The Brinell hardness number calculator will return the BHN, or Brinell hardness number, which helps estimate the indentation hardness of a material sample. It is not to be confused with water hardness. This hardness number is determined after performing an indentation experiment known as the Brinell hardness test.
Swedish engineer Johan August Brinell proposed this procedure for measuring indentation hardness in the year 1900. Since then, the Brinell hardness test has become a standardized test in metallurgy and materials science to estimate hardness — largely because of its non-destructive nature.
The basic idea behind this test is the calculation of pressure based on the force applied and the indentation area. Read on to understand the Brinell hardness scale and how to conduct the Brinell hardness test.
Brinell hardness test — What is the Brinell hardness number?
The Brinell hardness test is a non-destructive test performed using a small ball-shaped indenter that is pressed onto the material specimen with a standard load value. The depth and the diameter of the indentation are then recorded, and you use them to calculate the Brinell hardness number.
The indenter is a ball made of hardened steel or tungsten carbide with a diameter D. Consider the ball indenter pressed at a load (force) of P newtons. The Brinell hardness number is given by:
HBW = Test force ÷ Surface area of indentation
HBW = 0.102 × 2P ÷ (π × D × (D − √(D² − d²)))
where:
- P — test force (in newtons); and
- D — diameter of the indenter ball (in mm);
- d — diameter of the indentation (in mm).
The factor 0.102 converts the SI force in newtons into kilograms-force (1 kgf = 9.80665 N), so that the Brinell number keeps its traditional units of kgf/mm². You can find the details of the Brinell hardness test in the international standard ISO 6506-1 for metallic materials.
How to calculate the Brinell hardness number
To calculate the Brinell hardness number with this tool:
- Select your measurement system — Metric (N, mm) or American / Imperial (lbf, in).
- Enter the load applied, P.
- Insert the diameter of the indenter, D.
- Fill in the diameter of the indentation, d.
- Optionally set the dwell time (load duration) used in the standard designation.
The calculator will determine the surface area A, the indentation depth h, an estimated ultimate tensile strength, and the Brinell hardness number HBW.
Example: Using the Brinell hardness number calculator
Determine the Brinell hardness number for a material specimen with an indentation diameter of 3 mm. The test is conducted using an indenter with a 10 mm diameter and a test force of 294.2 N.
- Enter the load applied, P = 294.2 N.
- Insert the diameter of the indenter, D = 10 mm.
- Fill in the diameter of the indentation, d = 3 mm.
The Brinell hardness number (HBW) is then calculated:
HBW = 0.102 × (2 × 294.2) ÷ (10π × (10 − √(10² − 3²)))
HBW ≈ 4.15
Brinell hardness chart
You can represent the Brinell hardness of a material specimen as per ISO 6506-1. For example:
600 HBW 1 / 30 / 20
where:
- 600 — Brinell hardness value;
- HBW — hardness symbol (W = tungsten-carbide ball);
- 1 — ball diameter in mm;
- 30 — applied test force (in kgf); and
- 20 — duration time of the test force (in seconds).
The following table lists approximate Brinell hardness numbers for some common materials:
| Material | Brinell hardness (HBW) |
|---|---|
| Soft / pure aluminium | 15 – 30 |
| Pure copper (annealed) | 35 – 45 |
| Mild / low-carbon steel | 120 – 180 |
| Brass | 55 – 130 |
| Cast iron (grey) | 150 – 250 |
| Hardened tool steel | 500 – 650 |
| Tungsten carbide | ~1500 – 2000 |
Applications and similar tests
The Brinell test is widely used for materials with a coarse or inhomogeneous grain structure — such as castings and forgings — because its large indentation averages out local variations. It is common in quality control of metals, foundry work, and incoming-material inspection.
Other indentation hardness tests include:
- Rockwell hardness — fast and reads directly from the machine; ideal for thin or finished parts.
- Vickers hardness — uses a diamond pyramid indenter; suitable for very hard materials and micro-hardness.
- Knoop hardness — a micro-hardness test for brittle materials and thin coatings.
As a rule of thumb for steels, the ultimate tensile strength can be roughly estimated as UTS (MPa) ≈ 3.45 × HB, or UTS (psi) ≈ 500 × HB. This calculator shows that estimate for convenience, but it should be used only as a guide.
FAQs
What does HBW mean?
HBW stands for Hardness, Brinell, tungsten-carbide ball. Modern standards use a tungsten-carbide ball (W), which replaced the older hardened-steel ball (formerly written HB or HBS).
Why is the factor 0.102 used in the formula?
The factor 0.102 converts force from newtons to kilograms-force (1 / 9.80665 ≈ 0.102). It keeps the Brinell number numerically consistent with the historic kgf-based definition.
Is a higher Brinell number better?
A higher BHN means a harder material that resists indentation more strongly. Whether that is "better" depends on the application — harder materials are more wear-resistant but can be more brittle.
Why must the indentation diameter be smaller than the ball diameter?
The geometry requires d < D so that the term √(D² − d²) is real. Physically, the indentation can never be wider than the ball that produced it.
Can I use this calculator in imperial units?
Yes. Choose the American / Imperial system to enter the force in pounds-force (lbf) and diameters in inches; the calculator converts internally and returns the standard Brinell number along with the area and depth in imperial units.