Brinell Hardness Number Calculator – Material Testing
Calculate the Brinell Hardness Number (BHN) of any material by entering the test load, ball diameter, and indentation diameter.
Enter the Brinell hardness test parameters to determine the BHN value and assess your material's resistance to permanent deformation.
Brinell Hardness Number Calculator – Material Testing
Calculate the Brinell Hardness Number (BHN) of any material by entering the test load, ball diameter, and indentation diameter.
About the Brinell Hardness Number Calculator
The Brinell hardness test is one of the oldest and most widely used methods for measuring the hardness of metals and alloys. Hardness, in materials science, is a measure of a material's resistance to permanent plastic deformation — specifically, its resistance to having a harder body forced into its surface. The Brinell test quantifies this resistance by pressing a hardened steel or tungsten carbide ball of a specified diameter into the material's surface under a controlled load, then measuring the diameter of the resulting circular indentation.
The test was introduced by Swedish engineer Johan August Brinell in 1900 as a rapid, practical method for quality-control testing of metals. It remains codified in international standards including ASTM E10 and ISO 6506, and is particularly well-suited to coarse-grained materials such as cast iron, aluminum alloys, and forgings that would be damaged or give misleading results with micro-indentation methods.
The Brinell Hardness Number is calculated from the formula: BHN = 2F / (π × D × (D − √(D² − d²))), where F is the applied load in kilograms-force (kgf), D is the diameter of the indenter ball in millimeters, and d is the measured diameter of the indentation in millimeters. The denominator computes the curved spherical surface area of the indentation based on the geometry of a spherical cap, and dividing the load by this area gives the hardness in units of kgf/mm², conventionally written as HB.
Standard test conditions are specified in the relevant standards. The most common combination is a 10 mm ball with a 3000 kgf load for steel and cast iron (giving a force-to-diameter ratio F/D² = 30), a 10 mm ball with a 1000 kgf load for lighter alloys such as aluminum (F/D² = 10), and a 5 mm ball with 250 kgf for thin sections. The load must be applied steadily over 10–15 seconds and held for a specified dwell time, typically 10–15 seconds for steel.
Typical Brinell hardness ranges help interpret results. Pure soft metals like copper or aluminum typically measure 20–100 HB. Medium-carbon steels in the normalized state range from 130–200 HB. High-strength alloy steels in the hardened and tempered condition may reach 300–450 HB. The Brinell scale is generally limited to materials below about 450 HB because harder materials tend to flatten the indenter ball rather than the test piece.
Brinell hardness correlates empirically with other hardness scales and with ultimate tensile strength. A common approximation for steels is UTS (MPa) ≈ 3.45 × BHN, valid for steels in the range 100–400 HB. This relationship is used in foundries and manufacturing for rapid quality assessment without performing a full tensile test. The Brinell test is also valuable because the large-area indentation averages over microstructural features such as inclusions, porosity, and grain boundaries, giving a representative bulk hardness value.
Brinell Hardness Test Examples
Common material hardness measurements using standard Brinell test parameters.
| Test Parameters | BHN Result | Material / Application |
|---|---|---|
| F = 3000 kgf, D = 10 mm, d = 3.2 mm | ≈ 363 HB | Typical mild steel or normalized medium-carbon steel. The 3000 kgf / 10 mm combination is the standard steel test condition per ASTM E10. |
| F = 1000 kgf, D = 10 mm, d = 3.6 mm | ≈ 95 HB | Aluminum alloy (e.g., 6061-T6). Lighter load with 10 mm ball. Indentation diameter of 3.6 mm is typical for heat-treated aluminum at this load. |
| F = 250 kgf, D = 5 mm, d = 1.44 mm | ≈ 150 HB | Brass or bronze with 5 mm ball and 250 kgf. Smaller ball used for thin-walled parts or sections where a 10 mm ball would affect the result. |
| F = 3000 kgf, D = 10 mm, d = 2.1 mm | ≈ 856 HB | Hardened tool steel or white cast iron with very small indentation. Values above ~450 HB should be verified with Rockwell or Vickers methods as ball deformation may occur. |
How to Use the Brinell Hardness Calculator
- Select the appropriate test conditions: use a 10 mm ball with 3000 kgf for steels and cast iron, a 10 mm ball with 1000 kgf for copper and aluminum alloys, or a 5 mm ball with 250 kgf for thinner sections.
- Enter the load in kilograms-force (kgf) applied during the test. Do not convert to Newtons — the BHN formula uses kgf directly.
- Enter the diameter of the hardened steel or carbide ball indenter in millimeters.
- Measure the diameter of the circular indentation left in the specimen using a calibrated optical microscope or measuring magnifier, then enter this value in millimeters.
- Click Calculate Hardness to obtain the BHN value. Compare the result to published hardness ranges for your material to assess its condition and suitability for the intended application.
Frequently Asked Questions
What is the Brinell Hardness Number (BHN or HB)?
The Brinell Hardness Number is a numerical value that quantifies a material's resistance to indentation. It is calculated by dividing the applied load (in kgf) by the curved surface area of the spherical indentation (in mm²). A higher BHN indicates a harder material. Steel typically ranges from 100 to 500 HB, while aluminum alloys are usually 20–150 HB.
What is the difference between Brinell (HB), Vickers (HV), and Rockwell (HR) hardness?
All three methods measure indentation hardness but differ in the indenter shape, applied load, and measurement technique. Brinell uses a large ball and measures indentation diameter — best for coarse-grained materials. Vickers uses a diamond pyramid and measures diagonal length — good for thin sections and wide hardness range. Rockwell measures the depth of indentation and reports it directly on a dial — fastest for production testing. For steel, HB ≈ HV at values below ~400, and HB ≈ 10 × HRC is a rough rule of thumb.
Why must the indentation diameter be less than the ball diameter?
The Brinell formula assumes that the indentation is a spherical cap — a portion of a sphere whose radius equals the ball radius. If the indentation diameter equals or exceeds the ball diameter, the ball would have sunk past its equator into the material, which is physically impossible under normal test conditions and indicates either an extremely soft material, an incorrect reading, or an error in data entry.
How is the indentation diameter measured in practice?
After the load is removed, the circular indentation is measured using a low-power microscope with a calibrated reticle, typically accurate to ±0.02 mm. Two measurements are taken at right angles across the indentation and averaged to account for slight ellipticity. The indentation must be free of surface defects, and the test piece must be flat and at least 10 times as thick as the indentation depth.
What load and ball size should I use for my material?
The load-to-diameter-squared ratio F/D² should be chosen to produce an indentation diameter between 0.24D and 0.6D for valid results. Use F/D² = 30 (3000 kgf / 10 mm ball) for steels and cast iron; F/D² = 10 (1000 kgf / 10 mm ball) for copper, brass, and aluminum; F/D² = 5 (500 kgf / 10 mm ball) for light alloys and bearing metals. ASTM E10 provides the full selection guide.
Can Brinell hardness be converted to tensile strength?
Yes, for carbon and low-alloy steels there is a well-established empirical relationship: UTS (MPa) ≈ 3.45 × BHN, valid in the range 100–400 HB. This approximation is used in foundries for quick quality checks. The conversion is less reliable for stainless steels, non-ferrous alloys, and cast irons, where separate conversion tables should be consulted.