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Ohm's Law Calculator

Voltage equals current multiplied by resistance

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Ohm’s Law — Voltage

Ohm’s Law states that voltage equals current multiplied by resistance. Combined with the power equation (P = V × I), you can derive 12 formulas to find any one of four electrical quantities from any two of the others.

V = I × R

Ohm’s Law — Current

Current equals voltage divided by resistance. You can also find current from power and voltage (I = P/V) or from power and resistance (I = √(P/R)).

I = V / R

Ohm’s Law — Resistance

Resistance equals voltage divided by current. Alternatively, R = P/I² or R = V²/P when power is one of the known quantities.

R = V / I

Power Equation

Electrical power equals voltage times current. You can also compute power from I²R or V²/R depending on which two values you know.

P = V × I

How It Works

Ohm’s Law (V = I × R) and the power equation (P = V × I) together produce 12 formulas that let you find any one of four electrical quantities — voltage, current, resistance, or power — from any two of the others. Select what you want to solve for, choose which two values you know, and the calculator does the rest.

Example Problem

A 120 V circuit powers a 60 W light bulb. What is the current and resistance?

  1. Current: I = P / V = 60 / 120 = 0.5 A
  2. Resistance: R = V / I = 120 / 0.5 = 240 Ω

You can verify: P = I² × R = 0.25 × 240 = 60 W.

When to Use Each Variable

  • Solve for Voltage — when you know current and resistance (or power and current), e.g., finding the voltage drop across a resistor in a circuit.
  • Solve for Current — when you know voltage and resistance, e.g., determining the current draw of an appliance to size a circuit breaker.
  • Solve for Resistance — when you know voltage and current, e.g., selecting the right resistor value for an LED circuit.
  • Solve for Power — when you know voltage and current (or current and resistance), e.g., calculating the wattage of a heater or motor.

Key Concepts

Ohm's Law (V = IR) and the power equation (P = VI) combine to produce 12 formulas relating voltage, current, resistance, and power. Any single quantity can be calculated from any two of the other three. These relationships assume a linear (ohmic) resistor at constant temperature; non-ohmic devices like diodes and transistors do not follow V = IR.

Applications

  • Electrical wiring: sizing wire gauge and circuit breakers based on expected current draw
  • Electronics design: selecting resistor values for voltage dividers, current limiters, and LED circuits
  • Power systems: calculating transmission losses (P = I²R) to optimize conductor sizing
  • Troubleshooting: measuring voltage and current to diagnose faulty components in a circuit
  • Home energy: estimating appliance wattage to manage electricity costs

Common Mistakes

  • Using peak voltage instead of RMS voltage in AC circuits — household 120V is RMS; the peak is about 170V, and using it inflates power calculations by 41%
  • Assuming resistance is constant with temperature — resistance of metals increases with heat; a light bulb filament at operating temperature has 10x the cold resistance
  • Confusing series and parallel resistance — series resistances add directly (R_total = R1 + R2), but parallel resistances combine as reciprocals (1/R_total = 1/R1 + 1/R2)

Frequently Asked Questions

What is Ohm’s Law in simple terms?

Ohm’s Law says that voltage equals current times resistance (V = I × R). If you push more voltage through a circuit, more current flows. If you increase resistance, less current flows for the same voltage.

How do I calculate power from voltage and resistance?

Use P = V²/R. For example, a 240 V heater with 20 Ω resistance draws 240²/20 = 2,880 W of power.

Does Ohm’s Law apply to AC circuits?

Yes, but in AC circuits you replace resistance with impedance (Z), which includes both resistance and reactance. For purely resistive loads like heaters, V = I × R works directly.

What is the relationship between watts and amps?

Watts = Volts × Amps. A 1,500 W space heater on a 120 V circuit draws 1,500/120 = 12.5 A. This is why 15-amp circuits can barely handle one large heater.

Reference: Ohm, Georg Simon. 1827. Die galvanische Kette, mathematisch bearbeitet. Berlin: T. H. Riemann. See also Halliday, Resnick & Walker, Fundamentals of Physics.

Ohm's Law Wheel

The wheel organizes all 12 equations. Each quadrant solves for one variable using any combination of the other two.

Ohm's
Law
VI×RP/I√(P×R)
IV/RP/V√(P/R)
RV/IP/I²V²/P
PV×II²×RV²/R

Each quadrant shows three ways to calculate that variable from any two of the other three.

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Related Sites

Reference: Ohm, Georg Simon. 1827. Die galvanische Kette, mathematisch bearbeitet. Berlin: T. H. Riemann. See also Halliday, Resnick & Walker, Fundamentals of Physics.