Magnetic Force Between Wires Calculator

Two parallel conductors carrying current exert magnetic forces on one another. The first wire creates a circular magnetic field, and charges moving in the second wire experience a Lorentz force in that field. For wires that are long compared with their separation, the resulting force per unit length is F/L = μ₀I₁I₂ / (2πd). Here I₁ and I₂ are current magnitudes, d is centre-to-centre separation, and μ₀ is vacuum permeability. Multiplying by the chosen parallel length gives the total force over that segment. The interaction grows with either current. Doubling one current doubles the force, while doubling both makes the force four times as large. Increasing separation weakens the interaction inversely, so twice the distance produces half the force per metre. The equation assumes air or vacuum between the conductors. It also assumes thin, straight, parallel wires and neglects end effects, nearby magnetic materials, bends, and other current paths. Direction depends on current orientation. Currents flowing in the same direction attract, while currents flowing in opposite directions repel. This calculator accepts magnitudes and reports force magnitude, so identify attraction or repulsion from the actual current directions in your circuit. Each wire experiences an equal-magnitude force in the opposite spatial direction, consistent with Newton's third law. In practical installations those distributed forces can create stress, vibration, or movement in busbars and cable supports. Historically, this interaction helped define the ampere because it gives a direct mechanical consequence of electric current. Modern SI definitions no longer use the old exact force-based definition, but the relation remains central to electromagnetism. Use metres for both separation and length, amperes for currents, and interpret output in newtons per metre and newtons. Separation should be measured between conductor axes rather than between their nearest surfaces. For thick conductors, closely spaced conductors, finite lengths, or complex cable layouts, numerical field analysis may be required. This ideal calculator is most useful for textbook problems, quick busbar estimates, force comparisons, and checking detailed models. It clearly separates the geometry-independent distributed load from total force, helping prevent the common mistake of treating newtons per metre as a total newton value.