TAHA Engineering Toolsby TAHA Knowledge Lab

Electrical Engineering

Resistors in Series & Parallel Calculator

Total resistance of up to six resistors in series and in parallel.

Inputs

Top: three resistors R1, R2, R3 connected end to end in series. Bottom: the same three resistors connected side by side in parallel.SeriesR₁R₂R₃ParallelR₁R₂R₃
Series (top): resistors end to end — the same current flows through all of them and the resistances add. Parallel (bottom): resistors side by side — the same voltage is across each and the total is smaller than the smallest one. Diagram not to scale.

Result

Total in parallel
59.9768
Total in series
790
Resistors used
3resistors

Connected in series, the 3 resistors add up to 790 Ω. Connected in parallel, the total is 59.9768 Ω — always smaller than the smallest single resistor.

Educational estimate — check the assumptions below.

About this calculator

Resistors in series (end to end) carry the same current, and their resistances simply add. Resistors in parallel (side by side) share the same voltage, and the total resistance is lower than any one of them. Enter two to six values; leave unused boxes empty.

Formula

Series: Rtotal = R1 + R2 + … + Rn

Parallel: 1 ÷ Rtotal = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn

For two resistors in parallel: R = R1R2 ÷ (R1 + R2).

Worked example

100 Ω, 220 Ω and 470 Ω:

  • Series: 100 + 220 + 470 = 790 Ω
  • Parallel: 1 ÷ (0.01 + 0.004545 + 0.002128) = 1 ÷ 0.016673 = 59.98 Ω

Two equal 1 kΩ resistors in parallel give exactly half: 500 Ω.

Assumptions and limitations

  • Ideal resistors at their nominal values. Real resistors have a tolerance (for example ±1% or ±5%).
  • Check that each resistor’s power rating is enough for the current it will carry.

References

  • Kirchhoff’s circuit laws; series and parallel resistance formulas.