Series & Parallel Calculator
Combines any number of resistors, capacitors or inductors in series or parallel. Capacitors behave the opposite way round from resistors and inductors, which is the part worth remembering.
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The formula
resistors and inductors series: R₁ + R₂ + … parallel: 1 / (1/R₁ + 1/R₂ + …) capacitors — the rules swap over series: 1 / (1/C₁ + 1/C₂ + …) parallel: C₁ + C₂ + …
Resistors and inductors add when in series. Capacitors add when in parallel, because capacitance grows with plate area. The reciprocal form always produces a value smaller than the smallest component.
What to watch out for
The rules, and the sanity check for each:
- Resistors in series add. The total is always larger than the largest.
- Resistors in parallel combine reciprocally. The total is always smaller than the smallest — if your answer is not, the arithmetic is wrong.
- Capacitors are reversed. Parallel capacitors add; series capacitors combine reciprocally. Capacitance is about plate area, and parallel plates are more area.
- Inductors follow resistors. Series adds, parallel combines reciprocally — assuming no mutual coupling between them.
Two equal components in parallel always give half the value; two equal in series give double. That single fact catches most errors.
Frequently Asked Questions
What is the total of two 100 Ω resistors in parallel?
50 Ω. Two equal resistors in parallel always give half the value.
Why do capacitors work the opposite way?
Because capacitance depends on plate area. Wiring capacitors in parallel effectively increases the area, so they add. In series the plates are effectively further apart, so capacitance falls.
Can a parallel resistance be larger than a component?
No, never. Adding a parallel path always gives current somewhere else to go, so the total resistance must fall. If a calculation says otherwise, it is wrong.