Power Calculator (Physics)
Calculate power, work, or time using P = W/t — the fundamental power equation. Supports watts, kilowatts, and horsepower.
What Is Power in Physics?
Power is the rate at which work is done or energy is transferred. The SI unit is the watt (W), where 1 W = 1 joule per second (J/s). Power tells you not just how much work is accomplished but how quickly — two engines doing the same work differ in power if one does it faster.
The primary formula is P = W/t — power equals work divided by time. An equally important form is P = F·v (force times velocity), useful when dealing with moving objects under constant force. This form explains why a car needs far more engine power at high speed: aerodynamic drag grows with v², and since power = force × velocity, the required power grows as v³.
Power is distinct from energy. Energy (joules) is what gets stored or transferred; power (watts) is how fast that transfer happens. A 100 W appliance and a 1,000 W appliance both perform "electrical work," but the 1,000 W device does it 10× faster. Over time, energy used = power × time (in kWh for billing purposes, where 1 kWh = 3.6 MJ).
For rotational systems, power is P = τ·ω (torque × angular velocity), the exact rotational analog of P = F·v. An engine producing 200 N·m at 3,000 RPM outputs P = 200 × (3000 × 2π/60) ≈ 62.8 kW = 84 hp. Mechanical, electrical, thermal, and fluid power all express the same underlying rate-of-energy concept.
Formula Reference
| Quantity | Formula | Notes |
|---|---|---|
| Power | P = W / t
|
1 W = 1 J/s |
| Work | W = P × t
|
t in seconds |
| Time | t = W / P
|
— |
| Velocity form | P = F · v
|
Constant force & speed |
| Rotational | P = τ · ω
|
τ = torque, ω = rad/s |
| Horsepower | 1 hp = 745.7 W
|
1 kW = 1.341 hp |
3 Worked Examples
A car maintains 120 km/h against 3,000 N of total drag. What engine power is needed?
- Convert: 120 km/h = 33.33 m/s
- P = F·v = 3,000 × 33.33 = 99,990 W
- Rounding: P ≈ 100 kW (134 hp)
A crane lifts 5,000 kg by 8 m in 20 seconds. What is its power?
- Work = mgh = 5,000 × 9.8 × 8 = 392,000 J
- P = W/t = 392,000 / 20 = 19,600 W
- P = 19.6 kW (26.3 hp)
A cyclist outputs 280 W for 90 minutes. How much energy do they expend?
- t = 90 × 60 = 5,400 s
- W = P × t = 280 × 5,400 = 1,512,000 J
- = 1,512 kJ ≈ 361 kcal
Real-World Applications
Common Mistakes
Watts = power (rate). Watt-hours = energy (total). A 100 W bulb doesn't use 100 Wh in one minute — it uses 100/60 ≈ 1.67 Wh. Energy = Power × Time.
ω must be in rad/s. Convert: ω = RPM × 2π/60. At 1,500 RPM, ω = 157 rad/s, not 1,500.
A 10 kW motor at 85% efficiency outputs only 8.5 kW of useful mechanical power. Always specify electrical input vs. mechanical output.
P = W/t gives average power. For varying power, instantaneous P = dW/dt = F·v requires calculus or small time steps.
Don't mix SI and imperial. 1 BTU/hr ≠ 1 W. Convert everything to SI (watts) before calculating, then convert the result.
Frequently Asked Questions
Related Calculators
Formula Explorer connections
Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.