tools — force & field estimation

Magnet Pull Force Calculator

Enter any disc, block or ring geometry, pick a grade, and set an air gap. The calculator returns the estimated on-axis flux density at that gap — what a sensor or gaussmeter sees — and the estimated pull force against a thick mild-steel plate, in pounds, kilograms and newtons.

interactive — force & field estimate

diameter

thickness

grade — typical Br

air gap — inches

flux density at gap — on axis—

estimated pull force — thick steel—

same, metric—

magnet volume—

approx. weight — ndfeb 7.5 g/cm³—

calibration note — this is a conservative analytical estimate. Measured pull on a thick, flat, ground steel plate typically runs 10–25% higher than shown; thin sheet, paint, plating or air gaps cut it dramatically (see derating below). Treat results as sizing guidance, then verify with a sample — search our inventory to find the nearest stocked size.

method — how the estimate works

Two textbook results are combined, with no fudge factors:

1 — field at distance	The on-axis flux density of a uniformly magnetized cylinder or block has an exact closed-form solution (shown under formulas). Rings are computed as an outer cylinder minus an inner cylinder — superposition.
2 — force from field	Contact with thick steel is modeled by the image method: the plate behaves like a mirror-image magnet, doubling the normal field at the interface. Maxwell stress then gives F = B²·A / 2µ₀ integrated over the pole face.
magnet-to-magnet	By the same image argument, the attraction between two identical magnets in contact approximately equals the single-magnet-to-steel value shown.

reality check — what cuts pull force in the field

condition	typical effect on holding force
steel thinner than ~1/8″ under a strong magnet	plate saturates — force can drop 30–70% vs. thick plate
paint, powder coat or plating (each ~0.05–0.15 mm)	acts as an air gap — expect 5–30% loss per coated surface
rough or curved mating surface	effective gap at the interface — often 20–50% loss
shear (sliding) loading instead of direct pull	usable force ≈ pull × friction coefficient — often only 15–25% of rated pull
elevated temperature	force scales with B², so a 5% Br derate ≈ 10% force loss — see the temperature derating calculator

specifying for safety — for lifting or retention applications, apply at minimum a 3:1 safety factor to any calculated or catalog pull rating, and test in the actual assembly. Our magnets are not sold or approved for overhead-lifting-below-the-hook use without customer qualification.

reference — the formulas used

cylinder, on axis	`Bz(z) = (Br/2) · [ (z+L)/√((z+L)² + R²) − z/√(z² + R²) ]` z = gap from pole face, L = thickness, R = radius
rectangular block, on axis	`Bz(z) = (Br/π) · [ tan⁻¹( ab / (2z·√(4z² + a² + b²)) ) − tan⁻¹( ab / (2(z+L)·√(4(z+L)² + a² + b²)) ) ]` a, b = face dimensions, L = thickness
ring, on axis	`Bz(z) = Bz,cyl(OD) − Bz,cyl(ID)`
pull to thick steel	`F = (2·Bz(g))² · A / (2µ₀)` — image method + Maxwell stress over pole area A at gap g

going deeper — derivations and the full magnetic-circuit treatment (permeance coefficients, load lines, gap design) are covered in magnets 201 — advanced magnetics engineering. For arbitrary geometries and saved designs with quoting, use our magnet designer / calculator.

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