What this calculator does
Two parallel wires carrying current exert a magnetic force on each other. Currents in the same direction attract; currents in opposite directions repel, which is the reverse of what most people guess by analogy with electric charge.
The effect is small at ordinary currents but it is fundamental. For decades the ampere was defined by exactly this force between two wires a metre apart, which is why the constant in the formula used to be exact by definition.
The formula
Multiply the permeability of free space by both currents, then divide by two π times the separation. The result is force per unit length, which multiplied by the wire length gives the total force.
| Term | Meaning |
|---|---|
| Force per unit length | The natural output here, since the force grows with how much of the wires run parallel. |
| Attraction and repulsion | Parallel currents in the same direction attract; opposing currents repel. |
| Permeability of free space (μ₀) | The magnetic constant, 4π × 10⁻⁷ T·m/A. |
The inputs explained
| Field | What to enter |
|---|---|
| Current in wire 1 (A) | Current in the first wire, in amps. |
| Current in wire 2 (A) | Current in the second wire, in amps. Use a negative value for current flowing the opposite way. |
| Distance between wires (m) | The separation between the wire centres, in metres. |
| Wire length (m) | A number, measured in m. Starts at 1. |
| Current directions | Choose from Same direction, Opposite direction. |
When to use it
Assessing busbar forces under fault current
Normal currents give negligible force, but short-circuit currents can be thousands of amps and the force rises with their product.
Understanding the old ampere definition
The unit was defined by this exact force between two wires, which is why the formula once contained an exact constant.
Checking cable behaviour
Conductors in a cable carry opposing currents and therefore repel, which matters for mechanical design in high-current installations.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the force fall with separation?
Two wires carrying equal currents at a range of separations.
| Separation | Force per metre (mN/m) | Force per unit length |
|---|---|---|
| 25 mm | 0.800000 mN/m | 8.0000e-4 N/m |
| 50 mm | 0.400000 mN/m | 4.0000e-4 N/m |
| 100 mm | 0.200000 mN/m | 2.0000e-4 N/m |
Questions
Why do same-direction currents attract?
Each wire sits in the magnetic field created by the other, and the force on a current in a field is perpendicular to both. Working the directions through gives attraction for parallel currents, which is genuinely the opposite of the like-charges-repel rule for electrostatics.
Why does the force matter for switchgear?
Because it rises with the product of the two currents. At a fault current of tens of thousands of amps the force becomes large enough to bend busbars, so mechanical bracing is part of the design.
Is this how the ampere was defined?
It was, until 2019. The ampere was the current that produced a force of exactly 2 × 10⁻⁷ newtons per metre between two infinite parallel wires one metre apart. It is now defined from the elementary charge instead.
Does it work with a single wire and a magnet?
The same underlying physics applies: a current in a magnetic field experiences a force. That is exactly how electric motors work, with the field supplied by magnets rather than by a second wire.
For the field one wire produces, see the magnetic field of a straight wire calculator. For a coil's field, see the solenoid magnetic field calculator.