Ohm's law explained (V = IR)
Ohm's law ties together the three things every circuit has: voltage, current and resistance. Learn the formula, the triangle trick, and how to find any one value when you know the other two.
Enter any two of voltage, current and resistance and get the third, plus power.
Ohm's law is the single most useful equation in basic electronics, and it is far simpler than it looks. It connects the three quantities every electrical circuit has: voltage, current and resistance. Once you can rearrange it, you can work out any one of the three when you know the other two, which is most of what beginner circuit problems ever ask. Here is the law in plain words, the formula and its rearrangements, a memory trick, worked examples, and the cases where the law stops holding.
In short: Ohm's law says voltage = current times resistance, written V = I x R. The current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance, as long as temperature stays constant. Rearranged, I = V / R and R = V / I. A free Ohm's law calculator finds the missing value for you.
What each letter means
- V = voltage, measured in volts (V). Think of it as the electrical "push" driving the current.
- I = current, measured in amperes or amps (A). This is the rate of flow of electric charge. The symbol is I, from the French intensite (intensity), which is why it is not "C".
- R = resistance, measured in ohms (the symbol is the Greek letter omega). This is how much the component opposes the flow.
In words: more voltage pushes more current through; more resistance holds it back. That single sentence is Ohm's law.
A picture that helps: think of water in a pipe. Voltage is the water pressure, current is how much water flows per second, and resistance is how narrow the pipe is. Raise the pressure and more water flows; narrow the pipe and less does. The analogy breaks down in one place, electrons do not pile up at the end of a wire like water in a tank, but for getting the feel of V, I and R it is hard to beat.
The units at a glance
| Quantity | Symbol | Unit | Equals |
|---|---|---|---|
| Voltage | V | volt (V) | 1 V = 1 joule per coulomb |
| Current | I | ampere (A) | 1 A = 1 coulomb per second |
| Resistance | R | ohm | 1 ohm = 1 V per A |
| Power | P | watt (W) | 1 W = 1 V times 1 A |
The three formulas
There is really only one equation, rearranged three ways depending on what you are solving for:
| You want | You know | Formula |
|---|---|---|
| Voltage (V) | Current and resistance | V = I x R |
| Current (I) | Voltage and resistance | I = V / R |
| Resistance (R) | Voltage and current | R = V / I |
The Ohm's law triangle
The easiest way to remember all three is the triangle. Put V at the top, with I and R side by side underneath. Then cover the quantity you want to find, and the remaining two show you the sum:
- Cover V, and you see I next to R, so V = I x R.
- Cover I, and you see V over R, so I = V / R.
- Cover R, and you see V over I, so R = V / I.
The diagram on this page shows the layout. Learn the triangle once and you never have to memorise the three formulas separately.
Three worked examples
Finding voltage. A current of 0.5 A flows through a 50 ohm resistor. What is the voltage across it? V = I x R = 0.5 x 50 = 25 V.
Finding current. A 24 V supply is connected across a 120 ohm resistor. What current flows? I = V / R = 24 / 120 = 0.2 A, which is the same as 200 mA.
Finding resistance. A component has 18 V across it with 1.5 A flowing through it. What is its resistance? R = V / I = 18 / 1.5 = 12 ohms.
That is genuinely most of what Ohm's law problems ask. The Ohm's law calculator lets you enter any two values and returns the third, so you can check your own working.
Watch the units: the biggest mistake
The most common error is not the formula, it is the units. Circuits are full of prefixes, and mixing them up throws the answer out by a factor of a thousand or a million. Before you plug numbers in, convert everything to the base units of volts, amps and ohms:
- 1 mA (milliamp) = 0.001 A. So 200 mA = 0.2 A.
- 1 kilo-ohm = 1,000 ohms, and 1 mega-ohm = 1,000,000 ohms.
- 1 mV (millivolt) = 0.001 V.
For example, 5 V across a 2 kilo-ohm resistor is I = 5 / 2000 = 0.0025 A = 2.5 mA, not "2.5". If very large or very small numbers come up a lot, our scientific notation calculator helps keep the powers of ten straight.
Series and parallel circuits
Real circuits usually have more than one resistor, and Ohm's law still runs the show once you combine them. There are two ways to connect them:
- In series (one after another), resistances add: R total = R1 + R2. For example, 100 ohms and 200 ohms in series give 300 ohms. On a 12 V supply, the current is I = 12 / 300 = 0.04 A, or 40 mA. The voltage splits across them: 0.04 x 100 = 4 V across the first and 0.04 x 200 = 8 V across the second, which add back up to 12 V.
