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.
alnico — shape-dependent Br	NdFeB, SmCo and ferrite hold close to their catalog Br in almost any shape. Alnico does not: its coercivity is low, so a short or wide magnet works far down its demagnetization curve and delivers much less than catalog Br. For Alnico grades the calculator first finds the working point from the shape (permeance coefficient), then feeds that effective Br into the same field and force formulas. Grade curves use generic published values, so treat Alnico results as a guide and confirm with a sample — Alnico pull is also normally rated with a keeper or pole piece.
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)`
alnico working point	`Pc ≈ 2.7 · Leff / Deq` `(B/Br)ⁿ + (H/Hc)ⁿ = 1, B = µ₀ · Pc · (−H)` Leff = L·(1 + 1/(1 + g/L)) — doubles at steel contact, fades to L with gap; Deq = equal-pole-area diameter; n is fitted to the grade's BHmax. The resulting B becomes Br in the formulas above.
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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