Brinell Hardness Number Calculator (HBW)
Enter your test load, ball indenter diameter and measured indentation diameter to get the Brinell Hardness Number (HBW) per the ISO 6506-1 formula. The calculator shows every step of the arithmetic, the spherical-cap area of the indentation, and where your result sits in the standard material hardness scale. Switch between metric (N, mm) and imperial (lbf, in) units. Defaults are set to a typical 3000 kgf / 10 mm test on mild steel so the result is meaningful on first load.
Formula
Worked example
Test parameters: P = 3000 kgf, D = 10 mm, d = 3.8 mm. Convert load: 3000 x 9.80665 = 29419.95 N. Compute sqrt(D^2 - d^2) = sqrt(100 - 14.44) = sqrt(85.56) = 9.2499 mm. Indentation depth h = (10 - 9.2499)/2 = 0.3750 mm. Area A = pi x 10 x 0.3750 = 11.781 mm^2. HBW = 0.102 x (2 x 29419.95) / (pi x 10 x (10 - 9.2499)) = 5997.5 / (23.562 x 0.7501) = 5997.5 / 17.672 = approximately 339 HBW. This is in the hard range for normalized medium-carbon steel.
What is the Brinell Hardness Number?
The Brinell Hardness Number (HBW) measures a material's resistance to permanent deformation under a static load. The test presses a hard ball indenter into the surface and measures how wide the resulting dimple is. A harder material produces a smaller, shallower indentation, so its HBW value is higher. The method was introduced by Johan August Brinell in 1900 and remains one of the most widely used hardness tests for castings, forgings and large-grained metals because the ball averages over a relatively large area, making it less sensitive to local inhomogeneities than pin-based methods.
The "W" in HBW denotes the tungsten carbide ball now required by ISO 6506-1, replacing the hardened steel ball of older "HB" designations. Tungsten carbide is harder than hardened steel, so it deforms less during the test and gives more consistent results on hard materials up to about 650 HBW.
The HBW formula and how to use this calculator
The standard formula is:
HBW = 0.102 x 2P / (pi x D x (D - sqrt(D^2 - d^2)))
where P is the applied force in Newtons, D is the ball diameter in millimetres, and d is the mean indentation diameter in millimetres. The factor 0.102 converts Newtons to kilogram-force (1 kgf = 9.80665 N, so 1/9.80665 = 0.10197). The denominator is the spherical-cap surface area of the indentation in mm^2.
To use the calculator: choose your load unit (kgf, N or lbf), enter the load, ball diameter and indentation diameter, then read off the HBW result. The calculator also checks your d/D ratio against the ISO 6506-1 acceptance range of 0.24 to 0.60 and flags any out-of-range readings. Standard loads for 10 mm balls are 500 kgf (HBW 5/500), 1500 kgf (HBW 10/1500) and 3000 kgf (HBW 10/3000). The numbers in the designation encode the ball diameter and load: "10/3000" means 10 mm ball, 3000 kgf load.
Valid test conditions: the d/D ratio rule
ISO 6506-1 specifies that the indentation diameter d must lie between 0.24D and 0.60D. If d is too small (less than 0.24D), the indent is so shallow that measurement error dominates the result. If d is too large (greater than 0.60D), the material around the indentation piles up or the indentation depth approaches the ball radius, making the formula less accurate. When your d/D ratio is outside this window, choose a different test load: a higher load increases d, a lower load decreases it. The "Load Selection" guideline from ISO 6506-1 is to target d/D close to the midpoint of the valid range, around 0.4 to 0.5.
Specimen thickness is also critical: the piece must be at least 8 times the indentation depth h to prevent the hard support surface from affecting the reading. Space indentations at least 3d apart (centre to centre) to avoid work-hardening from adjacent impressions.
Reading your result and comparing materials
Typical HBW values span a wide range. Very soft metals like lead sit around 5 HBW, annealed pure aluminum is roughly 15-25 HBW, and mild structural steel runs 120-180 HBW. Heat-treated tool steels can reach 600-650 HBW, which is close to the practical upper limit of the Brinell method. Above that range, the ball itself deforms and the Vickers or Rockwell C test is preferred.
For everyday engineering work, rough conversions to tensile strength are widely used for steels: UTS (MPa) is approximately 3.4 x HBW, and UTS (psi) is approximately 500 x HBW. These are empirical rules of thumb and vary by alloy and heat treatment. ASTM E140 provides formal conversion tables between Brinell, Vickers, Rockwell B and Rockwell C scales for specific material groups.
