Power Calculator
Power is the rate of doing work. The same job done in half the time requires twice the power, which is what separates a sports car from a family hatchback.
Formula
P = W ÷ t · P = F × v
- Power in watts, work in joules, time in seconds
- 1 horsepower = 745.7 W
Lifting 50 kg through 2 m in 3 s: 981 J ÷ 3 = 327 W
The Formula
Power = Work ÷ Time
Measured in watts, where one watt is one joule per second.
Lifting 500 J worth of load in 10 seconds requires 50 W. Doing it in 5 seconds requires 100 W — the same work, twice the power.
For motion, this becomes P = F × v: force multiplied by velocity, which is why a vehicle needs more power to hold speed as drag rises.
Watts, Kilowatts and Horsepower
- 1 kW = 1,000 W
- 1 metric horsepower ≈ 735.5 W
- 1 mechanical horsepower ≈ 745.7 W
Watt chose the unit deliberately: he needed a way to sell steam engines against the draught horses they replaced, and defined horsepower from the rate at which a horse could lift coal.
Power Versus Energy
These are routinely confused on electricity bills. Power is a rate, in watts. Energy is power multiplied by time, in kilowatt-hours — and it is energy you pay for.
A 3 kW heater running for 2 hours uses 6 kWh. A 60 W bulb would need 100 hours to consume the same.
This is why a high-wattage appliance used briefly can cost far less than a modest one left on continuously.
Quick Reference
| Source | Power | In horsepower |
|---|---|---|
| Human at rest | 100 W | 0.13 hp |
| Cyclist, sustained | 200 W | 0.27 hp |
| Elite sprint cyclist | 1,500 W | 2.0 hp |
| Small family car | 75 kW | 101 hp |
| Mainline locomotive | 5 MW | 6,705 hp |
Frequently Asked Questions
- What is the difference between power and energy?
- Power is the rate of energy use, measured in watts. Energy is power multiplied by time, measured in kilowatt-hours, and it is what appears on your bill.
- How many watts is one horsepower?
- About 745.7 W for mechanical horsepower, or 735.5 W for the metric version used in much of Europe.
- How do I work out running costs?
- Multiply the appliance wattage by hours used and divide by 1,000 to get kilowatt-hours, then multiply by your unit rate.
- Why does a car need more power at higher speed?
- Power equals force times velocity, and aerodynamic drag rises with the square of speed, so the power needed climbs steeply.