Formula & Calculator
Brinell Hardness Number
Calculates hardness from the load applied and the diameter of the indentation made by a hardened steel or carbide ball.
Interpretation
HB = 2F/(πD(D−√(D²−d²))). Hardness from a steel or carbide ball indenter. F load, D ball diameter, d impression diameter. Used for macro‑hardness of metals.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| HB | Brinell hardness number | kgf/mm2 |
| F | Applied test load | kgf |
| D | Diameter of indenter ball | mm |
| d | Diameter of resulting indentation | mm |
What it means
The Brinell hardness test uses a hard spherical indenter (usually 10 mm diameter) pressed into the material under a known load. The Brinell hardness number (HB) is the ratio of the applied load F (in kgf) to the surface area of the indentation (a spherical cap). The formula HB = 2F/(πD(D−√(D²−d²))) uses the indenter diameter D and the measured impression diameter d. This test is widely used for metals and alloys, especially those with coarse microstructure, as it averages over a larger area. It is suitable for castings, forgings, and structural materials. Hardness numbers are correlated with ultimate tensile strength for many steels. Understanding HB is important for quality assurance, material specification, and field testing of components.
Worked example
Brinell Hardness – Two Examples
Real‑World| Parameter | Value |
|---|---|
| F | 3000 kgf |
| D | 10 mm |
| d | 4.5 mm |
| Parameter | Value |
|---|---|
| F | 500 kgf |
| D | 5 mm |
| d | 2 mm |
Common mistakes
- Brinell hardness number (HB): HB = 2F / (π·D·(D − √(D²−d²))) – where F is load (kgf), D is ball diameter (mm), d is indentation diameter (mm).
- Force units: F in kgf – if using N, convert.
- Ball diameter D: Typically 10 mm for standard test – but other diameters are used.
- Indentation diameter d: The average diameter of the indentation – in mm.
- Applicability: Suitable for softer materials (e.g., metals) – not for very hard or brittle materials.
Applications
The Brinell hardness number (HB) is determined by pressing a hard steel or carbide ball into the material surface with a known load, and measuring the indentation diameter. The formula HB = 2F/(πD(D − √(D² − d²))) yields hardness in units of kg/mm². Brinell testing is suitable for a wide range of metals and is often used for castings and forgings. Engineers use HB to estimate tensile strength and to assess material uniformity. Its large indentation averages out local microstructural variations, making it ideal for bulk hardness measurement. By using Brinell hardness, manufacturers can ensure that materials meet mechanical property requirements and are suitable for their intended applications.
- Hardness testing of castings, forgings, and large components
- Estimation of tensile strength from hardness data
- Quality control in steel and iron production
- Material acceptance and inspection
- Standardised hardness reporting in material data sheets
Frequently Asked Questions
The Brinell test uses a hardened steel (or carbide) ball indenter. The hardness number (HB) is calculated from the applied load (F, in kgf), the ball diameter (D, in mm), and the indentation diameter (d, in mm): HB = 2F / (πD (D – √(D² – d²))).
Standard tests use a 10 mm diameter ball (tungsten carbide for hard materials) and loads of 500, 1500, or 3000 kgf. The indentation diameter is measured with a microscope.
Using an indentation‑to‑ball diameter ratio (d/D) outside the recommended range (0.25‑0.5). The formula loses accuracy outside this range. Also, using a steel ball for very hard materials (use carbide).
The test uses a ball indenter, which can deform if used on hard materials. Also, the indentation is large, requiring thick specimens. For hard materials, Vickers or Rockwell tests are preferred.
For steels, UTS (MPa) ≈ 3.45 × HB. This is similar to the Vickers relation, but the constants may differ.
- Simple and robust.
- Insensitive to surface preparation.
- Works on rough surfaces.
- Good for bulk materials.
- Large indentation, which may be unsuitable for small parts.
- Limited to materials with hardness up to ~650 HB.
- Not suitable for thin sections.
- Indentation measurement can be subjective.
A low‑power microscope with a scale is used. The average of two perpendicular diameters is taken. The indentation should be round; if not, the test is invalid.
Both use similar load‑to‑area ratios, but the indenter geometry differs (ball vs pyramid). The scales are numerically close for many materials but not directly convertible without empirical correlations.
- Soft copper: ~40 HB.
- Mild steel: ~100 HB.
- Structural steel: ~200 HB.
- Tool steel: ~500 HB.