Power Calculator

How to use this calculator

Power is the rate of doing work. If you know the force applied and how far it moves its point of application, enter those two with the time taken. If you already know the energy transferred — from a battery rating or a food label — enter it directly as work, with the time.

For steady motion, power also equals force times speed, which is how vehicle and conveyor drives are sized: enter the force and the speed and the time and distance fields will follow as soon as one of them is known. Switch the power unit to hp or BTU/h to compare with equipment ratings.

The formula

W = F × d

P = W / t

P = F × v

F: force
d: distance moved
W: work (energy transferred)
t: time
P: power
v: average speed

Worked example

A winch pulls a boat 10 m up a ramp with a steady force of 500 N, taking 4 seconds.

Work W = F × d = 500 × 10 = 5,000 J.
Power P = W / t = 5,000 / 4 = 1,250 W (1.68 hp).
Average speed v = 10 / 4 = 2.5 m/s, and indeed P = F × v = 500 × 2.5 = 1,250 W.

The winch must deliver at least 1.25 kW, before allowing for motor and gearbox losses.

Assumptions and limits

The force acts along the direction of motion. For a force at an angle θ, use F cos θ.
Power is the average over the interval; instantaneous power can be higher during acceleration.
Mechanical output only: divide by efficiency to get the input power a motor draws.

Frequently asked questions

How many watts is one horsepower?

One mechanical (imperial) horsepower is 550 ft·lbf/s = 745.7 W. Metric horsepower (PS) is 735.5 W.

What is the difference between work and power?

Work is energy transferred (joules); power is how fast it is transferred (joules per second, or watts). Climbing stairs slowly or quickly takes the same work but different power.

How much power does it take to climb stairs?

Lifting 70 kg up 3 m takes 70 × 9.81 × 3 ≈ 2,060 J. Doing it in 4 seconds requires about 515 W.

Power Calculator (Work and Time)