Introduction to magnetic force between parallel wires
When two long conductors run side by side, each current creates a magnetic field that acts on the other conductor. The resulting force depends on the current in each wire, the distance separating their centers, and the parallel overlap length being considered. This calculator turns that arrangement into two practical values: force per unit length and total force over the section you enter. It is useful for comparing bus bars, cable runs, laboratory leads, and other parallel conductors without repeating the derivation by hand.
The direction of the current matters as much as its size. Currents flowing in the same reference direction pull the wires together; currents in opposite directions push them apart. The calculator reports a positive force magnitude and labels the interaction as attractive or repulsive, making the result easier to apply to a physical layout. It is an estimate for the magnetic interaction, not a complete mechanical design of the supports, insulation, or enclosure.
What magnetic-force question this parallel-wire calculator answers
This magnetic-force calculator answers a focused question: for two long, parallel wires at a given separation, what magnetic force acts over the length where they run alongside one another? The force per meter helps compare layouts of different lengths, while total force estimates the load on the specified parallel section. A useful question might be, “How does reversing one conductor change the force?” or “How much more force appears if the gap is reduced?”
Keep the geometry clear before entering values. The separation is normally the center-to-center distance between the conductors, and the length is the section over which they remain approximately parallel at that separation. A short crossing, a sharply bent cable, or a bundle with many nearby conductors needs a more detailed field and mechanical analysis than this two-wire model provides.
How to use the parallel-wire magnetic force calculator
Enter a current for each conductor in amperes, the wire separation in meters, and the parallel overlap length in meters. Then select Compute to update the live result panel. Positive and negative current values are allowed: use a shared reference direction for both wires, then give one current a negative sign when it flows opposite to that reference direction. This is how the calculator distinguishes attraction from repulsion.
- Enter the current in Wire 1, I₁, in amperes.
- Enter the current in Wire 2, I₂, in amperes, using a negative value if it is oppositely directed.
- Enter the center-to-center separation r in meters; it must be greater than zero.
- Enter the parallel overlap length L in meters; it must also be greater than zero.
- Read both the force per unit length and total force, then check the attraction or repulsion label.
If a current is uncertain, rerun the calculation with plausible high and low values. This simple sensitivity check quickly shows whether current uncertainty or wire spacing is the larger concern in your case.
Inputs for a reliable parallel-wire force estimate
All four inputs must describe the same physical pair of conductors. The current values may come from a measurement, a rated operating condition, or a planned fault-current case, but they should represent the same time period. The model assumes a uniform separation along the entered length, so an average gap is only an approximation when the wires bow, twist, or diverge.
The current product controls the force magnitude. Consequently, a zero current in either wire produces no net magnetic interaction in this model. Separation has an inverse effect: placing the same wires twice as far apart halves the force per unit length. Length affects only the total force; it does not change the per-meter result. Convert centimeters or millimeters to meters before entry, because a distance-unit mistake can change the result substantially.
Formulas for force between long parallel current-carrying wires
For two long, straight, parallel wires in free space or air, the calculator uses the standard long-wire form of Ampère’s force law. μ₀ is the permeability of free space, approximately 4π × 10⁻⁷ N/A². The signed product I₁I₂ determines the direction, while the result display uses the magnitude and names the direction separately.
The relationships are direct and useful for quick checks. Doubling either current doubles both results. Doubling r halves the force per meter and the total force. Doubling L doubles total force but leaves force per meter unchanged. Same-sign currents are attractive; opposite-sign currents are repulsive. These proportional changes are often more informative than a single isolated result.
Worked example: 10 A parallel wires at 5 cm spacing
Suppose two wires each carry 10 A in the same direction, remain 0.05 m apart, and run parallel for 1.5 m. The current product is 100 A². Substituting the values into the long-wire relation gives a force per unit length of 4.000e-4 N/m. Multiplying that value by 1.5 m gives a total force of 6.000e-4 N.
Because both currents have the same sign in this example, the interaction is attractive. If one 10 A current is entered as −10 A instead, the displayed magnitude remains 4.000e-4 N/m and 6.000e-4 N, but the label changes to repulsive. This is a helpful sanity check: reversing one current reverses the force direction without changing its magnitude.
Parallel-wire force sensitivity to current and spacing
The following comparisons retain a 10 A current in Wire 2 and a 1 m overlap length. They illustrate why both current and conductor spacing deserve careful attention when comparing parallel layouts.
| Scenario |
I₁ |
r |
Force per unit length |
Interpretation |
| Lower current |
8 A |
0.05 m |
3.200e-4 N/m |
A 20% reduction in one current reduces the force by 20%. |
| Baseline |
10 A |
0.05 m |
4.000e-4 N/m |
This is the reference same-direction case. |
| Wider spacing |
10 A |
0.10 m |
2.000e-4 N/m |
Doubling the separation halves the force. |
The table highlights the inverse-distance relationship. A modest change in spacing can matter greatly for closely packed, high-current conductors. For a real support design, consider the highest relevant current condition rather than only a normal operating current.
How to interpret a parallel-wire magnetic force result
The result panel provides a force magnitude in newtons per meter and a total force in newtons. Use force per unit length when comparing cable or bus-bar arrangements of unequal lengths. Use total force when considering the magnetic load over the entered parallel run. The attraction or repulsion label tells you which way the conductors tend to move relative to one another, assuming they are free enough for that motion to matter.
Very small answers are not necessarily errors; ordinary currents separated by centimeters often produce small steady magnetic forces. Conversely, high currents and close spacing can create much larger forces, particularly during short-duration high-current events. Record the entered currents, separation, length, and sign convention with any result so that another person can reproduce the scenario later.
Magnetic-force limitations and assumptions for parallel wires
This magnetic-force estimate intentionally uses the simplest useful geometry: two long, straight, parallel wires in air or vacuum with a clear, fixed separation. It is an excellent comparison tool, but it does not include every physical effect present in an installation.
- Long-wire approximation: end effects become more important when the overlap length is not large compared with the separation.
- Two-conductor model: nearby phases, return paths, ferromagnetic materials, shields, and enclosures can alter the actual field and force.
- Uniform geometry: curved conductors, nonuniform gaps, flexible cables, and changing orientations need more detailed treatment.
- Mechanical design: this page estimates magnetic force, not conductor deflection, restraint strength, vibration, heating, insulation performance, or safety compliance.
- Units and signs: enter meters and amperes, and use current signs only as a shared directional convention.
For engineering, laboratory, or safety decisions, use this result as a transparent starting point and confirm the assumptions against the actual equipment and applicable design standards. Its value is that it makes the influence of current, separation, and overlap length explicit before more complex analysis is needed.