Electrical Power Formula (P = IV)
Calculate electrical power with P = IV, P = I squared R, and P = V squared / R.
Worked examples for circuits and components.
The Formula
Electrical power measures the rate at which electrical energy is converted into another form of energy (heat, light, motion, etc.). The basic formula multiplies current by voltage to give power in watts.
By substituting Ohm's Law (V = IR), you can derive two additional forms that are useful when you only know two of the three quantities.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| P | Electrical power | watts (W) |
| I | Current flowing through the component | amperes (A) |
| V | Voltage across the component | volts (V) |
| R | Resistance of the component | ohms (omega) |
Alternative Forms
P = I² x R
P = V² / R
Example 1 — Light Bulb Power
A light bulb draws 0.5 A of current from a 120 V outlet. What is its power consumption?
P = I x V = 0.5 x 120
P = 60 W
Example 2 — Resistor Heat Dissipation
A 100 ohm resistor carries 0.3 A of current. How much power does it dissipate as heat?
P = I² x R = (0.3)² x 100 = 0.09 x 100
P = 9 W
Example 3 — Finding Current from Power
A 1500 W space heater runs on a 120 V circuit. How much current does it draw?
Rearrange P = IV to get I = P / V
I = 1500 / 120
I = 12.5 A
When to Use It
Use the electrical power formula when:
- Sizing circuit breakers and fuses for appliances
- Calculating energy consumption and electricity costs
- Choosing the right resistor wattage rating to avoid overheating
- Designing power supplies for electronic circuits
- Comparing efficiency of electrical devices
Key Notes
- DC power: P = VI = I²R = V²/R: All three forms are equivalent — choose the one matching your known quantities. P = I²R shows that power loss in a conductor scales as the square of current, which is why high-voltage transmission lines (low current) dramatically reduce distribution losses.
- Energy: W = P × t: Energy in joules = watts × seconds. One kilowatt-hour (kWh) = 3,600,000 J. Electricity billing uses kWh: a 1,000 W appliance running for 1 hour uses 1 kWh. At $0.15/kWh, that costs $0.15.
- Three-phase power: P = √3 × V_L × I_L × pf: For balanced three-phase AC systems, where V_L is line-to-line voltage and I_L is line current. Three-phase is more efficient for large power transmission and used in industrial motors and grid distribution.
- Maximum power transfer theorem: Maximum power is transferred from source to load when R_load = R_source. At this point, efficiency is 50% — half the power is dissipated in the source resistance. Used in audio amplifier design, antenna design, and RF circuits.
- Applications: Power formulas are used in every electrical engineering context: motor selection (power rating), cable sizing (allowable I²R heating), battery drain estimation (P = V × I for run-time), solar panel output calculations, and generator and UPS system sizing.