Ohm's Law Calculator

Ohm's law links four things in a circuit: the voltage (V, the push, in volts), the current (I, the flow, in amps), the resistance (R, how hard the part resists the flow, in ohms) and the power (P, how fast energy is used or turned into heat, in watts). Know any two and the other two follow.

The formula

voltage = current × resistance (V = I × R)
current = voltage ÷ resistance (I = V ÷ R)
resistance = voltage ÷ current (R = V ÷ I)
power = voltage × current (P = V × I)
power = current² × resistance = voltage² ÷ resistance

All 12 formulas of the wheel

Worked example

You know the voltage is 12 V and the current is 0.5 A. The resistance is R = V ÷ I = 12 ÷ 0.5 = 24 Ω. The power is P = V × I = 12 × 0.5 = 6 W. Check with a third formula: P = I² × R = 0.5 × 0.5 × 24 = 0.25 × 24 = 6 W, the same answer.

Unit prefixes

Small and large values use prefixes: m (milli) is ÷ 1,000, µ (micro) is ÷ 1,000,000, k (kilo) is × 1,000 and M (mega) is × 1,000,000. So 20 mA = 0.02 A, 4.7 kΩ = 4,700 Ω and 2.3 kW = 2,300 W. Always change to plain volts, amps, ohms and watts before you multiply or divide; this calculator does that for you, so you can mix units freely.

Series and parallel

series total = R1 + R2 + R3 + …
parallel total = 1 ÷ (1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3 + …)

100 Ω, 220 Ω and 330 Ω in series make 650 Ω. On 12 V the current is 12 ÷ 650 = 18.46 mA through all three, and the voltage splits in proportion: 1.846 V across 100 Ω, 4.062 V across 220 Ω and 6.092 V across 330 Ω (together 12 V).

In parallel they make 1 ÷ (1/100 + 1/220 + 1/330) = 3,300 ÷ 58 = 56.90 Ω. Each one gets the full 12 V, so the currents are 120 mA, 54.55 mA and 36.36 mA, 210.9 mA in total.

LED resistor

resistor = (supply − number of LEDs × LED voltage) ÷ LED current
resistor heat = voltage across it × current

A red LED (about 2 V) at 20 mA on a 5 V supply: (5 − 2) ÷ 0.02 = 150 Ω, which is a standard E12 value. The resistor turns 3 × 0.02 = 0.06 W into heat. Doubling it for a safety margin, which is common practice rather than a rule, gives 0.12 W, so a 1/8 W (0.125 W) resistor is enough and a 1/4 W one runs cooler. When the exact value is not standard, the calculator picks the next standard value above it, so the LED gets slightly less current, never more.

Voltage divider

Vout = Vin × R2 ÷ (R1 + R2)
R2 for a wanted Vout = R1 × Vout ÷ (Vin − Vout)

12 V with R1 = 10 kΩ and R2 = 4.7 kΩ: 12 × 4.7 ÷ 14.7 = 3.837 V, with 12 ÷ 14,700 = 0.8163 mA flowing. Anything you connect to Vout sits in parallel with R2 and pulls the voltage down; add it as the load to see by how much.

AC power and power factor

apparent power (VA) = V × I (single phase)
apparent power (VA) = √3 × V line-to-line × I (three phase)
real power (W) = VA × power factor
reactive power (VAR) = VA × √(1 − power factor²)

230 V and 10 A at a power factor of 0.8: 230 × 10 = 2,300 VA, 2,300 × 0.8 = 1,840 W and 2,300 × √(1 − 0.64) = 2,300 × 0.6 = 1,380 VAR. A three-phase motor drawing 10 A per line on 400 V at the same power factor uses √3 × 400 × 10 = 6,928 VA, or 5,543 W.

Ohm's law holds for resistors and wires at a steady temperature. LEDs, lamps and motors are not plain resistors: a filament's resistance rises a lot as it heats up, and an LED's current changes sharply with its voltage, which is why it needs a resistor. LED forward voltages here are typical figures; use the one in your LED's datasheet. Stay safe around mains voltage.