Ohm's Law: All 12 Formulas

Ohm's Law is the single most important relationship in electrical circuits. The base law V = I × R, combined with the power equation P = V × I, produces twelve derived formulas that let you solve for any of the four quantities (voltage, current, resistance, power) given any two of the others. This page lists all twelve, grouped by what you are solving for, with worked examples and the common mistakes to watch out for. The formulas apply directly to DC circuits and purely resistive AC loads (heaters, incandescent bulbs); for reactive or non-linear AC loads, substitute impedance (Z) for resistance (R) and use apparent power (VA) with power factor.

Formulas

Solve for Voltage (V)

V = I × R

V = P ÷ I

V = √(P × R)

Solve for Current (I)

I = V ÷ R

I = P ÷ V

I = √(P ÷ R)

Solve for Resistance (R)

R = V ÷ I

R = V² ÷ P

R = P ÷ I²

Solve for Power (P)

P = V × I

P = I² × R

P = V² ÷ R

Ohm's Law (V = IR) and the power equation (P = VI) are the two fundamental relationships in electrical circuits. Combined, they produce 12 formulas that let you solve for any value (voltage, current, resistance, power) given any two others. This is the foundation of every electrical calculation.

Worked Examples

Example 1: 120V across a 12Ω resistor

I = 120 / 12 = 10 amps, P = 120 × 10 = 1,200 watts

Example 2: 5A through 8Ω

V = 5 × 8 = 40 volts, P = 5² × 8 = 200 watts

Example 3: 240V and 2,400W

I = 2400 / 240 = 10 amps, R = 240² / 2400 = 24 Ω

Common Mistakes

Applying Ohm's Law directly to AC circuits with reactive loads. Use impedance (Z) instead of resistance (R).
Confusing power dissipation with power delivery. A resistor converts all power to heat.
Forgetting that halving resistance doubles current AND quadruples power (P = V²/R).

Try the Calculator

Use the interactive Ohm's Law Calculator for instant results with any values. Every result page shows the formula applied with your specific numbers.

All Formulas

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This is a formula reference page for educational use. Always consult a licensed electrician and verify compliance with the National Electrical Code (NEC) and local electrical codes before applying any of these formulas to real installations.

Standards & References

This page cites the following electrical codes and standards. Always consult the current edition of your local adopted standard for authoritative requirements.

NIST SP 811: SI Unit Definitions. Definitions of the volt, ampere, watt, ohm, coulomb, and joule under the International System of Units (SI). Authoritative reference for unit conversions and precision.
National Institute of Standards and Technology. Reference →

Disclaimer: The information on this page is provided for reference. Always consult a licensed electrician and the current edition of your local adopted electrical code before performing electrical work.