For applied load P kg, diameter of ball D mm and diameter of indentation d mm, the Brinell hardness number is given by

1
\({B_{HN}} = \frac{P}{{\frac{\pi }{2}\left( {D - \sqrt {{D^2} - {d^2}} } \right)}}\)
2
\({B_{HN}} = \frac{D}{{\frac{\pi }{2}\left( {D - \sqrt {{D^2} - {d^2}} } \right)}}\)
3
\({B_{HN}} = \frac{PD}{{\frac{\pi }{2}\left( {D - \sqrt {{D^2} - {d^2}} } \right)}}\)
4
\({B_{HN}} = \frac{P}{{(\frac{\pi D }{2})\left( {D - \sqrt {{D^2} - {d^2}} } \right)}}\)

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