How to use this calculator
- Choose magnet grade. Pick a representative grade or enter the Br value from the magnet datasheet.
- Enter magnet geometry. Use the circular pole diameter and the axial thickness in the magnetization direction.
- Enter distance. Measure z outward from one pole face along the centerline of the magnet.
- 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.