How this instrument works
Power measures how fast work gets done, and for anything spinning, work is done by torque acting through an angle, not through a straight-line distance. That is why the formula pairs torque with angular velocity rather than ordinary speed: P = τ · ω. Double the torque or double the spin rate and power doubles either way — the two factors are equally responsible for the answer, which is what makes a low-torque, high-speed motor and a high-torque, low-speed motor able to match each other watt for watt.
RPM is what a tachometer shows and what motor and engine spec sheets quote, but the formula wants angular velocity in radians per second, so the instrument converts for you: ω = RPM · 2π ⁄ 60. Each revolution sweeps 2π radians, and dividing by 60 turns revolutions-per-minute into revolutions-per-second before that multiplication happens. Skip this step by hand and a power figure comes out sixty times too large or too small, depending on which way the arithmetic slips.
The number this instrument returns is mechanical power delivered at the shaft, not the electrical power a motor draws from the wall. A motor pulling 1,000 W of electricity might deliver only 850 W here; the rest is lost to resistance and friction as heat, and the ratio of the two is the motor's efficiency. Sizing a battery or a breaker calls for the electrical figure, found by dividing this result by that efficiency, not by reading it straight off a nameplate.
- Enter the shaft torque in the Torque field — the unit menu accepts N·m or lb·ft, whichever your spec sheet or torque wrench reads in.
- Enter the shaft speed in the Rotational speed, RPM field, taken from a tachometer, a motor nameplate, or an engine's rated speed.
- Read the result in the Mechanical power field; switch its unit to see the same figure in watts, kilowatts, or horsepower.
- To sanity-check a nameplate power rating, compare the reading against it — a large gap usually means the torque or RPM value used was wrong, not the formula.
Worked example — a 50 N·m motor at 1,000 RPM
Take a motor delivering 50 N·m of torque while spinning at 1,000 RPM, figures typical of a mid-size industrial gear motor. First the angular velocity: ω = 1,000 · 2π ⁄ 60 = 104.71976 rad/s. Then the power: P = 50 · 104.71976 = 5,235.98776 W, which the instrument reports as roughly 5,236 W, or about 7 mechanical horsepower.
Switch the result to kilowatts and it reads 5.236 kW; switch to horsepower and it reads about 7.02 hp. That figure is worth sitting with: a diesel engine idling out 50 N·m at a lazy 1,000 RPM and a compact drone motor spinning at 20,000 RPM but delivering only 2.5 N·m both land at exactly the same wattage, because power only cares about the product of torque and speed, not how it is split between them.
Questions
Why does power depend on RPM and not just torque?
Because power is the rate work gets done, and a spinning shaft only does work by turning — the faster it turns, the more work each second, for the same twisting force. A wrench applying 50 N·m to a bolt that never turns transmits energy at zero watts; the same 50 N·m turning a shaft at 1,000 RPM transmits about 5,236 W. Torque alone describes a twisting force, not a rate of energy delivery.
How do I read the answer in horsepower instead of watts?
Switch the unit menu on the Mechanical power field to hp; the instrument divides by 745.7 W, the mechanical horsepower used in most engineering contexts. A 50 N·m, 1,000 RPM result of 5,236 W becomes about 7.02 hp. Electrical and metric horsepower use slightly different conversion factors, so check which definition a spec sheet is quoting before comparing figures across sources.
Where does the 2π ⁄ 60 in the RPM conversion come from?
One revolution equals 2π radians by definition of the radian, and RPM counts revolutions per minute rather than per second, so multiplying by 2π converts revolutions to radians and dividing by 60 converts minutes to seconds. Both steps are unit conversions, not physics — they turn a tachometer reading into the radians-per-second that the power formula requires.
Is the result electrical power or mechanical power?
Mechanical — the power actually delivered at the rotating shaft, sometimes called shaft power or brake power. A motor's electrical input is higher by whatever its efficiency loses to heat and friction; a shaft output of 5,236 W from a motor that is 85 percent efficient means roughly 6,160 W was drawn from the supply. This instrument computes only the shaft side of that ratio.
Can torque and RPM trade off and still give the same power?
Yes, and that trade-off is the whole reason gearboxes exist. A motor spinning at 20,000 RPM with 2.5 N·m of torque and one spinning at 1,000 RPM with 50 N·m both produce exactly 5,236 W, because power depends only on their product. Gearing trades speed for torque, or torque for speed, while leaving mechanical power roughly unchanged apart from friction losses.
Where does the name watt come from, and why is it tied to this formula?
The unit honors James Watt, the 18th-century engineer who needed a way to rate steam engines against the horses they replaced. He measured a horse's torque and turning speed hauling a mill wheel and multiplied them, exactly τ · ω, to define horsepower, the ancestor of today's SI watt. The formula in this calculator is the same one Watt used, just expressed in modern units.