Ohm’s law and the power formula
Two equations describe almost every simple electrical circuit:
- Ohm’s law: V = I × R. The voltage (volts) equals the current (amps) times the resistance (ohms).
- Power: P = V × I. The power (watts) equals the voltage times the current.
Combined, they give P = I² × R = V² ÷ R. Knowing any two of the four quantities is enough to find the other two, which is what this calculator does.
The twelve formulas
| Known | Current I | Resistance R | Voltage V | Power P |
|---|---|---|---|---|
| V and I | V ÷ I | V × I | ||
| V and R | V ÷ R | V² ÷ R | ||
| I and R | I × R | I² × R | ||
| P and V | P ÷ V | V² ÷ P | ||
| P and I | P ÷ I² | P ÷ I | ||
| P and R | √(P ÷ R) | √(P × R) |
Worked example: a 1,500 W space heater on 120 V
- Current: 1,500 ÷ 120 = 12.5 A.
- Resistance of the heating element when hot: 120 ÷ 12.5 = 9.6 Ω.
- Energy: 1.5 kWh for each hour of use, about 26 cents at $0.17 per kWh.
Current drawn by common appliances on 120 V
| Power | Current | Example |
|---|---|---|
| 100 W | 0.83 A | TV |
| 500 W | 4.17 A | desktop computer under load |
| 1,000 W | 8.33 A | microwave |
| 1,500 W | 12.5 A | space heater, hair dryer |
| 2,000 W | 16.7 A | not possible on a standard 15 A outlet |
Household circuits and the 80% rule
Most US outlets are on 15 A circuits, some kitchen and bathroom outlets on 20 A. The National Electrical Code limits a continuous load (running three hours or more) to 80% of the breaker rating: 12 A on a 15 A circuit and 16 A on a 20 A circuit. A 1,500 W heater at 12.5 A is already above that limit, which is why it should not share a circuit with other large loads, and should never be plugged into an extension cord or a power strip.
Good to know
- Resistance changes with temperature: a heater element or a light bulb filament has a much lower resistance when cold, so measuring it with an ohmmeter will not match the hot value.
- AC circuits: for motors and electronics, the power factor makes the real power lower than V × I. Ohm’s law applies directly to resistive loads such as heaters, kettles and incandescent bulbs.
- 240 V appliances (dryers, ranges, EV chargers) draw half the current of a 120 V device of the same power, which allows thinner wires for the same load.