Ohm's law calculator (V = IR)

The formula

$$V = IR$$

$V$ is the voltage across a component in volts, $I$ the current through it in amps and $R$ its resistance in ohms.

Where it comes from

Ohm’s law started as an experimental finding: in 1827 Georg Ohm showed that, for metal wires, current is proportional to the voltage driving it. Resistance is just the name for the constant of proportionality:

$$I = \frac{V}{R}$$

A simple model explains why. A voltage $V$ across a wire of length $L$ sets up an electric field $E = V/L$, which pushes each free electron with a force $eE$. The electrons keep colliding with the metal’s atoms, which on average stops them every $\tau$ seconds, so they never speed up indefinitely. They settle at an average drift velocity

$$v_d = \frac{eE\tau}{m}$$

Current is the charge passing per second: the number of free electrons per volume $n$, times the charge $e$, times the drift velocity, times the wire’s cross-section $A$:

$$I = n e v_d A = \frac{n e^2 \tau A}{m} \cdot \frac{V}{L}$$

Everything except $V$ is a property of the wire, so $I \propto V$. Collecting those properties into one number gives $R = \frac{mL}{ne^2\tau A}$ and the familiar $V = IR$. The model also explains why longer, thinner wires resist more.

Worked example

A 9 V battery across a 470 Ω resistor:

$$I = \frac{V}{R} = \frac{9}{470} = 0.0191\ \text{A} = 19.1\ \text{mA}$$

Watch out for

• Not everything is ohmic. LEDs, diodes and transistors don’t follow $V = IR$; their resistance changes with current.
• Power. The resistor above dissipates $P = IV = 9 \times 0.0191 = 0.17$ W, so a common ¼ W resistor is enough.

Last checked November 11, 2026