Electrical Power Formula
Calculate electrical power using P = VI, P = I²R, and P = V²/R.
Essential for circuit design, energy consumption, and component sizing.
The Formula
Electrical power measures the rate at which electrical energy is consumed or produced.
All three forms are equivalent — use whichever matches the values you know.
Variables
| Symbol | Meaning |
|---|---|
| P | Power (Watts, W) |
| V | Voltage (Volts, V) |
| I | Current (Amperes, A) |
| R | Resistance (Ohms, Ω) |
Which Form to Use
- P = V × I — when you know voltage and current
- P = I²R — when you know current and resistance
- P = V² / R — when you know voltage and resistance
Example 1
A 230 V appliance draws 4 A of current. What is its power consumption?
P = V × I
P = 230 V × 4 A
P = 920 W
Example 2
A 100 Ω resistor has 2 A flowing through it. How much power does it dissipate?
P = I²R
P = (2)² × 100
P = 4 × 100
P = 400 W
When to Use It
Use the electrical power formula when you need to:
- Calculate energy consumption of appliances and devices
- Size fuses, circuit breakers, and wiring
- Determine heat dissipation in resistors and components
- Calculate electricity costs (Power × Time = Energy in kWh)
For AC circuits, the formula becomes P = V × I × cos(φ), where cos(φ) is the power factor.
The power factor accounts for the phase difference between voltage and current in reactive circuits.
Key Notes
- Three equivalent formulas: P = VI = I²R = V²/R: All derived from P = VI combined with Ohm's law. Choose the form that matches your known quantities. P = I²R shows why high current causes disproportionate heating — doubling current quadruples heat dissipation.
- AC power — three types: Real power P (watts) does useful work. Reactive power Q (VAR) is stored and returned by inductors and capacitors. Apparent power S (VA) = V × I (RMS). They relate as S² = P² + Q².
- Power factor: pf = P/S = cosφ: The ratio of real to apparent power, where φ is the phase angle between voltage and current. A purely resistive load has pf = 1; motors typically run at 0.6–0.9. Utilities penalize industrial customers for low power factor because reactive current wastes transmission capacity.
- Energy and electricity billing: Energy = Power × time. One kilowatt-hour (kWh) is 1,000 W consumed for 1 hour — the standard billing unit. A 100 W bulb running 10 hours uses 1 kWh.
- Applications: Power calculations are used in circuit design, fuse and breaker sizing, motor selection, HVAC system rating, solar panel output estimation, and any electrical engineering context where heat dissipation or energy consumption matters.