⚡ Ohm's Law Calculator

Ohm's law, the power equations, and the twelve formulas they generate

Two equations describe almost everything in a simple DC circuit. Ohm's law relates voltage, current and resistance; the power equation relates voltage, current and power. Combine them and you get twelve formulas, which is why Ohm's law is usually drawn as a wheel — but there are only two facts to remember, and the rest is substitution.

V = I × R   ·   P = V × I

The units are volts, amps, ohms and watts, and they are defined so that no conversion factors appear anywhere: one volt across one ohm drives one amp and dissipates one watt. That coherence is the reason the SI system is worth the trouble.

What the law actually says

Ohm's law states that current through a conductor is proportional to the voltage across it, with resistance as the constant of proportionality. The word to notice is proportional: the law only holds for components where resistance stays constant, which is why they are called ohmic. Resistors are ohmic over their working range; diodes, LEDs, transistors, filament bulbs and most semiconductors are not.

An LED is the everyday example. It does not have a resistance you can divide by — it has a forward voltage, roughly 2 V for a red one and 3.2 V for a white one, and it draws whatever current the rest of the circuit allows. Connect one directly across a battery and it draws enough current to destroy itself, which is why an LED always needs a series resistor sized by the voltage left over, not by the LED.

Power is the number that breaks things

Voltage and current decide whether a circuit works; power decides whether it survives. A resistor dissipating more than its rating heats up, drifts in value, discolours and eventually fails. The convention is to choose a resistor rated at least double the calculated dissipation, both for reliability and because a part running near its limit is also running hot enough to affect everything around it.

The last two rows are the point: the arithmetic is trivial but the physical consequence is a component that glows. Power rises with the square of the current, so doubling the current quadruples the heat — which is also why thin wire is dangerous at high current and why the BTU calculator and electrical heating are the same subject from two directions.

Current is what injures people, not voltage, though voltage is what drives the current. Around 10 mA across the body causes muscle contraction strong enough to prevent letting go, and 100 mA through the chest can be fatal. Mains voltage across dry skin can deliver far more than that, which is why mains work belongs to qualified electricians and why this calculator is for low-voltage DC.

Series and parallel

Series: R = R₁ + R₂ + ...  ·  Parallel: 1/R = 1/R₁ + 1/R₂ + ...

In series the current is the same everywhere and the voltages add, which is how a voltage divider works. In parallel the voltage is the same across each branch and the currents add, so total resistance falls below the smallest individual resistor — two 100 Ω resistors in parallel give 50 Ω. Adding loads in parallel increases total current draw, which is the mechanism behind an overloaded circuit.

Where it stops applying

Ohm's law in this form is a DC law. With alternating current, capacitance and inductance introduce reactance, which opposes current without dissipating power, and the relevant quantity becomes impedance rather than resistance. Voltage and current also fall out of phase, so power is no longer simply V times I — it is V times I times the power factor. For resistive AC loads such as heaters and filament lamps the simple version still works.

Resistance also moves with temperature. Copper rises about 0.4% per degree Celsius, so a motor winding at 100 °C has noticeably more resistance than the same winding cold. A filament bulb is the extreme case: its cold resistance can be a tenth of its hot resistance, which is why bulbs fail at switch-on when the inrush current is at its highest.

A worked example

A white LED with a 3.2 V forward voltage is to run at 20 mA from a 12 V supply. The resistor must drop 12 − 3.2 = 8.8 V at 0.02 A, so R = 8.8 / 0.02 = 440 Ω. The nearest standard value is 470 Ω, which gives 18.7 mA — close enough. Power in the resistor is 8.8 × 0.0187 = 0.165 W, so a 0.25 W part is marginal and a 0.5 W part is the right choice. Note that the resistor dissipates more than twice what the LED does, which is the usual trade-off with a series resistor and the reason efficient designs use a constant-current driver instead.

The natural follow-ups are the conversion calculator, for what this figure feeds into, and the number base converter, for the closely related case.

Frequently Asked Questions (FAQs)