The Ohm's law formulas
Georg Ohm showed that, for a resistor, current is proportional to voltage. Add the definition of electrical power and you get every relationship an electrician uses day to day:
V = I × R · I = V ÷ R · R = V ÷ I
P = V × I · P = I² × R · P = V² ÷ R
Where V is voltage in volts, I is current in amperes, R is resistance in ohms (Ω) and P is power in watts. Solving each of those for the remaining unknowns gives the twelve formulas on the classic Ohm's law wheel:
| To find | Formulas |
|---|---|
| Voltage (V) | I × R · P ÷ I · √(P × R) |
| Current (I) | V ÷ R · P ÷ V · √(P ÷ R) |
| Resistance (R) | V ÷ I · V² ÷ P · P ÷ I² |
| Power (P) | V × I · I² × R · V² ÷ R |
Worked examples
1. Current drawn by a space heater
A 1500 W heater is plugged into a 120 V receptacle. Current is power divided by voltage:
I = P ÷ V = 1500 ÷ 120 = 12.5 A
R = V² ÷ P = 120² ÷ 1500 = 9.6 Ω
The heater's element is about 9.6 Ω when hot. Space heaters are continuous loads, so a dedicated circuit is sized at 125%: 12.5 × 1.25 = 15.6 A, which calls for a 20 A breaker and 12 AWG copper.
2. A 12 V DC load
A 4 Ω resistor sits across a 12 V battery:
I = V ÷ R = 12 ÷ 4 = 3 A
P = V × I = 12 × 3 = 36 W
The resistor needs a power rating comfortably above 36 W, typically 50 W, or it will overheat.
3. A 240 V water heater element
An element measures 20 Ω cold on a meter. At 240 V:
I = 240 ÷ 20 = 12 A
P = 240² ÷ 20 = 2880 W
Element resistance rises slightly as it heats, so the running current will be a little lower than this cold-resistance estimate. A common 4500 W element at 240 V works out to 12.8 Ω and 18.75 A.
4. Checking a voltage drop
Ohm's law is also the basis for voltage drop. A 100 ft run of 12 AWG copper has 200 ft of conductor, out and back. At 1.93 Ω per 1000 ft that is 0.386 Ω. At 16 A, V = I × R = 16 × 0.386 = 6.18 V lost in the wire, which is 5.15% of 120 V. The voltage drop calculator does this for any size and length.
Why power matters as much as Ohm's law
Most nameplates give watts, not ohms, so in the field you will usually use P = V × I to get current, then size the wire with the wire size calculator. The I² × R form explains why undersized wire runs hot: doubling the current through the same conductor quadruples the heat produced in it. It is also why a loose termination with a few hundredths of an ohm extra can become a fire risk at high current.
Limits of Ohm's law
Ohm's law describes resistive (linear) loads. Several common cases need more care:
- Reactive AC loads. Motors, ballasts and transformers have impedance (Z), and real power is V × I × power factor. See the amps to watts calculator.
- Three-phase circuits. Power is √3 × V × I × PF using line-to-line voltage. See the 3 phase power calculator.
- Non-linear devices. Diodes, LEDs and electronic power supplies do not have a fixed resistance.
- Temperature. Copper's resistance rises about 0.39% per °C. Tungsten lamp filaments can be more than ten times higher in resistance hot than cold.
Tips for using the calculator
Use RMS values for AC: a meter reading of 120 V is already RMS. Enter resistance in ohms, not kilohms (4.7 kΩ = 4700). If a result looks wrong, check the units first; a load in kW entered as watts is the most common slip. For safety, never measure resistance on an energized circuit.