Series and Parallel Circuit Calculator

Paste a series or parallel circuit question to get the full working, or combine any number of resistors, capacitors or inductors.

Quick total for any components

Assumes the inductors are not magnetically coupled (no shared magnetic field).

Resistors in series and parallel

In a series circuit the same current flows through every resistor, so their resistances simply add: R total = R1 + R2 + R3. In a parallel circuit every resistor has the same voltage across it and the current splits, so the reciprocals add: 1/R total = 1/R1 + 1/R2 + 1/R3.

For exactly two resistors in parallel there is a shortcut, product over sum: R = (R1 × R2) ÷ (R1 + R2). For example 100 Ω and 220 Ω in parallel give 22,000 ÷ 320 = 68.75 Ω, and in series they give 320 Ω.

Worked example: resistors in series

A 24 V supply is connected to 4 Ω and 8 Ω resistors in series. Find the current and the voltage across each resistor.

• Total R = 4 + 8 = 12 Ω
• V across 4 Ω = 2 × 4 = 8 V
• V across 8 Ω = 2 × 8 = 16 V (check: 8 + 16 = 24 V)

In series the current is the same everywhere and the supply voltage is shared, so the voltages across the resistors always add up to the supply voltage.

Worked example: resistors in parallel

A 12 V supply is connected to 6 Ω and 3 Ω resistors in parallel. Find the total current.

• Current through 6 Ω = 12 ÷ 6 = 2 A and through 3 Ω = 12 ÷ 3 = 4 A (check: 2 + 4 = 6 A)

In parallel every resistor has the full supply voltage across it and the currents through the branches add up to the total current.

Cells with internal resistance

A real cell has some resistance of its own, called its internal resistance r. The current is I = E ÷ (R + r), where E is the emf. The voltage across the external resistors, the terminal p.d., is V = I × R, and the difference E − V = I × r is called the lost volts. For a 12 V cell with r = 1 Ω driving 11 Ω, I = 12 ÷ 12 = 1 A, the terminal p.d. is 11 V and 1 V is lost inside the cell.

Capacitors in series and parallel

Capacitors follow the opposite rules. In parallel their capacitances add: C total = C1 + C2. In series the reciprocals add: 1/C total = 1/C1 + 1/C2, so two 10 µF capacitors in series give 5 µF. Series capacitors share the voltage, which is why they are sometimes used to reach a higher voltage rating.

Inductors in series and parallel

Inductors that are far enough apart not to affect each other combine like resistors: they add in series and their reciprocals add in parallel. Coupled inductors, such as two windings on one core, need the mutual inductance as well, which this calculator does not include.

Frequently Asked Questions

Need a single value? Read it with the Resistor Colour Code Calculator or the Capacitor Code Calculator.