Power Calculator — rate of doing work (P = W/t)

How it works

Power is the rate at which work is done — how quickly energy is transferred or converted:

P = W ÷ t

where W is the work done (or energy used) and t is the time taken. In SI units, joules divided by seconds give watts (W), where one watt is one joule per second. The same task done faster requires more power: lifting a load in 2 seconds takes twice the power of lifting it in 4.

This is mechanical power — the general work-over-time definition. It is the same quantity as the electrical power on the Ohm's law page (which computes it as I²R for a resistor); here it comes straight from an amount of work and a time. The calculator is unit-agnostic, so any consistent energy and time units work.

Worked example

OpenStax's stair-climbing example: a woman does 1884 J of work (120 J of kinetic energy plus 1764 J of potential energy) in 3.50 s, so her power output is 1884 ÷ 3.5 = 538 W. Simpler cases: 1000 J in 10 s is 100 W, 500 J in 2 s is 250 W, and a small engine doing 150 kJ in 10 s delivers 15 000 W (15 kW, about 20 horsepower).

Frequently asked questions

What is the formula for power?

Power is work divided by time: P = W ÷ t. It measures how quickly energy is used or transferred. Rearranged, work = power × time, which is why energy bills are in kilowatt-hours (power times time).

What is a watt?

The watt (W) is the SI unit of power: one watt is one joule of energy per second (1 W = 1 J/s). A typical LED bulb draws about 10 W; a person climbing stairs briefly produces several hundred watts.

How is power related to horsepower?

Horsepower is an older unit of power: one mechanical horsepower is about 746 watts. So 15 000 W is roughly 20 horsepower. Both measure the same thing — the rate of doing work — just in different units.

What is the difference between energy and power?

Energy (in joules) is the total amount of work done; power (in watts) is how fast it is done. A marathon runner and a sprinter might do similar total work, but the sprinter produces far more power because they do it in much less time.

Is this the same as electrical power?

It is the same physical quantity — the rate of energy transfer, measured in watts. This page computes it from work and time (P = W/t); for a resistor the Ohm's law calculator computes the same power as P = I²R = VI. Different inputs, same watts.

Why does the result disappear when time is zero?

Power divides work by time, and dividing by zero is undefined — no time has passed, so no rate can be formed. The calculator shows a blank result until you enter a positive time.