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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. Find the current draw and resistance of the filament.

  1. Identify known values: voltage V = 120 V and power P = 60 W
  2. Select the formula for current from power and voltage: I = P / V
  3. Substitute values: I = 60 W / 120 V
  4. Calculate current: I = 0.5 A
  5. Use the current to find resistance: R = V / I = 120 V / 0.5 A
  6. Calculate resistance: R = 240 Ω — verify with P = I² × R = 0.25 × 240 = 60 W ✓

This is the cold-start resistance. A tungsten filament at operating temperature (2,700 °C) has roughly 10× the resistance of a cold bulb.

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 the relationship between voltage, current, and resistance?

Voltage, current, and resistance are linked by Ohm's Law: V = I × R. Voltage is the electrical pressure that pushes charge through a conductor, current is the rate of charge flow, and resistance is the opposition to that flow. Doubling the voltage across a fixed resistance doubles the current; doubling the resistance at the same voltage halves the current.

How do you use Ohm's law to solve circuit problems?

Start by identifying which two of the four quantities (V, I, R, P) you know. Then pick the formula that solves for the unknown — for example, if you know voltage and resistance, use I = V/R to find current. For power problems, combine Ohm's law with P = VI to get derived formulas like P = I²R or P = V²/R.

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. For circuits with capacitors or inductors, use V = I × Z where Z accounts for phase shifts.

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.

Why does a light bulb draw more current when first turned on?

A cold tungsten filament has about 1/10th the resistance of a hot filament. When you flip the switch, the low resistance causes a high inrush current (I = V/R with small R). As the filament heats up in milliseconds, resistance rises and current drops to its steady-state value. This thermal shock is why bulbs most often burn out at the moment of switching on.

How do you calculate voltage drop in a wire?

Treat the wire as a resistor. Look up its resistance per unit length (e.g., 14 AWG copper is about 2.53 Ω per 1,000 ft), multiply by the round-trip distance, then use V = I × R. The NEC recommends keeping voltage drop below 3% for branch circuits — if your drop exceeds that, use a thicker gauge wire.

What happens if you short-circuit a battery?

A short circuit has near-zero external resistance, so I = V/R produces an extremely large current limited only by the battery's internal resistance. A typical car battery (12V, ~0.01 Ω internal) can deliver over 1,000 A in a short circuit. This generates intense heat, can melt wires, and may cause the battery to vent or explode.

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 Formula

Ohm's law defines the linear relationship between voltage, current, and resistance in an electrical circuit:

V = I × R

Where:

  • V — voltage (potential difference), measured in volts (V)
  • I — current (charge flow rate), measured in amperes (A)
  • R — resistance (opposition to current flow), measured in ohms (Ω)

Combined with the power equation P = V × I, these two formulas produce 12 derived equations that let you solve for any one of four electrical quantities — voltage, current, resistance, or power — from any two of the others.

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.

Worked Examples

Electronics

What resistor do you need for an LED on a 5V supply?

A standard red LED needs 2V forward voltage and 20 mA of current. With a 5V supply, the resistor must drop the remaining 3V.

  • Voltage across resistor: 5V − 2V = 3V
  • Required current: I = 0.02 A (20 mA)
  • R = V / I = 3 / 0.02
  • R = 150 Ω

Use the next standard resistor value up (150 Ω is standard). This limits LED current to exactly 20 mA, preventing burnout.

Home Electrical

How much voltage drop occurs in a long wire run?

A 100-foot run of 14 AWG copper wire (0.253 Ω per 100 ft, round trip = 0.506 Ω) carries 15 A to a workshop subpanel. What is the voltage drop?

  • Wire resistance (round trip): R = 0.506 Ω
  • Current draw: I = 15 A
  • V = I × R = 15 × 0.506
  • V = 7.59 V drop

That's 6.3% of 120V — above the NEC-recommended 3% maximum. Upgrading to 12 AWG (lower resistance) would reduce the drop.

Automotive

How much current does a car starter motor draw?

A 12V car battery powers a starter motor with an internal resistance of 0.06 Ω. Estimate the starting current.

  • Battery voltage: V = 12 V
  • Motor resistance: R = 0.06 Ω
  • I = V / R = 12 / 0.06
  • I = 200 A

Real starter current peaks even higher (200-300 A) because the motor's back-EMF is zero at initial crank. This is why starter batteries need high cold-cranking amps (CCA).

Related Calculators

Related Sites

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