Ohm’s law says that voltage equals current times resistance: V = I × R. Rearranged, current is I = V ÷ R and resistance is R = V ÷ I. If you connect a 220-ohm resistor to a 12-volt supply, the current is 12 ÷ 220 ≈ 0.0545 amperes (54.5 mA). Combined with the power formula P = V × I, it lets you find any electrical quantity from two others.
The law is named for Georg Simon Ohm, who published it in 1827. It remains the first tool for analyzing almost any circuit.
The three quantities
| Quantity | Symbol | Unit | Water analogy |
|---|---|---|---|
| Voltage (potential difference) | V (or E) | volt (V) | Water pressure |
| Current | I | ampere (A) | Flow rate |
| Resistance | R | ohm (Ω) | Narrowness of the pipe |
| Power | P | watt (W) | Rate of work done by the flow |
The analogy is imperfect but useful: more pressure pushes more flow through the same pipe, and a narrower pipe lets less flow through at the same pressure.
The formulas
Power, the rate at which electrical energy is converted to heat, light or motion, is voltage times current. Substituting Ohm’s law gives three equivalent forms:
The 12 combinations
| To find | From V and I | From V and R | From I and R | From P and … |
|---|---|---|---|---|
| V | — | — | I × R | √(P × R) or P ÷ I |
| I | — | V ÷ R | — | P ÷ V or √(P ÷ R) |
| R | V ÷ I | — | — | V² ÷ P or P ÷ I² |
| P | V × I | V² ÷ R | I² × R | — |
Use base units (volts, amperes, ohms) or keep prefixes consistent: volts ÷ kilohms gives milliamps, which is convenient for electronics.
Worked examples
Current through a resistor
A 220 Ω resistor is connected across 12 V.
I = V ÷ R = 12 ÷ 220 ≈ 0.0545 A = 54.5 mA
P = V² ÷ R = 144 ÷ 220 ≈ 0.65 W
A common ¼-watt resistor would overheat here. Choose a part rated for at least double the expected dissipation, so a 1 W or 2 W resistor. Resistor values are often printed as colored bands; see how to read resistor color codes.
A space heater
A heater draws 1,500 W from a 120 V outlet.
I = P ÷ V = 1,500 ÷ 120 = 12.5 A
R = V² ÷ P = 14,400 ÷ 1,500 = 9.6 Ω (when hot)
The National Electrical Code (NEC) generally sizes circuits so that continuous loads, those running three hours or more, stay at or below 80% of the breaker rating. On a 15 A circuit, that is 12 A or 1,440 W, so a 1,500 W heater running all evening is already at the limit. The watts to amps calculator handles these conversions, including three-phase power.
Choosing an LED resistor
An LED needs about 2.0 V and 20 mA, powered from a 9 V battery. The resistor must drop the remaining voltage:
R = (9 − 2.0) ÷ 0.020 = 350 Ω → use the next standard value up, 390 Ω
Actual current = 7 ÷ 390 ≈ 17.9 mA · Resistor power = 0.0179² × 390 ≈ 0.13 W
Rounding up to a standard value keeps the current slightly below the maximum, which extends LED life. The LED resistor calculator looks up forward voltages for common LED colors.
Series and parallel circuits
Ohm’s law applies to each component and to the circuit as a whole.
Series: resistances add, and the same current flows through every part.
100 Ω, 220 Ω and 330 Ω in series total 650 Ω. On 9 V, the current is 9 ÷ 650 ≈ 13.8 mA, and each resistor’s voltage is that current times its resistance.
Parallel: reciprocals add, and every branch sees the same voltage.
100 Ω and 220 Ω in parallel give 1 ÷ (0.01 + 0.004545) ≈ 68.75 Ω. The total is always less than the smallest branch. The series and parallel resistor calculator handles any network.
Voltage dividers use two series resistors to produce a fraction of the input: Vout = Vin × R₂ ÷ (R₁ + R₂). Two equal resistors on 5 V give 2.5 V. See the voltage divider calculator.
Where Ohm’s law does not apply
Ohm’s law describes materials whose resistance stays constant, called ohmic conductors. Many components are not:
- Diodes and LEDs conduct almost nothing below a threshold voltage, then let current rise steeply. That is why they need a series resistor.
- Incandescent filaments have a much lower resistance when cold than when glowing. A 60 W, 120 V bulb runs at about 240 Ω hot, but measures far less on a meter at room temperature, which is why bulbs often fail at the moment of switch-on.
- AC circuits with capacitors or inductors use impedance, which depends on frequency, in place of simple resistance.
- Temperature changes the resistance of most metals, typically raising it as they heat.
Even then, Ohm’s law still holds at any instant for the resistive parts of a circuit, so it stays the starting point for analysis.
Safety notes
Ohm’s law also explains electrical hazards. Dry skin has a high resistance, but wet skin can drop to a small fraction of that, so the same household voltage can drive a dangerous current. Treat mains wiring with respect, turn off breakers before working, and leave panel work to a licensed electrician.
For any calculation in this guide, the Ohm’s law calculator solves for voltage, current, resistance or power from any two known values.
Frequently asked questions
What is Ohm's law?
Ohm's law states that the current through a conductor is proportional to the voltage across it: V = I × R, where V is voltage in volts, I is current in amperes and R is resistance in ohms. Rearranged, I = V ÷ R and R = V ÷ I.
How do you calculate power from Ohm's law?
Power is voltage times current, P = V × I. Substituting Ohm's law gives two more forms: P = I² × R and P = V² ÷ R. A 220 Ω resistor across 12 V dissipates 12² ÷ 220 ≈ 0.65 W.
How many amps does a 1,500-watt heater draw?
On a 120-volt circuit, I = P ÷ V = 1,500 ÷ 120 = 12.5 amps. That is close to the 12-amp continuous limit for a 15-amp breaker, which is why space heaters should not share a circuit with other large loads.
Does Ohm's law apply to all components?
No. It describes ohmic materials, such as metal resistors at constant temperature, whose resistance does not change with voltage. Diodes, LEDs and transistors are non-ohmic, and a light bulb filament's resistance rises sharply as it heats up.
What is the Ohm's law triangle?
It is a memory aid with V on top and I and R side by side on the bottom. Cover the quantity you want: covering V leaves I × R, covering I leaves V over R, and covering R leaves V over I.