Torque and Power Calculator
Solve P = T x ω for torque, power or shaft speed in N·m, lb·ft, kgf·m, kW, mechanical hp and metric PS, with the 5252 rule and a torque-versus-rpm table.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Torque and Power Calculator?
Torque, power and rotational speed are tied together by one equation: power equals torque times angular velocity. Know any two and the third follows. A motor rated 7.5 kW at 1,450 rpm delivers 49.4 N·m at the shaft; an engine making 300 lb·ft at 4,000 rpm is producing 228.5 hp at that moment. This calculator does that rearrangement for you in whichever units the datasheet, the dyno sheet or the gearbox catalogue happens to use.
Pick what you want to solve for, type the other two values, and every unit appears at once: newton-metres, pound-feet, pound-inches and kilogram-force metres for torque; watts, kilowatts, mechanical horsepower and metric horsepower (PS) for power; rpm and radians per second for speed. Changing a unit converts the number you already typed, so the physical quantity never changes by accident.
A second table shows the torque needed to carry the same power at common motor and engine speeds, which is the quickest way to see why a slow output shaft needs a much bigger coupling than a fast one.
- Solves for any one of torque, power or speed
- Torque in N·m, lb·ft, lb·in and kgf·m; power in W, kW, mechanical hp and metric PS
- Unit changes convert the value already entered
- Table of torque at common speeds for the same power
- Formula panel with the 5252 and 9549 constants derived, plus copy and share
How to use the Torque and Power Calculator
- Choose Solve for: power, torque or speed. The field you are solving becomes the shaded result box.
- Type the two known values and pick their units. Unit menus convert the number in place.
- Read the answer in every unit in the result grid. Mechanical hp and metric PS are listed separately.
- Use the table below to see the torque the same power would need at 750 to 6,000 rpm.
- Copy the results or share a link with your inputs from the buttons under the result.
Worked examples
Motor shaft torque from the nameplate
Input
Solve torque: 7.5 kW at 1,450 rpm
Output
49.39 N·m (36.43 lb·ft)
This is the torque a coupling, key or gearbox input must transmit at rated load. Starting torque from a direct-on-line induction motor is often two to three times higher, so size the coupling for that.
Engine power from a dyno torque reading
Input
Solve power: 300 lb·ft at 4,000 rpm
Output
228.5 hp, 170.4 kW
Using 5,252: 300 x 4,000 / 5,252.1 = 228.5. At 5,252 rpm the same 300 lb·ft would be exactly 300 hp.
Default page example
Input
Solve power: 100 N·m at 3,000 rpm
Output
31.42 kW, 42.13 hp, 42.71 PS
ω = 2π x 3,000 / 60 = 314.16 rad/s, and 100 x 314.16 = 31,416 W. The gap between hp and PS is the 1.4% difference in their definitions.
Background and insight
The relation P = T·ω follows from the definition of work: a torque T turning through an angle θ does work T·θ, and dividing by time gives power. With T in N·m and ω in rad/s the result is in watts with no extra constant. Every other form of the formula is the same equation with unit conversions folded in. In metric shop units, kW = N·m x rpm / 9,549.3, because 60,000 / 2π = 9,549.3.
The familiar US form, hp = lb·ft x rpm / 5,252, comes from James Watt's definition of horsepower as 33,000 foot-pounds per minute. One revolution moves a torque through 2π radians, so 33,000 / 2π = 5,252.1. That is also why torque and horsepower curves on any dyno chart in lb·ft and hp cross at exactly 5,252 rpm. A metric chart in N·m and kW has no such crossing point at a round number.
Two different horsepowers are in common use. Mechanical (imperial) horsepower is 550 ft·lbf/s, or 745.70 W. Metric horsepower, written PS, CV or pk, is 75 kgf·m/s, or 735.50 W, about 1.4% smaller. European car brochures usually quote PS, so a 150 PS engine is 110.3 kW or 147.9 hp. The calculator labels the two separately so they cannot be mixed up.
Common use cases
Motor and gearbox selection
Turn a motor nameplate into shaft torque, then check the torque a reducer, coupling or keyed shaft has to carry.
Reading dyno sheets
Convert between torque and horsepower at any rpm, and between brochure PS and SAE hp figures.
Machine tool spindles
See how much cutting torque a spindle of a given power can deliver at low rpm for tapping or large drills.
Shaft and key sizing
Get the design torque for a shaft stress or key shear calculation from the power the shaft transmits.
Tips and limitations
- Use rad/s, not rpm, if you write the formula by hand in SI. P = T x rpm gives a number 9.55 times too large.
- Nameplate power on an electric motor is mechanical output at the shaft. Electrical input is higher by the motor efficiency.
- Engine brochure figures are usually at the crankshaft. Power at the wheels is lower by roughly 10 to 20% depending on the drivetrain.
- Peak torque and peak power occur at different speeds. Plug in the torque at the rpm you care about, not the headline peak torque.
- Gearboxes multiply torque and divide speed, but they do not create power. Power out equals power in times efficiency.
Frequently asked questions
What is the formula relating torque, power and rpm?
P = T x ω, where ω is angular speed in rad/s (ω = 2π x rpm / 60). In practical units: kW = N·m x rpm / 9,549.3, and hp = lb·ft x rpm / 5,252.1.
Why do torque and horsepower curves cross at 5252 rpm?
Because hp = lb·ft x rpm / 5,252. When rpm equals 5,252 the two numbers are equal. The constant is 33,000 ft·lbf/min (one horsepower) divided by 2π radians per revolution.
What is the difference between hp and PS?
Mechanical horsepower (hp) is 745.70 W. Metric horsepower (PS, CV, pk) is 735.50 W, about 1.4% less. A car rated 150 PS makes 147.9 hp or 110.3 kW.
How much torque does a 5 hp motor produce at 1750 rpm?
About 15.0 lb·ft (20.3 N·m): 5 x 5,252.1 / 1,750 = 15.0. That is full-load running torque; locked-rotor torque at start is typically two to three times higher for a standard induction motor.
How do I convert N·m to lb·ft?
Divide by 1.35582. One pound-foot is 0.3048 m x 4.44822 N = 1.35582 N·m, so 100 N·m is 73.76 lb·ft.
Does a gearbox change power?
Only by its losses. A reducer multiplies torque by its ratio and divides speed by the same ratio, so T x ω stays the same apart from friction. A 95% efficient gearbox delivers 95% of the input power.
Is more torque or more horsepower better?
They describe the same output at a given speed. Torque is the turning force; power is how fast that force does work. An engine with more torque at low rpm feels stronger pulling away, while peak horsepower sets top speed and acceleration at high rpm.
Is there an in-depth guide to the Torque and Power Calculator?
Yes. “Torque, Horsepower and RPM: Where 5252 and 9549 Come From” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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