Ohm's law says the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance: V = I × R. Push harder with more voltage and more current flows; add resistance and less flows. Named after Georg Ohm, who published it in 1827, it is the single most used relationship in electronics, and rearranging it gives I = V ÷ R and R = V ÷ I.

How do I calculate power in a circuit?

Power is voltage times current: P = V × I, measured in watts. Combining that with Ohm's law gives two more forms that are often more convenient — P = I²R when you know current and resistance, and P = V² ÷ R when you know voltage and resistance. All three give the same answer. A 12 V supply driving 3 A dissipates 36 W, and you get the same 36 W from 3² × 4 or from 12² ÷ 4.

Why does doubling the voltage quadruple the power?

Because voltage appears squared in P = V² ÷ R. Doubling V doubles the current as well, and since power is the product of the two, both doublings compound into a factor of four. The same logic applies to P = I²R. This is the most practically important consequence of the law: a resistor comfortable at 5 V may be dissipating four times its rated power at 10 V, and components fail from heat long before they fail from voltage.

What are the four quantities and their units?

Voltage is measured in volts (V) and is the electrical pressure driving charge. Current is measured in amperes (A) and is the rate of charge flow — one amp is one coulomb per second. Resistance is measured in ohms (Ω) and opposes that flow. Power is measured in watts (W) and is the rate at which energy is converted, usually into heat or light.

How do I choose a resistor for an LED?

Subtract the LED's forward voltage from your supply voltage, then divide by the current you want. A red LED dropping about 2 V on a 5 V supply leaves 3 V across the resistor, and for 20 mA that means R = 3 ÷ 0.02 = 150 Ω. Check the power too: 3 V × 0.02 A is 0.06 W, so a standard quarter-watt resistor is comfortable. Note that the LED itself is not ohmic, which is exactly why the resistor is needed to set the current.

Which materials obey Ohm's law?

Ohmic conductors — those whose resistance stays constant as voltage changes — include most metals and manufactured resistors at steady temperature. Plot current against voltage for these and you get a straight line. Non-ohmic components include diodes, transistors, filament lamps and electrolytes. A filament lamp is a good example: as it heats up its resistance rises significantly, so a cold measurement badly underestimates its resistance in operation.

How much current does a household appliance draw?

Divide its power rating by the supply voltage. A 3,000 W kettle on a 230 V UK supply draws 3000 ÷ 230 = 13.04 A, which is why UK plugs carry a 13 A fuse. On a 120 V US supply the same kettle would need 25 A, well beyond a standard 15 A circuit — which is why US kettles are typically rated around 1,500 W and boil more slowly. The element resistance follows from R = V² ÷ P, about 17.6 Ω in the UK case.

What happens if resistance is zero?

That is a short circuit, and Ohm's law predicts infinite current — which is why this calculator refuses zero resistance rather than returning a number. In reality the current is limited by the internal resistance of the supply and the resistance of the wiring, but it still rises to whatever those allow, which is typically enough to melt insulation, damage the source or start a fire. Fuses and circuit breakers exist precisely to interrupt this case.

Does Ohm's law work for AC circuits?

In simple form only for purely resistive AC circuits. Once capacitors or inductors are involved, resistance is replaced by impedance, written Z, which varies with frequency and shifts the phase between voltage and current. The relationship becomes V = I × Z. Power also splits into real, reactive and apparent components, related by the power factor. For a plain resistive load — a heater, a filament lamp, a kettle — the calculations on this page apply directly using RMS values.

Ohm's Law Calculator (V = I × R)

Enter any two of voltage, current, resistance and power, and this calculator returns the other two. Ohm's law states that the current through a conductor is proportional to the voltage across it and inversely proportional to its resistance: V = I × R. Add the power relationship P = V × I and those f...

V = I × R

Two values entered — solving for current and power.

VVOLTAGE

ICURRENT

solved: 3.000 A

RRESISTANCE

PPOWER

solved: 36.000 W

EVERYDAY CIRCUITS

THE COMPLETE CIRCUIT, IN SI UNITS

12.00

3.00

4.00

36.00

Gold values were solved for; grey values are the ones you supplied.

Power

36.000 W

In kilowatts

0.03600 kW

Energy in 1 hour

0.03600 kWh

As horsepower

0.04828 hp

Conductance

0.25000 S

Charge in 1 hour

10,800.00 C

STEPS

You supplied V = 12.0000 V and R = 4.0000 Ω

I = 3.0000 A

P = 36.0000 W

THE OHM'S LAW WHEEL — WHICH FORMULA APPLIES

VVOLTAGE · V

V = I × R

V = P ÷ I

V = √(P × R)

ICURRENT · A

▸ I = V ÷ R

I = P ÷ V

I = √(P ÷ R)

RRESISTANCE · Ω

R = V ÷ I

R = V² ÷ P

R = P ÷ I²

PPOWER · W

P = V × I

P = I² × R

▸ P = V² ÷ R

Twelve formulas, three for each quantity. You supplied V and R, so the arrowed formula in each gold-lettered box is the one that applies — one for I, one for P.

THE CIRCUIT

Power rises with the square. Doubling the voltage across a fixed resistor does not double the heat, it quadruples it, because P = V² ÷ R. The same applies to current through P = I²R. That squared term is why a small rise in supply voltage can destroy a component that was running comfortably.

HOW MUCH POWER IS THAT?

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type any two of the four values into the boxes. Known values get a solid black border; the two you leave blank are outlined in gold and fill in as soon as the second value is entered.
2
Pick units beside each field — millivolts to kilovolts, microamps to kiloamps, milliohms to megohms, milliwatts to megawatts or horsepower. Mixing scales is safe because everything converts to SI first.
3
Look at the wheel on the right. Each quantity has three formulas, and the arrowed one in each gold-lettered box is the formula that applies to your particular pair of inputs — one route to each answer.
4
Watch the circuit underneath. The charge carriers speed up as current rises and the resistor glows brighter as power increases, so you can see at a glance whether a change makes a circuit busier or hotter.

ALL TWELVE FORMULAS

voltage from current and resistanceV = I × R

voltage from power and currentV = P ÷ I

voltage from power and resistanceV = √(P × R)

current from voltage and resistanceI = V ÷ R

current from power and voltageI = P ÷ V

current from power and resistanceI = √(P ÷ R)

resistance from voltage and currentR = V ÷ I

resistance from voltage and powerR = V² ÷ P

resistance from power and currentR = P ÷ I²

power from voltage and currentP = V × I

power from current and resistanceP = I² × R

power from voltage and resistanceP = V² ÷ R

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Last updated: July 28, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.