How do resistors combine in series?

Series resistors share one current path, so their resistance values add directly to produce the equivalent resistance.

How do resistors combine in parallel?

For parallel branches, the reciprocal of equivalent resistance equals the sum of each reciprocal branch resistance. The result is lower than the smallest positive branch.

What happens with a zero-ohm resistor?

A zero-ohm resistor adds nothing in series. In parallel, a zero-ohm branch shorts the ideal network, making its equivalent resistance zero ohms.

Can this calculator analyze a supplied circuit?

Yes. Optional voltage analysis calculates total current, total power, and the voltage, current, and power for each resistor or branch.

Parallel & Series Resistor Calculator

Build a series or parallel resistor network, compare equivalent resistance instantly, and optionally inspect voltage, current, and power throughout the circuit.

Parallel & Series Resistor Calculator

Build a series or parallel resistor network, compare equivalent resistance instantly, and optionally inspect voltage, current, and power throughout the circuit.

Live resistor network

Series circuit

Equivalent resistance

3.2 kΩ1 kΩ + 2.2 kΩ in series

Connection: Series
Resistors: 2
Smallest: 1 kΩ
Largest: 2.2 kΩ

Network breakdown

Resistor relationships

Formula reference

Series and parallel relationships

Series network

R_total = R₁ + R₂ + … + R_n

One current path; resistance values add.

Parallel network

1 / R_total = 1 / R₁ + 1 / R₂ + … + 1 / R_n

Multiple branches; the total is below the smallest positive branch.

Two parallel resistors

R_total = (R₁ × R₂) / (R₁ + R₂)

A shortcut for exactly two non-zero resistors.

Quick examples

Common resistor combinations

1 kΩ + 2.2 kΩ + 470 Ω3.67 kΩ in series

1 kΩ ‖ 1 kΩ500 Ω in parallel

1 kΩ ‖ 2 kΩ≈ 666.67 Ω in parallel

Parallel & Series Resistor Calculator

Series circuit

Resistor relationships

Voltage analysis

Series and parallel relationships

Common resistor combinations