- In parallel (side by side), you add the reciprocals: 1 / R total = 1 / R1 + 1 / R2. Two 100 ohm resistors in parallel give 50 ohms. On 12 V that draws I = 12 / 50 = 0.24 A in total, split as 0.12 A down each branch.
Notice the pattern: series resistance is always larger than any single resistor, and parallel resistance is always smaller than the smallest one.
Adding power: the Ohm's law wheel
Ohm's law pairs naturally with the power equation, P = V x I, where P is power in watts. Combine the two and you can find power from any pair of values without knowing all three directly:
- P = V x I (power from voltage and current).
- P = I squared x R (power from current and resistance).
- P = V squared / R (power from voltage and resistance).
So the 50 ohm resistor from the first example, carrying 0.5 A, dissipates P = I squared x R = 0.25 x 50 = 12.5 watts. This extended set is often drawn as the "Ohm's law wheel", but you only need the basic triangle plus P = V x I to derive the rest. One practical warning: 12.5 watts is far more than a standard quarter-watt resistor can take, so in real life that part would need to be a power resistor rated 25 watts or more, or it would simply burn out. Power, not just resistance, decides which component you can actually use.
Real-world examples
Ohm's law is not just a classroom exercise. It quietly runs through everyday electrical life:
- A kettle on mains power. On a 230 V supply (standard across Botswana, Southern Africa, the UK and much of the world), a 2,000 W kettle draws I = P / V = 2000 / 230 = about 8.7 A. Its heating element has a resistance of R = V / I = 230 / 8.7 = about 26.5 ohms. That 8.7 A is why such appliances need a 13 A plug and not a 5 A one.
- A resistor for an LED. This is the most common hobby use of Ohm's law. To run an LED that drops 2 V from a 5 V supply at 20 mA, you need a resistor to absorb the extra 3 V: R = (5 - 2) / 0.020 = 150 ohms. Get this wrong and the LED burns out instantly.
- Why bulbs blow at switch-on. A 60 W, 230 V filament lamp has a hot resistance of V squared / P = 52,900 / 60 = about 880 ohms. Cold, the tungsten filament measures only a fraction of that, so a big inrush of current flows the instant you flick the switch, which is roughly when most bulbs fail.
A useful habit from these: cross-check any answer by working the power out two ways. The 12.5 W above also equals V x I = 25 x 0.5, which agrees, so the numbers are consistent.
Ohm's law for class 10 and class 12
If you are studying this for school, two extra ideas usually come up alongside V = IR:
The V-I graph. For an ohmic conductor at constant temperature, a graph of voltage (V) against current (I) is a straight line through the origin. The slope of that line is the resistance R: a steeper line means a higher resistance. A curved or bent line means the component is non-ohmic.
Resistivity: what sets a resistor's value. Resistance also depends on the material and shape of the conductor: R = rho x L / A, where L is the length, A is the cross-sectional area, and rho (the Greek letter rho) is the resistivity of the material, measured in ohm-metres. In plain terms, a longer wire resists more and a thicker wire resists less, which is why thin wires heat up. This links Ohm's law to why one component has a given resistance in the first place. Georg Simon Ohm published the voltage-current relationship in 1827, and the unit of resistance, the ohm, is named after him.
When Ohm's law does not apply
Ohm's law is a model, and it holds for "ohmic" conductors, things like metal wires and standard resistors, where resistance stays roughly constant. It does not hold for "non-ohmic" components whose resistance changes with conditions. A filament lamp gets hotter as more current flows and its resistance rises, so voltage and current are not proportional. Diodes and transistors are non-ohmic too, and thermistors change resistance with temperature (an NTC thermistor loses resistance as it warms, a PTC gains it). Ohm's law also assumes a constant temperature, which is why the "temperature held constant" caveat appears in the formal statement.
One subtlety students often miss: R = V / I still gives you the resistance of a lamp or diode at one operating point. What breaks for a non-ohmic part is the straight-line relationship, double the voltage and the current does not double. For a plain resistor kept cool, V = IR holds to within the resistor's tolerance, which is typically 1 to 5 percent. If you like this kind of physics, our explainer on how to calculate density uses the same rearrange-one-formula approach.