Field-at-Distance Calculator

Field at the sensor

Target field — find the gap

For a sensor, the target is its operate point Bop (datasheet value, typically 1–5 mT for a unipolar Hall switch, higher for reed switches). Add a margin to cover Br tolerance (±3–5 %), temperature, magnet position tolerance and sensor Bop spread. For a worst-case operate/release analysis use the Hall sensor air gap designer.

On-axis field table

How this is calculated — and what it does not include

• The magnet is modeled as a uniformly magnetized body using the equivalent surface-charge (Coulombian) method: each pole face carries a magnetic charge density equal to Br. Blocks use the exact closed-form field of a rectangular charged sheet; discs and rings are built from several hundred thin exact rectangular strips. On the axis this reproduces the standard formulas — for a disc, B(x) = (Br/2)·[(x+L)/√(R²+(x+L)²) − x/√(R²+x²)] — and off-axis it needs no further approximation.
• Uniform magnetization assumes a recoil permeability of 1. Real NdFeB is about 1.05, so expect the model to run 3–5 % high, on top of the ±3–5 % Br tolerance of the grade itself. Use the design margin to absorb this.
• No ferromagnetic material is assumed nearby. A steel backing plate or housing changes the field substantially (usually increases it on the working face). Coatings (Ni-Cu-Ni, epoxy) are non-magnetic and count as air gap.
• Temperature derates Br only. At high temperature and low permeance coefficient (thin, wide magnets) the operating point can cross the demagnetization knee and Br will not recover — check that with the temperature derating calculator or specify a higher temperature class (M, H, SH, UH, EH). To find the actual operating point and knee margin for your geometry, use the load-line calculator or the demagnetization & permeance calculator.
• Bz is positive when it points away from the pole face the sensor faces. Off-axis, Bz reverses sign beyond roughly the magnet edge; the chart shows this crossover, which matters for bipolar and latching sensors.
• Rings: the field is the outer cylinder minus the inner cylinder, so an axially magnetized ring reverses its on-axis field over the bore near the face and peaks some distance out. The chart shows this; the target-field solver searches outward from that peak.
• Diametric (angle-sensing) magnetization is a different field pattern and is not modeled here — ask us if that is your case.