# Magnetic Force Between Wires Calculator

URL: https://speedycalculator.com/calculators/physics/magnetic-force-between-wires/
Last updated: 2026-10-30

> The magnetic force between wires calculator finds the force per unit length (and total force) between two long parallel current-carrying wires, and whether they attract or repel.

## Inputs

- Current I₁ (A, mA, µA, kA)
- Current I₂ (A, mA, µA, kA)
- Distance between wires d (cm, mm, m, in, ft)
- Wire length L (m, cm, mm, km, in, ft, yd, mi)

## Results

- Force per unit length
- Total force
- Interaction

## Formula

```
F/L = μ₀·I₁·I₂ / (2π·d)
```

## Explanation

Two wires carrying currents push or pull on each other: parallel currents attract, opposite currents repel. Until 2019 this effect defined the ampere – 1 A in each wire 1 m apart gives exactly 2 × 10⁻⁷ N per metre.

### How to use the Magnetic Force Between Wires Calculator

- **Current I₁**
- **Current I₂**
- **Distance between wires d**
- **Wire length L**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter both currents (negative for the opposite direction), the separation and the wire length.

### Inputs explained

FieldWhat to enterCurrent I₁Units: A, mA, µA, kACurrent I₂Units: A, mA, µA, kADistance between wires dUnits: cm, mm, m, in, ftWire length LUnits: m, cm, mm, km, in, ft …

### What each result means

- **Force per unit length** = abs(1.25663706212e-06×[Current I₁]×[Current I₂]÷(2×pi×[Distance between wires d]))
- **Total force** = abs(1.25663706212e-06×[Current I₁]×[Current I₂]÷(2×pi×[Distance between wires d]))×[Wire length L]

### Example values

How the main result changes when **Current I₁** changes and everything else stays at the example values above:

Current I₁ (A)Total force (mN)517.51.510212.52.5153204

## Worked example

Inputs — Current I₁: 10 A; Current I₂: 10 A; Distance between wires d: 1 cm; Wire length L: 1 m.

Results — Force per unit length = 0.002 N/m; **Total force = 2 mN**; Interaction = Attraction (same direction).

## Key terms

- **Ampère's force law**: Force between current-carrying conductors.

## FAQ

**Why do parallel currents attract?**
Each wire sits in the other's magnetic field and feels a Lorentz force.

**How was the ampere defined?**
By this force: 2 × 10⁻⁷ N/m for 1 A at 1 m (until 2019).

**Can the force be large?**
Yes – short-circuit currents can bend busbars.

**Does it apply to short wires?**
Approximately, if the length is much greater than the separation.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)