Repulsive Force Between Two Magnets Calculator
Calculate magnetic repulsion using a practical dipole model or a classic pole strength model, then visualize how force changes with distance.
Dipole model equation used: F = (3 mu_0 mu_r m1 m2) / (2 pi r^4), valid when magnet separation is several times larger than magnet dimensions.
How to Calculate Repulsive Force Between Two Magnets: Complete Engineering Guide
Magnetic repulsion is one of the most useful and misunderstood effects in practical design. You see it in magnetic bearings, non contact couplings, latching systems, packaging closures, and precision alignment tools. If you are trying to calculate the repulsive force between two magnets, the key challenge is not only selecting the right equation, but also understanding the assumptions behind it. Magnet geometry, material grade, separation distance, alignment, and nearby ferromagnetic objects can all change the result significantly.
This guide gives you a reliable way to estimate repulsive force using two common mathematical approaches. You will learn when each model is valid, how to avoid calculation mistakes, and how to move from rough estimate to engineering confidence. The calculator above is built to support this exact workflow.
What Is Magnetic Repulsive Force
Magnetic repulsive force occurs when like poles face each other, such as north to north or south to south. At a physics level, the field interaction creates a force that pushes the magnets apart. The force depends strongly on distance. For many practical setups, if you halve the spacing, the force can increase dramatically. This non linear behavior is why a magnet pair may feel weak at moderate spacing and suddenly feel very strong when brought close.
In design, you usually want one of three outcomes:
- A target force at a known operating gap.
- A force curve across a range of gaps.
- A safe maximum force limit to protect parts and operators.
Core Equations Used in Practice
1) Dipole approximation
For coaxial magnets in repulsive orientation and sufficient separation, a useful approximation is:
F = (3 mu_0 mu_r m1 m2) / (2 pi r^4)
- F = force in newtons
- mu_0 = permeability of free space, approximately 1.25663706212 x 10^-6 N/A²
- mu_r = relative permeability of medium
- m1, m2 = magnetic moments in A m²
- r = center to center distance in meters
This model is best when the separation is much larger than magnet dimensions. It is excellent for trend analysis and fast comparisons.
2) Pole strength model
An educational and sometimes useful simplified model is:
F = (mu_0 mu_r p1 p2) / (4 pi r²)
- p1, p2 = pole strengths in A m
- r = separation distance in meters
This model is easier conceptually, but less physically complete for finite magnet bodies. Still, it can be helpful for baseline calculations and sensitivity checks.
Step by Step Method to Calculate Repulsive Force
- Define your geometry and orientation. Confirm like poles are facing for repulsion and that magnets are approximately coaxial.
- Choose model type. Use dipole approximation for far field estimation; use pole model for educational or quick checks.
- Convert all units to SI before calculation. Distance must be in meters.
- Enter material environment through mu_r. For air, mu_r is very close to 1.
- Compute force and record output in N and mN for usability.
- Generate a distance sweep curve to see how sensitive force is to gap variation.
- Apply safety factor for manufacturing tolerances, alignment error, and temperature drift.
Material Data That Influences Real Force
Although equations above use moment or pole strength, those quantities come from magnet materials and geometry. The table below gives representative statistics used by engineers for early stage selection.
| Magnet Material | Typical Remanence Br (T) | Typical Coercivity Hc (kA/m) | Typical Max Energy Product BHmax (kJ/m³) | Common Use |
|---|---|---|---|---|
| Ferrite (Ceramic) | 0.35 to 0.45 | 150 to 300 | 26 to 40 | Low cost motors, speakers |
| Alnico | 0.6 to 1.35 | 40 to 160 | 10 to 88 | High temperature sensors, fixtures |
| SmCo | 0.8 to 1.1 | 600 to 2000 | 120 to 240 | Aerospace, high temperature systems |
| NdFeB (Neodymium) | 1.0 to 1.45 | 800 to 2400 | 200 to 440 | Compact high force applications |
These ranges are representative engineering values compiled from standard magnet manufacturer datasheets and materials handbooks. Actual values vary by grade and temperature.
Distance Sensitivity Example Using Dipole Model
To illustrate how quickly repulsive force changes with distance, assume m1 = m2 = 0.8 A m², mu_r = 1. The following values come from the dipole approximation used in the calculator.
| Distance r (m) | Estimated Force F (N) | Estimated Force (mN) | Relative to 0.10 m Case |
|---|---|---|---|
| 0.20 | 0.000048 | 0.048 | 0.06x |
| 0.10 | 0.000771 | 0.771 | 1.00x |
| 0.05 | 0.01234 | 12.34 | 16.00x |
| 0.025 | 0.1974 | 197.4 | 256.00x |
This table makes a critical point: under a fourth power distance relationship, small gap reductions can produce very large force increases. In tolerance sensitive assemblies, that can create snap together behavior and damage risk unless you plan mechanical stops.
Common Sources of Error
- Using edge to edge distance instead of center to center distance. This is one of the most frequent mistakes.
- Applying dipole formulas at very short gaps. Near field behavior can differ significantly from far field assumptions.
- Ignoring misalignment. Even small angular tilt changes effective force direction and magnitude.
- Forgetting temperature effects. Magnetic properties change with temperature; high heat can reduce available force.
- Ignoring nearby steel parts. Ferromagnetic structures can redirect flux and alter force.
How to Improve Accuracy Beyond Basic Equations
Once your quick calculations indicate a promising design window, improve confidence with a staged validation process:
- Build a parametric spreadsheet using the same equation as the calculator.
- Measure force at multiple gaps using a force gauge and rigid fixture.
- Fit an empirical correction factor against your geometry and alignment quality.
- If required, use finite element magnetic simulation for final geometry optimization.
- Validate at minimum and maximum expected operating temperatures.
This approach keeps costs low early and precision high at release.
Unit Handling and Practical Conversions
- 1 m = 100 cm = 1000 mm
- 1 N = 1000 mN
- Air is usually modeled with mu_r close to 1
When teams report different force numbers, the disagreement is often unit related, not physics related. A disciplined SI workflow removes that problem quickly.
Safety and Reliability Notes
Repelling magnets can slip, rotate, or snap unexpectedly, especially during alignment attempts. Use eye protection and keep fingers clear of pinch zones. Strong magnets can affect sensors, magnetic stripe media, and implanted medical devices. Keep clear process controls in production environments.
Authoritative Learning Sources
For deeper reference, use reputable scientific sources:
- NIST fundamental constant reference for mu_0
- Georgia State University HyperPhysics overview of electromagnetism
- NOAA educational resource on magnetic fields and magnetosphere context
Final Design Checklist
- Choose a physically appropriate model for your gap and geometry.
- Use SI units and verify conversions before reviewing results.
- Plot force versus distance, not just a single point.
- Apply safety factors for tolerance, heat, and alignment variation.
- Prototype and measure before finalizing hardware.
If you follow this method, you can estimate repulsive force quickly, communicate assumptions clearly, and avoid late stage surprises. The calculator and chart above are designed for exactly that engineering workflow.