Resistor Series & Parallel Calculator

Combining resistors

Resistors in series carry the same current, so their resistances add. Resistors in parallel share the same voltage, so their conductances (1/R) add — giving a total that is always smaller than the smallest resistor.

Series: R = R₁ + R₂ + … + Rₙ

Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ

For just two resistors in parallel this simplifies to the "product over sum" rule: R = R₁·R₂ / (R₁ + R₂). Two equal resistors in parallel give half the value; N equal resistors give R/N.

Why it matters

Series and parallel combinations let you reach a value you don't have in stock from resistors you do, or spread power dissipation across several parts. Need a specific ratio instead? Try thepotential divider calculator.

Worked example: making 6.8 kΩ from what you have

You need roughly 6.8 kΩ but only have 10 kΩ and 22 kΩ in the drawer. In series they make 32 kΩ; in parallel, 1 / (1/10k + 1/22k) = 6.875 kΩ — about 1% above the standard 6.8 kΩ value, and usually close enough to use directly.

Tolerance and power do not divide evenly

The combined value is exact arithmetic on nominal values, and real resistors are not nominal. Tolerances partly average out in a long chain but never cancel, so a network of 5% parts is still roughly a 5% network. The more practical trap is power: in a series chain the largest resistor dissipates the most, and in a parallel bank the smallest does. Sizing every part for an equal share of the total will underrate one of them — check the dissipation of the extreme value rather than the average.