How To Calculate Magnetic Force Between Two Magnets

Use this interactive calculator based on the axial dipole-force approximation, then read the expert guide below for assumptions, units, and engineering best practices.

Expert Guide: How to Calculate Magnetic Force Between Two Magnets

Calculating magnetic force between two magnets sounds simple at first, but the details matter. Real magnets have finite size, nonuniform magnetization, and geometry effects that strongly influence force at close range. If you need a practical estimate, however, you can still get a highly useful result by choosing the right model, using consistent SI units, and checking the validity range of your assumptions.

The calculator above uses a classical far-field dipole approximation for two magnets arranged on a common axis. In this model, each magnet is represented by a magnetic dipole moment (A·m²), and the force is estimated from distance to the fourth power. This gives a fast engineering approximation and helps you understand sensitivity: small distance changes produce large force changes.

1) Core Formula Used in the Calculator

For two coaxial magnetic dipoles, the axial force magnitude is approximated by:

F = (3 μ0 m1 m2) / (2 π r⁴)

• F: force in newtons (N)
• μ0: permeability of free space, approximately 1.25663706212 × 10^-6 N/A²
• m1, m2: magnetic dipole moments in A·m²
• r: center-to-center separation in meters

If opposite poles face each other, the force is attractive. If like poles face each other, it is repulsive. The calculator reports both magnitude and direction label.

2) Why Distance Dominates the Result

The r^-4 dependency is the most important takeaway. If distance doubles, force drops by a factor of 16. If distance is cut in half, force increases by 16 times. This is why magnet fixtures, latches, magnetic couplings, and sensor designs can change behavior dramatically from just a few millimeters of mechanical tolerance.

In practical design reviews, engineers often perform a quick sweep over distance values rather than calculating only one point. The chart generated by the calculator does exactly that so you can visualize how sharply force decays.

3) Typical Magnetic Material Statistics for Real Designs

Force calculations become more realistic when your magnetic moment estimate comes from real material data. The table below summarizes typical magnetic performance ranges used in industry. Values vary by grade and manufacturer, but these ranges are representative for engineering pre-design.

Magnet Material	Typical Remanence Br (T)	Typical Coercivity Hc (kA/m)	Typical Max Energy Product BHmax (kJ/m³)	Approx. MGOe Range
Ferrite (Ceramic)	0.20 to 0.45	120 to 300	10 to 40	1 to 5
Alnico	0.60 to 1.35	40 to 120	10 to 88	1 to 11
SmCo	0.80 to 1.20	600 to 2000	120 to 260	15 to 33
NdFeB	1.00 to 1.45	750 to 2000	200 to 440	25 to 55

These are commonly cited engineering ranges from permanent magnet industry datasheets and standards references. Final values depend on exact grade, temperature, and geometry.

4) Worked Comparison: Same Magnets, Different Distances

Assume two magnets each have magnetic moment 0.05 A·m², aligned on axis. Using the dipole formula, the force curve looks like this:

Distance r	Distance (m)	Estimated Force Magnitude (N)	Equivalent (mN)
1 cm	0.01	0.150	150
2 cm	0.02	0.0094	9.4
3 cm	0.03	0.00185	1.85
5 cm	0.05	0.00024	0.24

This table is exactly why distance management is central in magnetics. At 5 cm, the force is roughly 625 times smaller than at 1 cm for the same two moments.

5) Step-by-Step Method You Can Reuse

1. Define a model: dipole approximation for far-field estimates, or finite element modeling for close-range precision.
2. Collect magnet properties and estimate dipole moments in A·m².
3. Measure center-to-center distance and convert to meters.
4. Apply the formula with SI units only.
5. Assign interaction type: attraction or repulsion.
6. Run a distance sweep and inspect curve sensitivity.
7. Validate experimentally with a force gauge when safety or reliability matters.

6) Common Mistakes That Cause Large Errors

• Using edge-to-edge distance instead of center-to-center distance.
• Mixing units such as mm, cm, and m without conversion.
• Applying dipole formula too close to large magnets where near-field effects dominate.
• Ignoring angle and alignment, which can reduce or redirect force.
• Ignoring steel structures nearby that distort field lines and force.
• Ignoring temperature, especially with NdFeB magnets where elevated temperature changes magnetic performance.

7) When This Calculator Is Most Reliable

You should treat dipole estimates as strongest when magnet dimensions are small relative to separation distance and when the pair is approximately coaxial. If magnets are almost touching, have unusual shapes, or operate near ferromagnetic parts, force can deviate substantially from this model. In those situations, laboratory measurement or simulation is recommended.

For product engineering, a practical workflow is:

1. Use this calculator to size early concepts quickly.
2. Prototype and measure pull or push force over expected tolerances.
3. Refine with CAD-integrated magnetic simulation if required.
4. Build design safety factors for assembly variation and temperature drift.

8) Unit Intelligence for Better Communication

Force can be communicated as N, mN, or μN depending on scale. For mechatronics and sensing systems, mN is often intuitive. For latch or fixture applications, N is usually better. Always include distance in mm or cm plus SI conversion in technical documentation to avoid integration errors between teams.

9) Useful Physical Context and Real-World Numbers

Magnetic field and force often get confused. Field strength and force are related but not identical. A strong field does not guarantee a large force unless there is a significant field gradient and suitable orientation. By comparison, Earth’s magnetic field is typically in the tens of microtesla range, while engineering permanent magnets can produce much stronger local fields near their surface. This difference helps explain why compact magnets can create meaningful mechanical forces at short distances, yet drop off quickly as spacing increases.

10) Authoritative References

For standards-quality constants and background physics, review: NIST CODATA value of μ0, NOAA geomagnetism resources, and Georgia State University HyperPhysics magnetics overview.

Final Takeaway

To calculate magnetic force between two magnets in a fast and disciplined way, start with the dipole approximation, protect unit consistency, and always respect distance sensitivity. Then validate with data if your application has tight tolerances, safety implications, or high loads. With that workflow, you can move from rough estimate to dependable engineering result efficiently.