Power Formula
The power formula P = W/t calculates the rate at which work is done or energy is transferred.
Learn to calculate power in watts with examples.
The Formula
P = W / t
Power is the rate at which work is done or energy is transferred. One watt equals one joule of energy per second.
Variables
| Symbol | Meaning |
|---|---|
| P | Power (measured in watts, W) |
| W | Work done or energy transferred (measured in joules, J) |
| t | Time taken (measured in seconds, s) |
Example 1
A motor does 6,000 J of work in 12 seconds. What is its power output?
Identify the values: W = 6,000 J, t = 12 s
Apply the formula: P = W / t = 6,000 / 12
P = 500 W
Example 2
A 60 W light bulb runs for 5 minutes. How much energy does it use?
Convert time: t = 5 × 60 = 300 s
Rearrange: W = P × t = 60 × 300
W = 18,000 J (or 18 kJ)
When to Use It
Use the power formula when you need to find how quickly energy is used or work is done.
- Comparing the output of engines, motors, or appliances
- Calculating energy consumption over time
- Determining how long a task will take at a given power level
- Electrical power calculations (often combined with P = IV)
Key Notes
- Power also equals P = F × v (force times velocity) — a car delivering 300 N of drive force at 30 m/s produces 9,000 W; P = W/t and P = Fv are equivalent expressions and both produce watts when SI units are used
- One horsepower = 745.7 W; this was defined by James Watt to compare his steam engine output to draft horses — quick conversion: 1 kW ≈ 1.34 hp; a 100 hp car engine produces about 74.6 kW
- In electrical circuits, P = IV (voltage × current); combined with Ohm's law (V = IR) gives P = I²R and P = V²/R — these three forms are algebraically identical and used depending on which quantities are known
- Instantaneous power P = dW/dt differs from average power P̄ = W_total / t_total — a defibrillator delivers a short pulse at very high peak power (several thousand watts) but very low average power; component ratings must account for peak, not just average