Ohm’s Law Calculator

Ohm’s law is named for the German physicist Georg Simon Ohm, who published the relationship in May 1827 in Die galvanische Kette, mathematisch bearbeitet ("The Galvanic Circuit Investigated Mathematically"), based on experiments he had carried out the previous year. His finding — that current through a conductor is directly proportional to the voltage across it, and inversely proportional to its resistance — was initially met with a cool reception from parts of the German scientific establishment, and it took recognition from scientists elsewhere in Europe and the United States before it was widely accepted as one of the foundational relationships of circuit theory.

The law itself, V = IR, is simple enough to state in one line, but it underlies essentially all analysis of electrical circuits: every resistor, wire and load in a circuit relates its voltage, current and resistance through this same equation, and analysing a larger circuit is largely a matter of applying it repeatedly alongside a small number of other circuit laws.

The most common way to build intuition for Ohm’s law is a water analogy: voltage is like water pressure pushing through a pipe, current is like the rate of water flow, and resistance is like how narrow the pipe is. Push harder — more voltage — and more water flows; narrow the pipe — more resistance — and less flows for the same push. It is a genuinely useful mental model for a first pass at DC circuits.

The analogy has real limits, though. Water is effectively incompressible and flows continuously through a pipe, while electric current is the movement of charge carriers that can be stored, released and reversed — none of which has a clean water equivalent. It also says nothing about power, frequency, or the behaviour of components like capacitors and inductors, which store and release energy rather than simply resisting its flow.

A component is called ohmic when its resistance stays constant regardless of the voltage or current passing through it — a plot of current against voltage is a straight line. Most simple resistors and plain conducting wires behave this way over a normal operating range, which is exactly why Ohm’s law applies so cleanly to them.

Many everyday components are not ohmic. A filament light bulb’s resistance rises sharply as it heats up, so its cold resistance — the value a multimeter reads when it is off — is far lower than its resistance while lit. Diodes, transistors and other semiconductor devices have resistance that depends heavily on the voltage applied, which is precisely what makes them useful for switching and amplification rather than just standing in the way of current like a resistor does.

Adding power to the picture — the rate at which electrical energy converts to heat, light or motion — turns Ohm’s law into a small family of related formulas. Because P = VI and V = IR are both true, power can also be written as I²R or V²/R, and any one of voltage, current, resistance or power can be found from any two of the others. This full set is sometimes drawn as an "Ohm’s law wheel," which is exactly the set of routes this calculator’s results table shows.

These formulas describe direct current and purely resistive AC loads. Real AC circuits containing motors, transformers or anything with a coil or capacitor need the related but more general concept of impedance, plus power factor, because voltage and current in a reactive circuit are no longer simply in step with each other.