About the Mechanical Power Calculator
This mechanical power calculator finds how fast work is being done, in four common ways: work divided by time, force multiplied by velocity, torque multiplied by rotational speed, or the power needed to lift a mass through a height in a given time. Results are given in watts, kilowatts, mechanical horsepower, metric horsepower (PS) and foot-pounds per second.
It is useful for physics problems on work, energy and power, for estimating the output of an engine or motor from its torque and rpm, for sizing a winch, hoist or conveyor, and for seeing how much power a person produces climbing stairs or cycling. The table shows how the power changes if the same job is done faster or slower.
All results are the mechanical power delivered to the load. Motors and engines draw more input power than they deliver because of losses; divide by the efficiency to estimate input power. The lifting mode uses standard gravity (9.80665 m/s²) and ignores acceleration and friction.
With the default inputs, the power is 200 W. Change any value above to recalculate instantly.
How to use the mechanical power calculator
- 1Choose how you want to calculate power.
- 2Enter the values for that method (work and time, force and speed, torque and rpm, or mass, height and time).
- 3Read the power in watts, kilowatts and horsepower.
- 4Check the table to see how doing the job faster or slower changes the power.
Formula and method
Power is the rate of doing work. The most basic form is work (or energy transferred) divided by time. When a constant force moves something at a steady speed in the direction of the force, power equals force times velocity. For rotating shafts, power equals torque times angular velocity in radians per second, which is rpm × 2π ÷ 60. Lifting a mass m through height h does work m × g × h, so the power is that work divided by the time taken.
One watt is one joule per second. Conversions use 1 mechanical horsepower = 745.70 W, 1 metric horsepower (PS) = 735.50 W and 1 ft·lbf/s = 1.3558 W. Results are average power; peak power during acceleration can be higher, and drive efficiency is not included.
- P
- Power (W)
- W
- Work done (J)
- t
- Time (s)
- F, v
- Force (N) and velocity (m/s)
- τ, ω
- Torque (N·m) and angular velocity (rad/s)
- m, g, h
- Mass (kg), gravity (9.80665 m/s²), height (m)
Worked examples
1,000 J of work in 5 seconds
P = 1,000 J ÷ 5 s = 200 W, or about 0.27 hp — roughly what a fit cyclist can sustain for an hour.
Pushing with 500 N at 3 m/s
P = F × v = 500 N × 3 m/s = 1,500 W, which is 1.5 kW or just over 2 hp.
Engine making 200 N·m at 3,000 rpm
ω = 3,000 × 2π ÷ 60 = 314.16 rad/s, so P = 200 × 314.16 ≈ 62,832 W — about 62.8 kW, 84.3 hp or 85.4 PS.
Climbing a 3 m flight of stairs in 4 seconds (75 kg)
The work against gravity is 75 × 9.80665 × 3 = 2,206.5 J. Doing it in 4 s takes 2,206.5 ÷ 4 ≈ 551.6 W, about three quarters of a horsepower.
Frequently asked questions
What is mechanical power?+
Mechanical power is the rate at which work is done or energy is transferred by forces and motion. It is measured in watts, where one watt equals one joule of work per second.
How do you calculate power from torque and rpm?+
Multiply torque in newton-metres by angular speed in radians per second (rpm × 2π ÷ 60). In imperial units, horsepower = torque in lb·ft × rpm ÷ 5,252.
How many watts is one horsepower?+
One mechanical (imperial) horsepower is about 745.7 W. One metric horsepower (PS or CV) is 735.5 W, and an electrical horsepower is defined as exactly 746 W.
What is the difference between work and power?+
Work is the energy transferred when a force moves something (force × distance, in joules). Power is how quickly that work is done (joules per second). Lifting a box slowly or quickly takes the same work but different power.
How much power can a human produce?+
A healthy adult can sustain roughly 75–200 W for an hour of steady exercise, well-trained amateur cyclists around 250–300 W and professional riders 400 W or more. Short sprints can briefly exceed 1,000 W.