# Parallel Resistance Calculator

> Calculate parallel resistance step by step: 1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn.

Page: https://freecalculator.tech/tools/parallel-resistance-calculator
Last reviewed: 2026-11-03

## Formula

1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn. For two: R1·R2 ÷ (R1 + R2).

- Every resistance must be above zero (a zero-ohm branch is a short circuit).
- The total is always smaller than the smallest branch.
- Blank optional boxes are skipped.
- 1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn. For two: R1·R2 ÷ (R1 + R2).
- Inputs used: R1, R2, R3 (optional), R4 (optional), R5 (optional).

## Inputs

- R1
- R2
- R3 (optional)
- R4 (optional)
- R5 (optional)

## Worked example: 100 Ω ∥ 220 Ω

Two resistors side by side.
1. 1/100 + 1/220 = 0.014545 S.
2. R = 1 ÷ 0.014545 = 68.75 Ω.

## Common questions

### Why is the result smaller than every resistor?

Each extra branch gives current another path, so the combination conducts more easily than any one branch alone.

### What happens with a 0 Ω branch?

It is a short circuit and the total becomes zero, so the calculator asks for values above zero.

### How do I get an unusual value?

Combining standard resistors in parallel or series is a common way to reach values that are not sold individually.

### How do I use the Parallel Resistance Calculator?

Enter the required values for R1, R2, R3 (optional), R4 (optional), R5 (optional). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Parallel Resistance Calculator use?

1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn. For two: R1·R2 ÷ (R1 + R2). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Parallel Resistance Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Up to five branches.
- Ignores tolerance and temperature drift.
- Ideal connections assumed.
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this parallel resistance calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- OpenStax (Rice University) — https://openstax.org/details/books/university-physics-volume-2

## Cite this page

- APA: Free Calculator. (2026, November 3). Parallel Resistance Calculator. https://freecalculator.tech/tools/parallel-resistance-calculator
- MLA: "Parallel Resistance Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/parallel-resistance-calculator.
- Link: Parallel Resistance Calculator — Free Calculator, https://freecalculator.tech/tools/parallel-resistance-calculator