Series & Parallel Resistor Calculator
Add as many resistors as you like, pick series or parallel, get the equivalent with a diagram.
Formulas
Series: Rtotal = R1 + R2 + R3 + …
Parallel: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
Parallel: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
Physics behind series vs parallel
In series, the same current flows through every resistor, so voltages add and resistance adds. In parallel, all resistors share the same voltage, so currents add, meaning conductances (1/R) add. The parallel formula is always less than the smallest single resistor, which is why adding more paths for current to flow reduces the overall resistance.
Worked example
Three resistors 10 Ω, 20 Ω, 30 Ω in parallel
1/Rt = 1/10 + 1/20 + 1/30 = 11/60 Rt = 60/11 ≈ 5.4545 Ω
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FAQs
Formula for series resistors?
R = sum of the individual resistances.
Formula for parallel resistors?
1/R = sum of 1/R_i.
Is parallel total smaller than any resistor?
Yes — always smaller than the smallest resistor.