Magnetic Force Between Parallel Wires Calculator
Find the magnetic force per unit length between two parallel current-carrying wires and determine whether they attract or repel each other.
A
A
m
Attractive — currents flow in the same direction
- 1
I₁ × I₂
5 × 5 = 25 - 2
μ₀ × I₁ × I₂
0.000001257 × 25 = 0.0000314159 - 3
2π × d
2π × 0.02 = 0.12566371 - 4
Force per unit length F/L
μ₀·I₁·I₂ ÷ (2π·d) = 0.0000314159 ÷ 0.12566371 = 0.000250Positive = attractive (same-direction currents); negative = repulsive.
How does this calculator work?
Two parallel wires carrying currents I₁ and I₂ separated by distance d experience a force per unit length F/L = μ₀·I₁·I₂ / (2π·d). Same-direction currents attract (positive result), opposite-direction repel (negative result). The force decreases as 1/d — double the gap and halve the force.
Formula
How this is calculated
Each current-carrying wire produces a circular magnetic field around it. The field from wire 1 exerts a force on the current in wire 2, and vice versa. Applying the Biot-Savart law and integrating along an infinite straight conductor gives a force per unit length of F/L = μ₀ · I₁ · I₂ / (2π · d), where d is the centre-to-centre distance between the wires. When both currents flow in the same direction the product I₁ · I₂ is positive and the force is attractive. When they are in opposite directions the product is negative and the force is repulsive. To model a reversed current, enter a negative value for one of the currents.
This interaction was historically used to define the ampere: before 2019 the SI ampere was defined as the constant current which, if maintained in two straight parallel conductors of infinite length placed 1 m apart in vacuum, would produce a force of 2 × 10⁻⁷ N per metre of length — which corresponds exactly to μ₀/(2π). The current SI definition uses the elementary charge instead, but the formula remains unchanged.
The formula assumes ideal infinite straight wires; for short conductors or wires at an angle, the full Biot-Savart integral must be evaluated. The result is the magnitude of the force per unit length; multiply by the wire length to get the total force between segments of finite length, provided the length is much greater than the separation.
Frequently asked questions
Wire 1's circular field points into the plane between the wires when current flows upward, which creates a force on wire 2's upward current directed toward wire 1 (F = I L × B). The reverse happens from wire 2's field on wire 1, so both wires are pulled toward each other — attraction.
The force per unit length falls off as 1/d. Doubling the separation halves the force; halving it doubles the force. The XY plot shows this 1/d relationship over a range around your input distance.
Enter a negative value for one current and a positive value for the other. The product I₁ · I₂ becomes negative, and the calculator reports the force as repulsive with a negative F/L value.
TG we-Calculate Editorial Team. (2026). Magnetic Force Between Parallel Wires Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnetic-force-between-wires-calculator
TG we-Calculate Editorial Team. "Magnetic Force Between Parallel Wires Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnetic-force-between-wires-calculator.
TG we-Calculate Editorial Team, "Magnetic Force Between Parallel Wires Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnetic-force-between-wires-calculator
@misc{wecalculate_magnetic_force_between_wires_calculator, title = {Magnetic Force Between Parallel Wires Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnetic-force-between-wires-calculator}}, year = {2026}, note = {TG we-Calculate} }
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