Brinell hardness of common materials
| Material | Typical HBW range | Notes |
|---|---|---|
| Lead | 3-8 | Very soft, creeps under load |
| Tin | 5-9 | Used for bearing alloys |
| Pure aluminum (1100) | 15-25 | Annealed condition |
| Aluminum alloy 6061-T6 | 95-105 | Precipitation-hardened |
| Pure copper | 35-45 | Annealed sheet |
| Brass (70/30) | 55-100 | Varies with cold-work |
| Gray cast iron | 150-280 | Varies by grade and section |
| Mild steel (A36) | 120-160 | As-rolled condition |
| Medium-carbon steel (1045) | 160-220 | Normalized |
| Tool steel (H13) | 200-260 | Annealed; up to 600 hardened |
| Stainless steel 316 | 140-200 | Annealed condition |
| Titanium alloy Ti-6Al-4V | 310-350 | Annealed, mill product |
| Glass | 1500-1700 | Vickers test preferred above 650 HBW |
Approximate HBW values. Alloy composition, heat treatment and testing load all affect the result.
Frequently asked questions
What is a normal Brinell hardness number for steel?
It depends on the steel grade and condition. Mild structural steels (A36, S275) typically read 120-180 HBW in the as-rolled state. Medium-carbon steels (1045) normalized are around 160-220 HBW, and the same steel quenched and tempered can reach 280-380 HBW. Hardened tool steels such as H13 can approach 550-600 HBW, near the practical limit of the Brinell test.
What is the d/D ratio and why does it matter?
The d/D ratio is the measured indentation diameter divided by the ball indenter diameter. ISO 6506-1 requires this ratio to be between 0.24 and 0.60. Below 0.24 the indentation is too shallow and measurement errors dominate; above 0.60 the formula becomes less accurate because the geometry of the spherical cap no longer approximates the formula assumptions well. If your ratio is outside this range, adjust the test load: use a larger load to increase d, or a smaller load to decrease it.
How do I convert Brinell hardness to tensile strength?
For steels, a widely used rule of thumb is: UTS in MPa is approximately 3.4 x HBW, and UTS in psi is approximately 500 x HBW. For example, a steel with 200 HBW has an estimated tensile strength of about 680 MPa. These are empirical correlations that work reasonably well for carbon and low-alloy steels in the 100-400 HBW range, but they are less reliable for very hard steels, cast irons, and non-ferrous alloys.
What is the difference between HB, HBS and HBW?
All three refer to Brinell hardness, but they indicate the indenter material. "HB" is the historic general symbol used before standardization. "HBS" uses a hardened steel ball (obsolete under ISO 6506-1, limited to materials below 450 HBW). "HBW" uses a tungsten carbide ball, which deforms less and is required by the current ISO 6506-1 and ASTM E10 standards. Modern test reports should always specify HBW.
Can I use the Brinell test on thin parts or surface-hardened components?
Generally no, for two reasons. First, the specimen must be at least 8 times the indentation depth to prevent the hard platen from influencing the reading; thin sheet metal usually fails this requirement. Second, the large ball averages hardness over its indentation area, so it reads through a hard surface layer into the softer core beneath. For thin specimens or surface-hardened parts, micro-hardness tests (Vickers HV 0.3 or Knoop) are more appropriate because they leave tiny indentations that fit within a thin layer.
What loads and ball sizes are standard for Brinell testing?
ISO 6506-1 standardizes ball diameters of 1, 2.5, 5 and 10 mm and loads that maintain a constant force-to-ball-area ratio (P/D^2 = constant). The most common designation for steel and cast iron is HBW 10/3000, meaning a 10 mm ball at 3000 kgf. For softer materials, lower loads such as HBW 10/500 or HBW 5/250 are used to keep d in the valid ratio range.
How is the Brinell test different from Vickers and Rockwell?
The Brinell test uses a large ball, making it good for coarse-grained or inhomogeneous materials like castings and forgings, but unsuitable for very hard materials or thin sections. The Vickers test uses a square pyramidal diamond indenter at lower loads, giving a small indentation that suits hard, coated, or thin materials. The Rockwell test measures indentation depth electronically and gives a direct dial reading without measuring the indentation optically, making it faster for production-line testing but less flexible across material types.