What Is Ohm's Law?

Ohm's Law is the fundamental relationship in electrical circuit analysis: the voltage across a conductor equals the current flowing through it multiplied by its resistance (V = I × R). Published by German physicist Georg Simon Ohm in 1827, this simple equation underpins all of electrical engineering and electronics. This calculator solves for any one of the three variables — voltage, current, or resistance — given the other two, and also computes power using the three equivalent power formulas.

Pre-filled with 12V and 4Ω (a common 12V automotive circuit), the calculator immediately shows that 3 amperes of current flow and 36 watts of power are consumed — typical for a small automotive accessory.

Ohm's Law Formula and Variations

V = I × R (Voltage = Current × Resistance)

I = V / R (Current = Voltage ÷ Resistance)

R = V / I (Resistance = Voltage ÷ Current)

Power equations: P = V × I = I² × R = V² / R. All three power forms are mathematically identical — use whichever two quantities you know.

The Ohm's Law Triangle

A memory aid: draw a triangle with V at the top, I at bottom-left, R at bottom-right. Cover the quantity you want to find: covering V reveals I × R. Covering I reveals V/R. Covering R reveals V/I. This triangle works the same way for the power triangle: P at top, I at bottom-left, V at bottom-right.

Series and Parallel Circuits

Series: Resistors in series add directly: R_total = R1 + R2 + R3. Current is the same through all components; voltage divides proportionally. Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3. Voltage is the same across all branches; current divides inversely with resistance. For two resistors in parallel: R_total = (R1 × R2)/(R1 + R2) — the product-over-sum shortcut.

Practical Applications

LED circuits: An LED needs 2V forward voltage and 20mA current from a 5V supply. Required series resistor: R = (5 − 2) / 0.02 = 150Ω. Power dissipated in resistor: P = 0.02² × 150 = 0.06W — safely within a ¼W resistor rating. Fuse sizing: A 120V appliance drawing 1,200W needs a current of I = P/V = 10A — use a 15A fuse for safety margin. Battery drain: A 12V car battery powering a 60W load: I = 60/12 = 5A. If the battery is 60Ah, it lasts 60/5 = 12 hours.

Limitations of Ohm's Law

Ohm's Law applies only to ohmic (linear) conductors where resistance is constant regardless of applied voltage. Non-ohmic devices include diodes (exponential V-I curve), transistors, thermistors (resistance changes with temperature), and incandescent bulb filaments (resistance increases when hot). For AC circuits, resistance is replaced by impedance Z = √(R² + X²), where X is reactance from capacitors or inductors. Use the impedance calculator for AC analysis.

Tips for Using This Calculator

Select "Solve For" to choose which variable to calculate. The two known values auto-populate the visible input fields. The calculator verifies Ohm's Law in the breakdown table (V = I × R should equal your entered voltage). The pie chart shows all four quantities for quick visual comparison. Pair with the power calculator for complete electrical circuit analysis.