How to Calculate Power (P = W/t): Work Rate in Watts

Calculate power with P = W/t and P = Fv. Work vs watts, unit traps, worked examples, and a free power calculator.

What Power Asks

Power is how fast work is done or energy is transferred. Two jobs can do the same work (same joules), but the one finished in less time has higher power.

The core formula is P = W/t. Work W in joules divided by time t in seconds gives power in watts (W). One watt equals one joule per second: 1 W = 1 J/s.

If you already have W and t (or P and one unknown), open the free power calculator first, then return here for P = Fv, units, and the link to work.

The Formulas

P = W/t — power from work and time.

W = P × t — rearrange for work.

t = W / P — rearrange for time.

P = Fv — when a constant force F acts along motion at speed v (same direction).

P = Fv comes from P = W/t with W = Fd and v = d/t, so W/t = F(d/t) = Fv. Use it when the problem gives force and speed instead of total work.

Power vs Work

Work W is energy transferred (joules). It does not include time. See work for W = Fd and W = Fd cos θ.

Example: lifting 100 J in 2 s gives P = 50 W. Lifting the same 100 J in 10 s gives P = 10 W. Same work, different power.

For stored energy at height, potential energy PE = mgh describes joules gained — power tells you how quickly that energy was added.

Units

W (work) → joules (J).

t → seconds (s).

P → watts (W). 1 W = 1 J/s.

Convert minutes to seconds (× 60) and kJ to J (× 1000) before substituting.

Horsepower is a non-SI power unit. Use the horsepower calculator when the question asks for hp instead of watts.

Worked Examples

Example 1: 600 J in 12 s

P = W/t = 600 / 12 = 50 W.

Example 2: find work

P = 120 W for 25 s. W = P × t = (120)(25) = 3000 J = 3.0 kJ.

Example 3: P = Fv

A motor pulls with F = 200 N at steady v = 3.0 m/s along the force. P = Fv = (200)(3.0) = 600 W.

Example 4: time to do 1500 J at 75 W

t = W/P = 1500 / 75 = 20 s.

Common Mistakes

Confusing power (watts) with work (joules) or with weight (newtons).

Leaving time in minutes while work is in joules — convert to seconds.

Using P = Fv when force is not parallel to velocity (need the component along motion).

Mixing mechanical power (P = W/t) with electric power (P = VI) — different tools for different contexts.

Check It on the Calculator

Power calculator — P = W/t.

Work calculator.

Kinetic energy calculator.

Horsepower calculator.

Learn P = W/t and confirm every homework number on the calculator.

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