How this calculator works
Brinell hardness divides the applied force by the curved area of a spherical impression, using the conventional kgf/mm2 numerical scale. The ball and indentation diameters must use the same geometry. The calculation does not verify test force ratio, specimen thickness, dwell time or the standard indentation-diameter window. HBW denotes a tungsten-carbide ball. Very large or small impressions can be outside the applicable test procedure even when the geometry is mathematically valid.
Formula
A = pi D [D-sqrt(D^2-d^2)]/2; HBW = F/(9.80665 A_mm2), with F in newtons.
Worked example
A 10 mm ball making a 5 mm impression has curved area 21.04468 mm2. At a test force of 29419.95 N (3000 kgf), HBW is approximately 142.55384.
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Frequently asked questions
Why not divide by the projected circular area?
Brinell uses the curved spherical-cap area, not the flat projected circle.
Why does the formula include 9.80665?
It converts force in newtons to the conventional kilogram-force basis of the hardness number.
Can I use a diameter equal to the ball?
It is the hemispherical mathematical limit. A proper Brinell test normally uses a much smaller indentation according to the relevant standard.