206.5
HB
14.526
mm²
0.4624
mm
713
MPa
30
kgf/mm²
206.5
HB
14.526
mm²
0.4624
mm
713
MPa
30
kgf/mm²
The Brinell Hardness Calculator computes the Brinell hardness number (HB) from the applied force, ball indenter diameter, and measured indentation diameter using the standard formula $$HB = \frac{2F}{\pi D\left(D - \sqrt{D^2 - d^2}\right)}$$ where F is the applied force in kgf, D is the ball diameter in mm, and d is the measured indent diameter in mm. The denominator represents the curved surface area of the spherical indentation.
Developed by Swedish engineer Johan August Brinell in 1900, the Brinell test was the first widely adopted standardized hardness test and remains one of the most important. It is particularly valuable for materials with coarse or non-uniform microstructures — castings, forgings, and rough surfaces — because the large indentation averages out local variations. The test is specified by ASTM E10 and ISO 6506, and the standard condition for steel is a 10 mm tungsten carbide ball at 3000 kgf (designated HBW 10/3000).
The Brinell test presses a hard ball of diameter D into the test surface under a known force F for a specified dwell time (10-15 seconds for standard tests). After unloading, the resulting circular indentation diameter d is measured using a microscope, typically at two perpendicular directions, and averaged.
The indentation depth is related to the measured diameter by geometry: $$h = \frac{D - \sqrt{D^2 - d^2}}{2}$$
The curved surface area of the spherical cap indent is: $$A = \pi D h = \frac{\pi D}{2}\left(D - \sqrt{D^2 - d^2}\right)$$
Brinell hardness is defined as force divided by this curved surface area: $$HB = \frac{F}{A} = \frac{2F}{\pi D\left(D - \sqrt{D^2 - d^2}\right)}$$
Critical testing parameters and requirements:
The F/D² ratio output helps verify that the correct load-diameter combination was used. For standard steel testing at 3000 kgf with a 10 mm ball, this ratio is 30 kgf/mm². Maintaining this ratio when using smaller balls (5 mm at 750 kgf, or 2.5 mm at 187.5 kgf) ensures geometrically similar indentations and comparable hardness values.
The Brinell hardness number has units of kgf/mm² but is conventionally reported without units. Typical values range from ~60 HB for pure aluminum to ~700 HB for hardened tool steel. The indent surface area and indent depth help verify that the test was conducted within valid limits. The approximate UTS uses the empirical relationship $$\sigma_{UTS} \approx 3.45 \times HB$$ valid for carbon and alloy steels. Check that the F/D² ratio matches the standard for the material being tested.
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Results
A 4.2 mm indent diameter with standard steel test conditions gives HB ≈ 212, consistent with normalized AISI 1045 steel. The estimated UTS of 733 MPa matches published data well.
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Results
With the reduced F/D² = 5 load for aluminum, a 3.8 mm indent gives HB ≈ 44. The UTS approximation (~150 MPa) is reasonable for annealed 6061 aluminum, though the 3.45× factor is less precise for non-ferrous metals.
The Brinell test measures a material's hardness by pressing a hard ball (typically 10 mm tungsten carbide) into the surface under a known force and measuring the resulting indent diameter. Hardness is calculated as $$HB = \frac{2F}{\pi D(D - \sqrt{D^2 - d^2})}$$ where F is force, D is ball diameter, and d is indent diameter. It was the first standardized hardness test (1900) and remains widely used.
For steel and iron, the standard F/D² ratio is 30 kgf/mm². This means 3000 kgf for a 10 mm ball, 750 kgf for a 5 mm ball, or 187.5 kgf for a 2.5 mm ball. Using the correct ratio ensures the indent diameter falls between 0.24D and 0.60D, which is necessary for valid, comparable results. Different materials use different ratios: 10 for copper alloys, 5 for aluminum.
Above approximately 450 HB, hardened steel balls begin to deform during testing, giving falsely large indents and artificially low hardness readings. Tungsten carbide (WC-Co) balls are much harder (~1500 HV) and do not deform, allowing accurate testing up to ~650 HBW. ASTM E10 now recommends WC balls (HBW designation) for all testing.
The specimen thickness must be at least 8 times the indent depth (h) to avoid the anvil effect, where the hard support surface beneath influences the result. For a typical steel test with h ≈ 0.5 mm, the minimum thickness is about 4 mm. If the specimen is too thin, the hardness reading will be artificially high.
For carbon and low-alloy steels in the range 120-450 HB, the empirical relationship $$\sigma_{UTS} \approx 3.45 \times HB$$ (in MPa) is accurate within about ±10%. This is widely used in industry for quick strength estimation. The relationship is less reliable for stainless steels, non-ferrous metals, and highly work-hardened materials.
Major error sources include: poor surface preparation (roughness obscures indent edges), non-perpendicular loading (elliptical indent), insufficient specimen thickness (anvil effect), incorrect dwell time (creep in soft materials), using steel balls above 450 HB (ball deformation), and inaccurate indent measurement (subjective microscope reading). Digital image analysis reduces measurement subjectivity.
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