# Resistors in Series and Parallel Calculator

> Enter any list of resistor values to get the equivalent resistance in series and in parallel, using R = R₁ + R₂ + … and 1/R = 1/R₁ + 1/R₂ + ….

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/resistor-series-parallel-calculator

Resistances in series add; in parallel their reciprocals add, so the result is always smaller than the smallest resistor. Paste a list of values to see both.

Also called: Parallel resistance calculator, Equivalent resistance calculator.

## Inputs
- Connection (options: Series, Parallel; default parallel)
- Resistor values (default 100, 220, 470)

## Results
- Equivalent resistance
- If connected in series
- If connected in parallel
- Number of resistors

## Formula

```
Series: R = R₁ + R₂ + … + Rₙ;  Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ
```

Where:
- R₁ … Rₙ: individual resistances in ohms

## Worked example
1. Series: 100 + 220 + 470 = 790 Ω.
2. Parallel: 1/100 + 1/220 + 1/470 = 0.0100 + 0.004545 + 0.002128 = 0.016673 S.
3. R = 1 ÷ 0.016673 = 59.98 Ω.

**Result:** 100 Ω, 220 Ω and 470 Ω give 59.98 Ω in parallel and 790 Ω in series.

## What the result means

For mixed networks, reduce the circuit step by step: combine each parallel group, then add the groups in series.

## Assumptions and limits
- Ideal resistors at their nominal values.
- Tolerance (±1% or ±5%) and temperature drift are not included; use the Resistor Calculator to read colour bands.

## Questions

### Why is parallel resistance smaller than any single resistor?

Each extra path lets more current flow for the same voltage, which is what lower resistance means.

### Two equal resistors in parallel?

Half of one: two 100 Ω resistors in parallel make 50 Ω.

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Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/resistor-series-parallel-calculator