The relationship at the heart of every circuit
Georg Ohm published this relationship in 1827, and it's still the first equation anyone learns in electronics: the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. Written as a formula, that's V = I × R.
V = I × R
I = V ÷ R
R = V ÷ I
Because it's just one equation rearranged three ways, knowing any two of the three quantities always pins down the third. A 12-volt battery pushing current through a 6-ohm resistor draws 12 ÷ 6 = 2 amps — that's the whole calculation, and it's the one this tool automates for whichever value you're missing.
Bringing power into the picture
Power — how fast energy is being converted to heat or work, measured in watts — sits right alongside Ohm's law as P = V × I. Substitute in V = I × R or I = V / R and you get two more useful forms, which is why this calculator offers three ways to solve for power depending on which two values you actually have on hand.
P = V × I
P = I² × R
P = V² ÷ R
That same 12V, 2A example draws P = 12 × 2 = 24 watts. It's worth checking a component's power rating against this number before wiring it up — a resistor rated for less than the power it will actually dissipate tends to overheat and fail.
A worked troubleshooting example
Say a multimeter reads 9V across an unknown resistor, and a separate current reading shows 30 mA flowing through it. Converting 30 mA to amps (0.03 A) and solving for resistance:
R = V ÷ I = 9 ÷ 0.03 = 300 Ω
That's the same logic used to sanity-check a suspect component: measure two values, calculate the third, and compare it against what the part's rating or color code says it should be. A reading far outside that expected number usually points to a bad connection, a failing component, or the wrong part in the circuit.
Where the simple version stops applying
Ohm's law assumes resistance stays constant, which is true for a plain resistor over a normal operating range but not for everything. Diodes, LEDs, and transistors have resistance that changes with the voltage across them, so V = I × R doesn't describe their behavior directly. Heat also matters — a wire's resistance rises as it warms up, which is why the same fixed resistor can draw slightly different current cold versus after running for a while. And for AC circuits, resistance alone isn't the whole story — inductors and capacitors add reactance, requiring impedance calculations that extend beyond this basic DC relationship.
Related electrical calculations
For appliance running costs and amperage from wattage and voltage, the electricity calculator covers the full power-wheel of formulas. If you're identifying a specific resistor value from its color bands rather than a measured reading, the resistor color code calculator decodes that directly, and for longer wire runs, the voltage drop calculator accounts for the resistance of the cable itself.