This power calculator computes mechanical power all three standard ways: from work over time (P = W/t), from force at a velocity (P = F·v), and from torque at a rotation rate (P = τ·ω) — the physics of how fast energy moves.

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Rate, Not Amount

Energy asks “how much”; power asks “how fast.” A crane and a toddler can both lift a brick one meter — the same work from our Work Calculator — but their power differs by orders of magnitude, which is why engines, motors and athletes are rated in watts. The rotational form P = τ·ω is how dynamometers turn a torque reading (from the Torque Calculator‘s world) at a given rpm into the horsepower figure on the spec sheet. Unit-only conversions (hp ⇄ kW) live on the Power Converter. Part of our Physics Calculators collection.

Worked Examples (Verified)

  • 1,000 J of work in 5 s = 200 W — the default: a strong human effort sustained (elite cyclists hold 250–400 W for an hour; a casual rider about 100 W)
  • A car cruising against 800 N of drag at 30 m/s needs 800 × 30 = 24,000 W ≈ 32 hp just for air and rolling resistance — which is why highway economy is an aerodynamics story
  • An engine making 300 N·m at 4,000 rpm (ω = 418.9 rad/s): P = 125,664 W ≈ 168 hp — the dyno formula in action
  • Stairs check: a 70 kg person climbing 3 m of stairs in 4 s outputs mgh/t = 515 W — briefly superhuman-looking, which is why the “stair sprint” is a classic lab-power demo

Average vs Peak

  • These formulas yield average power over the interval (or the instantaneous value when force/velocity are steady). Real engines and muscles have peaks far above their sustained ratings.
  • Electrical power (P = V×I and friends) has its own sibling: the Electric Power Calculator on this hub.
  • Human benchmarks worth memorizing: ~75 W resting metabolic rate, ~100 W easy cycling, ~1,000+ W for a few seconds of sprint — we are 1.3-horsepower animals only in very short bursts and Watt chose his unit’s scale kindly.

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Frequently Asked Questions

How do you calculate power in physics?

Power = work ÷ time (P = W/t). Equivalently, for a force pushing at speed, P = F·v; for rotation, P = τ·ω. All three give watts. 1,000 J in 5 s is 200 W.

What is the difference between power and energy?

Energy is the total (joules); power is its delivery rate (joules per second = watts). A battery and a capacitor can hold similar energy while differing a thousandfold in deliverable power — the reason both exist.

How do I get power from torque and RPM?

Convert RPM to rad/s (× 2π/60), then P = τ × ω. 300 N·m at 4,000 rpm = 300 × 418.9 ≈ 125.7 kW ≈ 168 hp. Divide watts by 745.7 for horsepower, or use the converter.

How much power can a human produce?

Roughly 75–100 W sustained for untrained adults, 250–400 W for elite endurance athletes over an hour, and 1,000–2,000 W in a 5-second maximal sprint. Horsepower comparisons should be made humbly.

Is mechanical power the same as electrical power?

Same unit, same concept — different formulas. Mechanical starts from work/force/torque; electrical from voltage and current (P = VI), meeting in motors and generators where the two worlds exchange energy at an efficiency.

Is this power calculator free?

Yes — free, instant, no sign-up.