Brinell Hardness Calculator

What is Brinell Hardness?

The Brinell hardness test is one of the oldest and most widely used methods for measuring the hardness of metals and other materials. Developed by Swedish engineer Johan August Brinell in 1900, the test works by pressing a hardened steel or tungsten-carbide ball into the surface of a material under a precisely controlled load. The diameter of the resulting indentation is measured, and the Brinell Hardness Number (BHN) is calculated as the applied load divided by the curved surface area of the indentation.

Brinell testing is particularly well suited for materials with coarse or non-uniform grain structures such as cast iron and forgings. Because the ball creates a relatively large indentation (2 to 6 mm across), the result averages the hardness across many grains, providing a more representative value than microhardness tests like Vickers or Knoop.

The Brinell Hardness Formula

The Brinell hardness number is calculated using the following formula:

BHN = 2P / [πD(D − √(D² − d²))]

Where:

• BHN = Brinell Hardness Number (dimensionless)
• P = Applied load in kilogram-force (kgf)
• D = Diameter of the indenter ball in millimeters (typically 1, 2.5, 5, or 10 mm)
• d = Mean diameter of the indentation in millimeters

How to Use This Calculator

Select the variable you want to calculate from the "Solve For" dropdown, then enter the required values. The result updates automatically as you type.

• Solve for BHN — Enter the applied load, ball diameter, and measured indentation diameter to calculate the Brinell hardness number. Use this when you have test data and need the hardness value.
• Solve for Load — Enter the target BHN, ball diameter, and expected indentation diameter to find the required test load. Use this to set up a test machine for a specific material.
• Solve for Diameter — Enter the target BHN, applied load, and ball diameter to predict the indentation diameter. Use this to estimate the indent size before running a test.

The P/D² Ratio Rule

For Brinell test results to be comparable across different ball sizes, the load must scale with the square of the ball diameter. This is the P/D² ratio requirement defined in ASTM E10 and ISO 6506:

Typical Brinell Hardness Ranges

Worked Example

Scenario: A mild-steel bar is tested with a 10 mm tungsten-carbide ball at an applied load of 3,000 kgf. The resulting indentation measures 5.0 mm in diameter. Calculate the Brinell hardness number.

1. D = 10 mm, d = 5 mm, P = 3,000 kgf
2. D² − d² = 100 − 25 = 75 mm²
3. √75 ≈ 8.660 mm
4. D − √(D² − d²) = 10 − 8.660 = 1.340 mm
5. π × 10 × 1.340 ≈ 42.097 mm²
6. BHN = 2 × 3,000 / 42.097 = 6,000 / 42.097 ≈ 142.6 HB

This result falls in the typical mild-steel range (120-180 HB). The value would be reported as HBW 10/3000 = 143, where 10 is the ball diameter, 3000 is the load, and W indicates a tungsten-carbide indenter was used.

Applications

• Incoming Material Inspection — Verify that shipped steel, aluminum, brass, or cast iron meets mill-certificate hardness values before accepting delivery.
• Heat Treatment Verification — Confirm that quenched-and-tempered parts achieved the target hardness before release to production.
• Material Selection — Choose alloys for gears, bearings, dies, and tooling by cross-referencing hardness with wear resistance requirements.
• Failure Analysis — Map hardness near a fracture or heat-affected zone to locate softened or embrittled regions in failed components.
• Weld Inspection — Test parent metal, heat-affected zone (HAZ), and weld bead to ensure acceptable hardness gradients per welding procedure specifications.