Brinell Hardness Number Calculator

Calculate the Brinell Hardness Number (BHN) from indentation test measurements. Determine material hardness using ball indenter diameter and impression diameter.

BRINELL HARDNESS
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BHN
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Indentation Depth
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Contact Area
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Approx. Tensile Strength
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What is Brinell Hardness?

The Brinell hardness test, developed by Swedish engineer Johan August Brinell in 1900, is one of the oldest and most widely used methods for measuring the hardness of metals. The test involves pressing a hardened steel or tungsten carbide ball of a specified diameter into the surface of the material under a known load, then measuring the diameter of the resulting impression.

The Brinell Hardness Number (BHN or HB) is calculated by dividing the applied load by the curved surface area of the indentation. This gives a value in units of kgf/mm squared. The test is particularly well-suited for materials with coarse or uneven grain structures, such as castings and forgings, because the relatively large indentation averages out local variations in hardness.

BHN Formula

BHN = 2F / (πD(D - √(D² - d²)))

Where F is the applied force in kgf, D is the ball diameter in mm, and d is the diameter of the indentation in mm. The standard test uses a 10mm ball with 3000 kgf for steel, 1500 kgf for copper alloys, and 500 kgf for aluminum.

Typical Values

MaterialBHN RangeApprox. UTS (MPa)
Pure Aluminum15-2550-90
Brass60-120200-400
Mild Steel120-180400-620
Tool Steel200-600690-2070
Cast Iron150-300520-1035

Frequently Asked Questions

How does BHN relate to tensile strength?

For many steels, there is an approximate linear relationship between Brinell hardness and ultimate tensile strength: UTS (MPa) is roughly equal to 3.45 times BHN. This relationship is widely used in industry as a quick estimate but should not replace actual tensile testing for critical applications. The relationship is less reliable for non-ferrous metals and hardened or cold-worked steels.

What is the difference between Brinell and Rockwell hardness?

The Brinell test uses a large ball indenter and measures impression diameter, while the Rockwell test uses a small diamond cone or ball and measures indentation depth. Rockwell testing is faster and less destructive, making it preferred for production quality control. Brinell is better for coarse-grained materials and provides a larger indentation that is more representative of bulk properties.

Why must d be less than D?

The impression diameter d must always be less than the ball diameter D because the ball can only create an impression up to its own diameter. In practice, the impression should be between 0.24D and 0.6D for reliable results. If the impression is too small, measurement errors become significant. If too large, the material may have deformed plastically in ways not accounted for by the formula.