MachineCalcs

Magnetic Field of a Magnet Calculator

Estimate the on-axis magnetic field of an axially magnetized disc or cylinder magnet from grade, diameter, thickness and distance from the pole face.

Calculator

Representative remanence values for common permanent-magnet materials. Use the supplier Br value when available.

Diameter of the circular pole face.

mm

Axial length of the magnet in the magnetization direction.

mm

Distance measured outward from the magnet pole face along the symmetry axis.

mm

Results

Default result
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Axial magnetic field(B_z)
171.5mT
Pass

Also computed

Axial field(B_z)Pass0.1715T

Axial field(B_z)1,715G

Pole-face field(B_0)295.2mT

Field vs pole face(B_z/B_0)58.11%

Remanence used(B_r)1.32T

Thickness / diameter(L/D)0.25

Axial field (mT) vs Distance from pole faceThe field falls quickly with distance from the pole face. This curve is along the magnet axis only; off-axis fields are not represented.Axial field (mT) vs Distance from pole face0100200300010203040entered distanceDistance from pole face (mm)Axial field (mT)
The field falls quickly with distance from the pole face. This curve is along the magnet axis only; off-axis fields are not represented.
Method notes 3 notes
  • Uses the closed-form on-axis field for an axially magnetized cylinder: B = Br/2*((L+z)/sqrt(R^2+(L+z)^2) - z/sqrt(R^2+z^2)).
  • The result is only for the symmetry axis outside one pole face. Off-axis fields, nearby steel, keeper plates, arrays and demagnetization need field solving or measurement.
  • Grade Br values are representative. Temperature, tolerance, magnetization quality and vendor grade data can shift the real field.

The axial field of a cylindrical permanent magnet can be estimated from its remanence and geometry: Bz = Br/2*((L+z)/sqrt(R²+(L+z)²) - z/sqrt(R²+z²)). This calculator returns field in mT, tesla and gauss at a distance from the pole face, plus a field-versus-distance chart.

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How to use this calculator

  1. Choose magnet grade. Pick a representative grade or enter the Br value from the magnet datasheet.
  2. Enter magnet geometry. Use the circular pole diameter and the axial thickness in the magnetization direction.
  3. Enter distance. Measure z outward from one pole face along the centerline of the magnet.
  4. Read field and chart. Use the mT/T/G output at the entered distance and the chart to see how quickly the field falls with gap.

How it works

This calculator models an axially magnetized disc or cylinder magnet and returns the magnetic flux density on the north-south symmetry axis outside one pole face. The geometry is intentionally narrow, because a general magnetic-field map is a field-solving problem.

B_z = B_r/2 · ((L + z)/sqrt(R² + (L + z)²) − z/sqrt(R² + z²))

Here B_r is remanence, R is magnet radius, L is magnet thickness and z is the distance from the pole face. At z = 0, the same expression gives the ideal pole-face field on the axis.

Use this field-strength page when you need a gauss/mT estimate for a sensor, reed switch, Hall switch, encoder magnet or classroom field comparison. If you need holding force instead, use the magnet pull force calculator. For powered coils, compare against the solenoid magnetic field calculator.

Worked example

Verified against the live calculator

Suppose an N42 disc magnet has a 20 mm diameter, 5 mm thickness and the field is needed 5 mm from the pole face. Use representative B_r = 1.32 T.

The radius is R = 10 mm. The two geometry terms are (L + z)/sqrt(R² + (L + z)²) = 10/sqrt(200) and z/sqrt(R² + z²) = 5/sqrt(125).

Their difference is about 0.260, so B_z = 1.32/2 x 0.260. The estimated axial field is about 172 mT, or roughly 1,715 G. At the pole face, the same magnet is about 295 mT on axis.

Frequently asked questions

How do you calculate the magnetic field of a cylindrical magnet?

On the pole axis of an axially magnetized cylinder, use B = Br/2 * ((L + z)/sqrt(R^2 + (L + z)^2) - z/sqrt(R^2 + z^2)), where Br is remanence, R is radius, L is thickness and z is distance from the pole face.

Does this calculate the magnetic field everywhere around the magnet?

No. It calculates the field on the symmetry axis outside one pole face. The full 3D field around a magnet depends on geometry and nearby steel, so use measurement or finite-element analysis when off-axis values matter.

Why is the field much lower than the magnet grade Br?

Br is the material remanence, not the external field at every point. Magnet shape, aspect ratio, distance from the pole face and magnetic circuit all reduce the field you measure outside the magnet.

Is this the same as pull force?

No. Field strength is flux density at a point. Pull force also depends on pole area, air gap, target steel, contact quality and safety factor. Use the magnet pull force calculator for that screening step.

Method & assumptions

  • The magnet is a uniformly magnetized circular cylinder or disc, magnetized through its thickness.
  • The field point is outside one pole face on the magnet symmetry axis.
  • The formula ignores off-axis field components, nearby steel, keeper plates, magnet arrays, temperature and manufacturing variation.
  • Common grade Br values are representative. Use the actual vendor remanence when available.

References

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