What is the formula for converting horsepower to torque?

The underlying relationship is Power = Torque x Angular velocity, or P (W) = T (N·m) x RPM x 2pi / 60. Rearranged: T (N·m) = P (W) x 60 / (RPM x 2pi). In imperial units this simplifies to lb·ft = hp x 5252 / RPM, where 5252 is 33000 divided by 2pi (the "5252 constant").

What is the 5252 constant?

5252 (more precisely 5252.113) is the result of dividing 33,000 ft·lbf/min (one horsepower in British engineering units) by 2pi (to convert from revolutions to radians). When you multiply it by HP and divide by RPM the unit arithmetic cancels perfectly and you get torque in lb·ft.

What is the difference between mechanical hp (SAE) and metric PS?

One mechanical horsepower (hp) equals exactly 550 ft·lbf/s, which converts to roughly 745.7 W. One metric horsepower (PS, also CV or pk) equals 75 kgf·m/s, which is exactly 735.499 W. European and Japanese manufacturers often quote PS; American manufacturers quote SAE hp. The difference is about 1.4%.

Why does torque change with RPM even if power stays the same?

Because power is the rate of doing work. At low RPM an engine spins slowly, so each revolution takes longer — the same power output over a longer time means more force (torque) per revolution. At high RPM the engine must produce the same energy per second in shorter bursts, so the torque per burst is lower. Diesel engines produce peak torque at low RPM; high-revving petrol engines produce peak torque much higher in the rev range.

At what RPM does torque equal horsepower (in imperial)?

Because lb·ft = hp x 5252 / RPM, torque (in lb·ft) equals horsepower (numerically) exactly when RPM = 5252. This is why the torque and power curves on a dyno chart always cross at 5252 rpm when both are plotted in the same imperial units.

Can this calculator handle electric motors?

Yes. The power–torque–speed relationship is identical for electric motors: P = T x omega. Electric motors typically develop peak torque from zero RPM, so entering a low RPM like 0 is not valid (it would give infinite torque). Enter the RPM at which you want to evaluate the torque — for example the rated RPM on the motor nameplate.

Horsepower to Torque Calculator

Whether you are tuning an engine, reading a dyno report, comparing car specs, or studying for a mechanical engineering exam, the relationship between horsepower, torque and RPM sits at the heart of every power-plant calculation. This calculator solves for any one of the three quantities given the other two, shows you the exact step-by-step working, and lets you switch freely between imperial (hp, lb·ft) and metric (PS, N·m) units — all without leaving your browser.

How it works

Every engine and motor converts stored energy into rotational motion. The three quantities are linked by a single physical law:

P = T × ω

where P is power in watts, T is torque in newton-metres, and ω (omega) is angular velocity in radians per second. Because one full revolution equals 2pi radians and there are 60 seconds in a minute, angular velocity connects to the more familiar RPM as:

ω = RPM × 2pi / 60

Substituting and rearranging for each unknown:

Torque (N·m) = P (W) × 60 / (RPM × 2pi)
Power (W) = T (N·m) × RPM × 2pi / 60
RPM = P (W) × 60 / (T (N·m) × 2pi)

In imperial units one mechanical horsepower equals exactly 550 ft·lbf/s = 745.699 87 W, so the torque formula collapses to the well-known shortcut:

lb·ft = hp × 5252 / RPM

The 5252 “magic number” is simply 33,000 (ft·lbf/min per hp) divided by 2pi. Metric horsepower (PS) uses 75 kgf·m/s = 735.499 W instead.

Worked example

A petrol engine produces 300 hp at 5000 RPM. What is its torque?

Convert power: 300 hp × 745.70 W/hp = 223,710 W
Convert speed: 5000 rpm × 2pi / 60 = 523.60 rad/s
Torque: 223,710 W / 523.60 rad/s = 427.3 N·m (= 315.1 lb·ft)

Or using the imperial shortcut: 300 × 5252 / 5000 = 315.1 lb·ft — same answer.

Now find the RPM where that same engine produces peak torque of 380 lb·ft:

300 hp × 5252 / RPM = 380 → RPM = 300 × 5252 / 380 = 4148 rpm

At exactly 5252 rpm the torque in lb·ft and horsepower are numerically equal — this is why every dyno chart shows the two curves crossing at that point.

Scenario	HP	Torque	RPM
Family saloon	140 hp	187 lb·ft	3930 rpm
Performance coupe	300 hp	315 lb·ft	5000 rpm
High-revving track car	450 hp	315 lb·ft	7500 rpm
Torquey diesel van	150 hp	310 lb·ft	2540 rpm

Notice how the diesel produces similar torque to the performance coupe at roughly half the RPM — lower speed, same force, same power.

Formula note

The exact conversion constants used here are:

1 mechanical hp = 745.699 871 58 W (defined: 550 ft·lbf/s, with 1 ft = 0.3048 m exactly and 1 lbf = 4.448 221 6 N exactly)
1 metric hp (PS) = 735.498 75 W (defined: 75 kgf·m/s, with g = 9.806 65 m/s²)
1 lb·ft = 1.355 817 948 33 N·m (same exact foot and pound-force values above)
The “5252 constant” is more precisely 5252.113 = 33000 / (2pi)

All four constants are embedded in the calculator — no rounding occurs until the final display step.