Work & Power Calculator (W = Fd, P = W/t)

Work and power

In physics, work is done when a force moves something through a distance, and power is how fast that work happens. They're different quantities that people often blur together: work is energy transferred, power is the rate of transfer.

W = F × d × cos θ  ·  P = W / t

Work is measured in joules, power in watts (one joule per second). The cos θ term accounts for direction: only the part of the force that lies along the motion does work.

When no work is done

If the force is perpendicular to the motion, cos 90° = 0 and the work iszero — which is why carrying a heavy box across level ground does no work against gravity, however tiring it feels. Likewise, pushing hard against a wall that doesn't move does no physical work at all, because the distance is zero.

Worked example

Pushing with 100 N over 5 m in the direction of motion does 100 × 5 = 500 J of work. Do it in 10 seconds and the power is 500 / 10 = 50 W; do the same job in 2 seconds and you need 250 W. Same work, five times the power — that's the whole distinction in one example.

Related

Find the force first with the force calculator, convert the power into horsepower or BTU/h with thepower converter, or see how work becomes motion in the kinetic energy calculator.

Only force along the motion counts

Work is the component of force in the direction of travel, which is what the angle term captures — and it means a force perpendicular to the motion does no work at all. Carrying a heavy box across level ground does no work against gravity in the physics sense, however tiring it is. The power figure also assumes the work is delivered evenly over the time given; a task done in bursts has a higher peak power than the average implies, which is usually the number that sizes a motor.