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Power is the rate at which work is done or energy is transferred. A powerful engine doesn't necessarily do more work than a weaker one — it does the same work in less time. The fundamental formula is P = W/t, where W is work (Joules) and t is time (seconds). Power is measured in Watts (W): 1 W = 1 J/s.
In mechanics, when a constant force F moves an object at constant velocity v, power can be computed directly as P = Fv. This form is useful for calculating engine power requirements — a lorry maintaining 25 m/s against 4000 N of drag requires P = 4000 × 25 = 100,000 W = 100 kW of engine power just to maintain speed.
In electrical circuits, P = IV (current × voltage) for DC circuits, or P = IV·cos(φ) for AC circuits where cos(φ) is the power factor. A 240 V appliance drawing 5 A consumes P = 240 × 5 = 1200 W = 1.2 kW.
Horsepower (hp) is an older unit: 1 mechanical horsepower = 745.7 W. A 200 hp car engine produces 200 × 745.7 ≈ 149 kW. Metric horsepower (PS or CV) ≈ 735.5 W. To convert hp to kW, multiply by 0.7457.
P = W/t | P = F·v | P = I·V
P = W / t
Power Formulas Reference
| Formula | Variables | Units |
|---|---|---|
| P = W / t | W = work (J), t = time (s) | Watts (W) |
| P = F × v | F = force (N), v = velocity (m/s) | Watts (W) |
| P = I × V | I = current (A), V = voltage (V) | Watts (W) |
| P = I²R | I = current (A), R = resistance (Ω) | Watts (W) |
| P = V²/R | V = voltage (V), R = resistance (Ω) | Watts (W) |
| 1 hp = 745.7 W | Horsepower conversion | — |
| 1 kW = 1000 W | Kilowatt conversion | — |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.