Ohm’s law explained: voltage, current, resistance and power

Ohm's law says that the current through a conductor is proportional to the voltage across it: V = I × R, where V is the voltage in volts, I the current in amps and R the resistance in ohms. Know any two and you can find the third, and adding the power law P = V × I lets you work out watts as well. I built the Ohm's law calculator to do the rearranging for you; this guide explains what the numbers mean and where the law stops working.

Volts, amps and ohms

Three quantities describe a simple circuit. Voltage (V, measured in volts) is the electrical push: the energy each unit of charge gains from a battery or power supply, or gives up as it passes through a component. Current (I, measured in amperes or amps) is the rate at which charge flows past a point. Resistance (R, measured in ohms, symbol Ω) is how strongly a component opposes that flow. A common analogy is water in a pipe: voltage is the pressure, current is the flow rate and resistance is a narrow section of pipe. It is imperfect, but it captures the key idea.

The German physicist Georg Ohm published the relationship in 1827 after experiments with wires of different lengths. Materials and components that follow it closely, with a resistance that stays the same whatever voltage is applied, are called ohmic.

Using V = I × R

The formula rearranges three ways: V = I × R, I = V ÷ R and R = V ÷ I. Some worked examples:

• A 220 Ω resistor connected across a 9 V battery carries I = 9 ÷ 220 ≈ 0.041 A, or 41 mA.
• A device drawing 2 A from a 12 V supply presents a resistance of R = 12 ÷ 2 = 6 Ω.
• An LED needs about 20 mA and drops about 2 V, so on a 5 V supply its series resistor must drop the remaining 3 V: R = 3 ÷ 0.02 = 150 Ω. The LED resistor calculator does this and rounds to a standard value.

Keep the units consistent. Milliamps must become amps (20 mA = 0.02 A) and kilohms must become ohms (4.7 kΩ = 4,700 Ω) before you divide, or the answer will be out by a factor of a thousand.

Adding power: watts

Power, the rate at which energy is converted, is P = V × I, measured in watts. Substituting Ohm's law gives two more forms, P = I² × R and P = V² ÷ R, so any two of the four quantities fix the other two; the calculator lists all twelve rearrangements. Examples:

• A 2 kW kettle on 230 V mains draws I = 2,000 ÷ 230 ≈ 8.7 A, and its hot element has a resistance of about 230² ÷ 2,000 ≈ 26.5 Ω.
• A 1,500 W heater on a 120 V supply draws 12.5 A through 9.6 Ω.
• That 220 Ω resistor on 9 V dissipates 9² ÷ 220 ≈ 0.37 W. A common quarter-watt resistor would overheat; a half-watt part is the safe choice.

Beginners often miss that last point: resistors have a power rating as well as a resistance. To find the current from a known wattage, including AC and three-phase loads, the watts to amps calculator is quicker, and the electricity cost calculator turns watts and hours of use into money.

Series and parallel

Real circuits combine resistances. In series, one after another, the same current flows through each and the resistances add: 1 kΩ plus 2.2 kΩ makes 3.2 kΩ. In parallel, side by side, each sees the same voltage and the currents add, so the total resistance is lower than the smallest one: 1/R = 1/R₁ + 1/R₂, and two 1 kΩ resistors in parallel make 500 Ω. The series and parallel resistor calculator handles longer chains and finds pairs of standard values that make an awkward target. Once you know the value you need, How to read resistor colour codes (4-band and 5-band) shows how to find it in a parts drawer.

Where Ohm's law stops

The ratio V ÷ I always defines a resistance at that moment, but the useful claim, that the ratio stays constant, only holds for ohmic components at a steady temperature. The exceptions are everywhere:

• Temperature. A metal's resistance rises as it heats up. An incandescent filament has a much lower resistance cold than hot, so it draws a surge of current at switch-on.
• Diodes and LEDs. Almost no current flows below a threshold voltage, and above it the current rises steeply. That is why an LED needs a resistor rather than a direct connection to a battery.
• AC loads with motors or electronics. Coils and capacitors add reactance, so the current is not simply V ÷ R, and volts times amps is not the same as the real power in watts. Power factor explained: real, reactive and apparent power covers that.

A note on safety

Ohm's law also explains why electricity is dangerous: the current through a body depends on the voltage and on the body's resistance, which is much lower when skin is wet. Low-voltage electronics, small batteries and breadboard circuits are fine for learning, though even a 12 V car battery can deliver enough current through a short circuit to melt a wire, so fuses matter. Mains voltage is a different matter. Calculate as much as you like, but leave work on household wiring to a qualified electrician; the calculators do arithmetic, not safety checks.