5 watts. Because PS is the smaller unit, a given engine scores about 1.4 percent more PS than hp, so 238 hp is roughly 241 PS. The kilowatt is the SI figure and removes the ambiguity entirely.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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