Hong Life CalculatorsUnderstanding the Brinell hardness calculator — concept and principle
The Brinell test presses a hard ball into a material with a known force and measures the diameter of the dent. This calculator converts the force, ball diameter and indentation diameter into the Brinell hardness number (HBW) and checks whether the test conditions are valid.
How it is calculated
- HBW = 0.102 × 2F ÷ (πD (D − √(D² − d²))), with F in newtons and D, d in mm. With F in kgf, the 0.102 factor drops out.
- d = mean of two diameters measured at right angles.
- Indentation depth h = (D − √(D² − d²)) ÷ 2; surface area = πDh.
- Validity: d should lie between 0.24D and 0.6D.
- Force–diameter index 0.102F ÷ D² should suit the material (30 for steel and cast iron, 10 or 5 for copper and aluminium alloys, 2.5 or 1 for soft metals).
The principle
Hardness here means resistance to permanent indentation. Dividing the force by the curved surface area of the dent gives a pressure-like number: a harder material leaves a smaller dent, a smaller area and a higher HBW. The 0.102 factor (1 ÷ 9.80665) keeps the traditional kilogram-force scale when the force is in newtons. Rules on d ÷ D and the force–diameter index make results comparable between tests.
Worked example
Default inputs: 3,000 kgf, 10 mm ball, readings 4.20 and 4.24 mm.
- Mean d = (4.20 + 4.24) ÷ 2 = 4.22 mm; d ÷ D = 0.422, within 0.24D–0.6D.
- √(10² − 4.22²) ≈ 9.066 mm; depth h = (10 − 9.066) ÷ 2 ≈ 0.467 mm.
- Surface area = π × 10 × 0.467 ≈ 14.67 mm².
- HBW = 3,000 ÷ 14.67 ≈ 205.
- Force–diameter index = 3,000 ÷ 10² = 30, suitable for steel.
| Indentation diameter, reading 2 at 90° (mm, 0 = none) | Brinell hardness (HBW) |
|---|---|
| 1.06 | 543 |
| 2.12 | 373 |
| 3.18 | 271 |
| 4.24 | 205 |
| 5.3 | 159 |
| 6.36 | 127 |
| 8.48 | 84 |
How to read the result
Around 200 HBW is typical of many medium-carbon or normalised steels. Brinell is good for coarse or uneven materials such as castings because the large dent averages the structure. Conversions from HBW to other scales or to tensile strength exist for specific materials but are approximate.
Common mistakes
- Measuring only one diameter on an elliptical dent.
- Testing thin samples, where the dent reaches the far side.
- Using a force–diameter index unsuited to the material.
- Reading the HBW from a different ball diameter's table.
Frequently asked questions
What is a typical Brinell hardness of steel?
Many structural and medium-carbon steels fall roughly between 120 and 250 HBW, depending on composition and heat treatment.
Why must d be between 0.24D and 0.6D?
Outside that range the result depends too much on the force and ball size, making it unreliable.
What does HBW stand for?
Brinell hardness measured with a tungsten carbide ball.
Sources: ISO 6506-1, Metallic materials — Brinell hardness test — Part 1: Test method · ASTM E10, Standard Test Method for Brinell Hardness of Metallic Materials