Resistors in Series & Parallel Calculator
Find the equivalent resistance of up to four resistors connected in series and in parallel.
Add resistors end to end or side by side — this is what the circuit sees.
How the resistors in series & parallel calculator works
In series, current has to pass through every resistor in turn, so resistances add: R = R₁ + R₂ + …. In parallel, current has more paths, so the equivalent resistance is always less than the smallest branch: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + …. Two equal resistors in parallel give half of one.
Enter up to four values; leave unused slots at 0 and they are ignored.
Formula: series: R = R₁ + R₂ + … · parallel: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + …
Worked examples
| Inputs | Series total | Note |
|---|---|---|
| 100 Ω and 220 Ω | 320 Ω | series 320, parallel 68.75 |
| Two 1 kΩ | 2,000 Ω | parallel gives exactly half |
| 10, 20, 30 and 40 Ω | 100 Ω | series 100, parallel 4.8 |
FAQFrequently asked questions
Why is parallel resistance smaller than any branch?
Because adding a path lets more current flow at the same voltage. The equivalent must be less than the easiest single path.
What is the shortcut for two resistors in parallel?
Product over sum: R₁ R₂ ÷ (R₁ + R₂). 100 and 220 give 22,000 ÷ 320 = 68.75 Ω.
How do I handle a mixed circuit?
Reduce it in stages — combine the parallel groups first, then add the series parts. Pin a result and enter the next stage.
Do the same rules apply to inductors and capacitors?
Inductors follow the same rules as resistors; capacitors are the reverse (add in parallel, reciprocal in series). See the capacitor calculator.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.