Brinell Hardness Number (BHN) Calculator

Formula

How this is calculated

The Brinell hardness test (standardised in ISO 6506 / ASTM E10) presses a hard tungsten carbide ball of diameter D into the material under a fixed load P for a defined dwell time. The ball leaves a circular indentation of diameter d. The Brinell Hardness Number is the load divided by the curved surface area of the spherical indentation cap: BHN = 2P / (πD(D − √(D² − d²))). A smaller indentation for the same load means a harder material and therefore a higher BHN.

Standard test conditions combine load and ball size according to the material: 3000 kgf on a 10 mm ball for ferrous metals (steel, cast iron); 500 kgf for copper alloys; 100 kgf for aluminium. This gives comparable HB values across different test set-ups because the load-to-diameter-squared ratio (HBS load/D² = 30 for steel) is kept constant. The indentation diameter is measured optically in two perpendicular directions and averaged.

For steels, there is a well-established empirical relationship between BHN and ultimate tensile strength: UTS (MPa) ≈ 3.45 × HB. This approximation is reasonably accurate for annealed and normalised steels (HB 100–400) but less reliable for hardened or heavily cold-worked steels. For HB values below about 300, BHN is also approximately convertible to Vickers hardness (HV ≈ 0.95 × HB). Above 650 HB the Brinell test becomes impractical — Rockwell or Vickers methods are preferred for very hard materials.