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Calculate mechanical power (P = W/t = Fv), convert between watts, kilowatts, horsepower, and BTU/hr. Find the time to complete work at given power, or work done from power and time.
Power is the rate of doing work or transferring energy: P = W/t = F × v. The SI unit is the Watt (W = J/s). Higher power means the same work is done in less time. A 100 kW engine and a 10 kW engine doing the same job take different times — power determines speed of energy delivery.
Power (P) is the rate of energy transfer or rate of doing work: P = W/t = ΔE/Δt. It is measured in Watts (W), where 1 Watt = 1 Joule per second. Power tells you how quickly energy is being used or generated. A light bulb rated at 60W converts 60 joules of electrical energy to light and heat every second. A car engine rated at 150 kW can deliver 150,000 joules of mechanical work per second.
Power can also be expressed as force times velocity: P = F × v. This form is useful for calculating power in continuous motion — pushing with 500 N force at 10 m/s requires P = 500 × 10 = 5000 W = 5 kW. This explains why maintaining high vehicle speed requires enormous power: aerodynamic drag increases with v², so drag power (F_drag × v ∝ v³) grows with the cube of velocity.
| Unit | Value | Common Use |
|---|---|---|
| 1 Watt (W) | 1 J/s | SI base unit |
| 1 Kilowatt (kW) | 1000 W | Common for motors, appliances |
| 1 Megawatt (MW) | 1,000,000 W | Power plants |
| 1 Horsepower (hp) | 745.7 W | Engine ratings, US/UK |
| 1 Metric horsepower (PS) | 735.5 W | European auto spec |
| 1 BTU/hour | 0.2931 W | HVAC and heating |
| 1 kcal/hour | 1.163 W | Nutritional/metabolic rate |
Human body at rest (basal metabolic rate): ~80W. Moderate cycling: ~150-300W. Elite cyclist (Tour de France): ~400-450W sustained, ~1000W peak sprint. Usain Bolt peak sprint: ~2,600W (2.6 kW). Car engine: 75-500 kW typical. Boeing 747 engines: 4 × 58 MW = 232 MW total thrust power. Large nuclear power plant: ~1,000 MW (1 GW) = 1,000,000,000 W. Sun total power output: 3.8 × 10²⁶ W — Earth intercepts about 1.74 × 10¹⁷ W = 174 petawatts. Solar irradiance at Earth surface: ~1,000 W/m² on a clear day (solar constant 1,361 W/m², reduced by atmosphere).
Electrical power: P = V × I (DC circuits and AC resistive). For AC circuits: Active power P (W) = V_rms × I_rms × cos φ. Reactive power Q (VAR) = V × I × sin φ. Apparent power S (VA) = V × I. Power factor (PF) = cos φ = P/S. S² = P² + Q². Poor power factor (inductive loads like motors): apparent power exceeds real power — utility bills for apparent power. Power factor correction capacitors improve PF. Industrial facilities maintain PF > 0.95 to avoid utility penalties. Three-phase power: P = √3 × V_line × I_line × PF — standard for high-power industrial equipment.
Understanding power requirements for vehicles: P = F_total × v. At 100 km/h (27.78 m/s): Rolling resistance ~200 N, aerodynamic drag ~800 N (typical sedan). Total resistance ~1000 N. Required power = 1000 × 27.78 = 27,780 W ≈ 28 kW ≈ 37 hp just to maintain speed. This is why small engines can sustain highway speeds but struggle with hills (additional F = mg sin θ). Electric vehicles: 90%+ efficient vs ICE 30-35%, so EV requires 25-30% of the fuel energy for same work. Regenerative braking recovers 60-70% of kinetic energy during deceleration.
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.