Series and Parallel Resistor Calculator (Equivalent Resistance)

What is equivalent resistance?

It is the single resistor that would draw the same current as a group of resistors. Two basic rules cover the two ways of connecting them.

Series

The resistors are connected end to end and carry the same current. The equivalent is the sum of the values:

R_eq = R1 + R2 + … + Rn

The result is always larger than the largest resistor.

Parallel

Both ends of every resistor are common, so each sees the same voltage. The reciprocals add up:

1 / R_eq = 1 / R1 + 1 / R2 + … + 1 / Rn

The result is always smaller than the smallest resistor. For two resistors the shortcut is R1 × R2 / (R1 + R2). For n equal resistors in parallel the equivalent is R / n.

Example

Put 12 Ω, 6 Ω and 4 Ω in parallel. 1/12 + 1/6 + 1/4 = 6/12, so the equivalent is 2 Ω. The same three in series give 12 + 6 + 4 = 22 Ω.

Mixed networks

The tool handles resistors that are all in series or all in parallel. For a mixed network solve the inner group first and enter its result as one resistor in the outer group. Use the same approach for more than 10 resistors.

Limits

Tolerance and temperature effects are ignored. The power shown when a voltage is entered is the total for all resistors, so check the dissipation of each part separately.