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ΣR · 1 ÷ Σ(1/R)

Resistor calculator

Enter any number of resistances to get the series sum, the parallel total and the reciprocal working for each.

Kilohm and megohm prefixes are accepted: 4k7, 10k, 1M.

Short answer: 100 Ω, 200 Ω and 300 Ω in series is 600 Ω; in parallel it is 54.55 Ω, because 1/R = 0.01 + 0.005 + 0.00333 = 0.01833 and R = 1 ÷ 0.01833.

Reading the reciprocal step

The parallel formula is where mistakes happen, so the sum of the reciprocals is shown before the division. If the parallel answer comes out above the smallest resistor then a reciprocal was taken wrongly — the check under the result states the smallest value so that error is visible.

Worked example

An LED that wants 20 mA from 9 V with a 2 V forward drop needs a resistor of (9 − 2) ÷ 0.02 = 350 Ω, so a standard 330 Ω is chosen. Two 680 Ω parts in parallel give 340 Ω, which is what is done when only one value is in the drawer.

Resistor questions

How do resistors add up?

In series the values add: R = R₁ + R₂ + R₃. In parallel the reciprocals add: 1/R = 1/R₁ + 1/R₂ + 1/R₃, so the total is always smaller than any single resistor.

Why is parallel resistance smaller?

Because the current has more paths, so the same voltage pushes more through. Two 10 Ω resistors in parallel give 5 Ω — half the resistance, twice the current — which is the check printed under the result.

Which one do I want?

Series adds voltage drops at the same current, so it is used to limit current in an LED string. Parallel shares the current at the same voltage, so it is used for power rails and for spreading heat across several parts.

Can I mix three or more values?

Yes — up to 100 values, comma separated. Mixed values are the normal case: 10 Ω parallel with 4.7 Ω is 3.20 Ω, not 7.35 Ω, and rounding to a preferred value afterwards is a separate step this page does not invent for you.

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