What are the three formulas for Ohm's law?

The one relationship rearranges three ways: V = I × R to find voltage, I = V ÷ R to find current, and R = V ÷ I to find resistance. Add power and you get the full wheel of 12 formulas, but those three cover the core of Ohm's law.

How do you calculate current from voltage and resistance?

Rearrange V = I × R to I = V ÷ R, then divide the voltage by the resistance. For example, 12 volts across 4 ohms gives 12 ÷ 4 = 3 amperes. Resistance must not be zero.

How do you find power using Ohm's law?

Electrical power is voltage times current: P = V × I, measured in watts (W). With 12 V and 3 A the power is 12 × 3 = 36 W. When you only know two of the four quantities you can also use P = I² × R or P = V² ÷ R.

What are the units of voltage, current, resistance, and power?

Voltage is measured in volts (V), current in amperes or amps (A), resistance in ohms (Ω), and power in watts (W). In V = I × R, volts equal amperes times ohms; in P = V × I, watts equal volts times amperes.

Why do electronics use mA and kΩ instead of A and Ω?

Real circuits often run tiny currents through large resistances, so amperes and ohms produce awkward decimals. Milliamps (mA = 0.001 A) and kilohms (kΩ = 1000 Ω) keep numbers readable. This calculator lets you pick the unit per field and converts everything to base units internally.

Does Ohm's law work for AC circuits?

For purely resistive AC circuits, yes — using RMS values of voltage and current. When capacitors or inductors are involved, resistance is replaced by impedance (Z) and Ohm's law becomes V = I × Z with phase taken into account.

What is a non-ohmic device?

A non-ohmic device is one whose resistance changes with voltage or current, so it does not follow a straight V = I × R line. Diodes, transistors, and incandescent bulbs are common examples — their current-versus-voltage graph is curved, not a straight line.

Physics

Ohm's Law Calculator

Enter any two of voltage, current, resistance, and power — the other two solve instantly, in the units you choose. Built on the full power wheel (V = I × R and P = V × I), with the working shown.

Enter any two values

2 of 2

Fill exactly two of the four boxes — the other two are solved instantly.

VVoltage

ICurrentsolved

RResistance

PPowersolved

Results

VVoltage· given

12V

ICurrent

RResistance· given

4Ω

PPower

36W

How each was found

I = V ÷ R = 12 V ÷ 4 Ω → I = 3 A
P = V² ÷ R = 12 V² ÷ 4 Ω → P = 36 W

Live — every value recomputes as you type.

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The basics

What is Ohm's law?

Ohm's law is the relationship between three quantities in an electric circuit: voltage, current, and resistance. Push harder (more voltage) and more current flows; add resistance and less current flows. It holds for ordinary resistive components and is the foundation every other circuit calculation is built on.

V = I × R

The core law

Voltage equals current times resistance. The same equation, rearranged, lets you find whichever of the three quantities is unknown from the other two.

12 V = 3 A × 4 Ω

P = V × I

Adding power

Power — the rate energy is used, in watts — completes the picture. Together these two equations give four quantities and twelve formulas: the power wheel.

36 W = 12 V × 3 A

Method

How to solve it by hand

Whatever you're solving for, the routine is the same three moves.

1
Note what you know
Identify which two of the four quantities you have — voltage V, current I, resistance R, or power P.
Known: I = 3 A, R = 4 Ω
2
Pick the matching formula
From the wheel, choose the formula for your unknown that uses only the two values you have. To get voltage from current and resistance, that's V = I × R.
V = I × R
3
Substitute and compute
Put the numbers in, keeping the units consistent (convert mA to A, kΩ to Ω first), and evaluate.
V = 3 × 4 = 12 V

The wheel

The Ohm's law power wheel

Four quantities, twelve formulas. Each of V, I, R, and P can be found three ways depending on which pair you already know. Tap a quantity to spotlight its three formulas.

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

Worked examples

See it solved four ways

The same three-step routine, applied to find each quantity in turn.

Given I = 2 A, R = 6 Ω — find voltage.

Pick the formula that uses the two knowns:

V = I × R = 2 × 6

V = 12 V

Quick chart

How much current flows through a resistor?

Pick a supply voltage and read off the current and power for every common resistor value — handy for sizing LED resistors and checking a part's power rating.

Supply voltage

Resistance	Current (I = V ÷ R)	Power (P = V² ÷ R)
10 Ω	500 mA	2.5 W
47 Ω	106.383 mA	531.915 mW
100 Ω	50 mA	250 mW
220 Ω	22.7273 mA	113.636 mW
330 Ω	15.1515 mA	75.7576 mW
470 Ω	10.6383 mA	53.1915 mW
1 kΩ	5 mA	25 mW
4.7 kΩ	1.06383 mA	5.31915 mW
10 kΩ	500 µA	2.5 mW

Values for a resistor placed directly across a 5 V supply. Pick another voltage to refill the table.

Where it shows up

Why Ohm's law matters

It's the first thing you reach for in any practical circuit, from a breadboard LED to a household appliance.

R = (Vs − Vf) ÷ I

LED resistors

Sizing the series resistor for an LED is pure Ohm's law: divide the leftover voltage by the LED's target current.

P = I² × R

Power & heat

The same current through a resistor heats it. Power tells you whether a part needs a quarter-watt or a two-watt rating.

I = V ÷ R

Safety & fuses

Knowing the current a fault would draw — voltage divided by resistance — is how fuses and breakers are chosen.

Worth knowing

Rules and gotchas

A few facts that keep your answers honest.

V = I × Z

AC uses impedance

In AC circuits with capacitors or inductors, resistance becomes impedance Z, and Ohm's law is written V = I × Z.

R ≠ constant

Non-ohmic devices

Diodes, transistors, and bulbs change resistance with voltage, so they don't plot as a straight line — Ohm's law only approximates them.

mA, kΩ, mW

Mind your units

Mixing milliamps with ohms gives wrong answers. Convert everything to base units (A, Ω, V, W) before computing, then convert back.

R = 0 → ∞ I

No dividing by zero

Solving for current with zero resistance, or resistance with zero current, has no finite answer — a short circuit or an open circuit.

series & parallel

Combine resistances first

Ohm's law works on a single resistance. For networks, reduce series (R₁ + R₂) and parallel resistors to one value first.

V = I × R

It's a definition of R

Strictly, the law defines resistance as the ratio V ÷ I. A component is “ohmic” only if that ratio stays constant.

Reference

Symbols, units, and prefixes

The four quantities, their symbols and SI units, and the engineering prefixes you'll meet most.

Quantity	Symbol	Unit	Common prefixes
Voltage	V	volt (V)	mV, kV
Current	I	ampere (A)	µA, mA
Resistance	R	ohm (Ω)	Ω, kΩ, MΩ
Power	P	watt (W)	mW, kW

Origin

Where the law comes from

The relationship is named for the German physicist Georg Simon Ohm, who published it in 1827 after careful experiments with wires of different lengths and thicknesses. He found that, at a fixed temperature, the current through a metal conductor is directly proportional to the voltage across it — the constant of proportionality being what we now call resistance. The unit of resistance, the ohm (Ω), and its inverse, the siemens, both carry the names of the scientists who mapped this territory.

FAQ

Common questions

Ohm's law states that the voltage across a conductor equals the current through it multiplied by its resistance: V = I × R. It links voltage (V), current (I), and resistance (R) for any ohmic (resistive) component, and is the single most-used relationship in basic electronics.

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