Brinell Hardness Calculator
Compute the Brinell hardness number (HBW / BHN) from your test load, ball diameter, and measured indentation diameter, per Machinery’s Handbook 29th Ed., p. 505 and ASTM E10.
The Brinell hardness test measures a metal’s resistance to permanent indentation by pressing a hardened ball into the surface under a known load and measuring the diameter of the resulting impression. The Brinell hardness number (HBW, formerly HB or BHN) is the test load in kilogram-force divided by the spherical surface area of the indentation in square millimeters. Engineers also call this calculation a Brinell hardness number calculator or a BHN calculator.
Brinell Hardness Formula
HBW = 2P ÷ [π × D × (D − √(D² − d²))]
HBW = Brinell hardness number [dimensionless] — the “W” designates a tungsten carbide ball per ASTM E10 / ISO 6506. Identical algebra applies to BHN (steel ball) and HBS (Hultgren ball).
P = test load [force] — standard units are kgf (e.g., 3000, 1500, 500 kgf)
D = ball diameter [length] — mm (10 mm standard; 5, 2.5, and 1 mm also defined in ASTM E10)
d = mean indentation diameter [length] — mm; mean of two readings 90° apart (per ASTM E10)
Machinery’s Handbook 29th Ed., p. 505 (Brinell Hardness Test — algebraic BHN formula in textbook form). ASTM E10 / ISO 6506 standards.
Tensile Strength from Brinell (Steels Only)
TS (psi) = BHN × 515 (for BHN ≤ 175)
TS (psi) = BHN × 490 (for BHN > 175)
TS = approximate tensile strength of steel [force / area] — psi (formula as-given)
BHN = Brinell hardness number [dimensionless]
Machinery’s Handbook 29th Ed., p. 509. Steels only — does not apply to non-ferrous metals except certain aluminum alloys. This calculator suppresses the estimate above BHN 500 (a derived cutoff, not stated on p. 509) because the linear relation is anchored on the standard-ball Brinell test, which is past its normal range there.
How to Use This Calculator
Pick the standard test load that matches the material’s expected hardness range (3000 kgf for steel and cast iron, 1500 kgf for medium-hardness, 500 kgf for soft non-ferrous), select the ball diameter you tested with (10 mm is the standard), and enter the measured indentation diameter as the mean of two readings 90° apart. The calculator returns the Brinell hardness number (HBW) and, for steels in the in-range hardness band, an approximate tensile strength estimate per MH29 p. 509.
After a Brinell test on a raw casting, forging, or bar stock, use the result to verify a heat-treat spec. Once you have the Brinell number, use our hardness conversion calculator to find the equivalent Rockwell C, Rockwell B, Vickers, or Shore Scleroscope reading. For drawing-callout context, see our stainless steel properties chart for typical hardness values by grade.
Worked Example
Problem: A receiving inspector at a Salem, Oregon shop runs a Brinell test on an incoming 4140 prehard bar with a 10 mm carbide ball at 3000 kgf. The indentation reads 3.50 mm. What is the Brinell hardness, and does it meet the drawing spec of 28–32 HRC?
Given: P = 3000 kgf, D = 10 mm, d = 3.50 mm
HBW = 2 × 3000 / [π × 10 × (10 − √(100 − 12.25))]
HBW = 6000 / [π × 10 × (10 − 9.367)] = 6000 / 19.87 = 302 HBW
Per MH29 Table 1 (pp. 508–509), HBW 302 corresponds to HRC 32 — right at the top of the 28–32 HRC drawing range, so the bar passes with no margin to spare. The approximate tensile strength is 302 × 490 = 148,000 psi (1,020 MPa) per MH29 p. 509.
Standard Brinell Test Setups
Per MH29 p. 505, each standard load is paired with an expected BHN range, and the target indentation diameter for all setups is 2.50–4.75 mm. The load-to-ball-diameter-squared ratio (F/D²) shown below is calculated from those MH29 load/ball pairings.
| Load (kgf) | Ball (mm) | F/D² (kgf/mm²) | Expected BHN | Typical Materials |
|---|---|---|---|---|
| 3000 | 10 | 30 | 160–600 | Steel, cast iron |
| 1500 | 10 | 15 | 80–300 | Medium-hardness alloys |
| 500 | 10 | 5 | 26–100 | Brass, bronze, soft aluminum |
| 250 / 125 / 100 | 10 | 2.5 / 1.25 / 1 | below 26 (approx.) | Soft non-ferrous (Pb, Sn, soft Al) |
Source: Machinery’s Handbook 29th Ed., p. 505. F/D² values are calculated as load ÷ ball diameter² from the MH29 pairings; “below 26” is an approximate downward extrapolation (MH29 lists no BHN range for the 250/125/100 kgf loads). Per ASTM E10-66 (cited on MH29 p. 505), a steel ball may be used on material with BHN not over 450, a Hultgren ball not over 500, and a tungsten carbide ball not over 630.
Frequently Asked Questions
How do you calculate Brinell hardness?
Brinell hardness is calculated from the test load and the diameter of the permanent indentation left by a hardened ball. The formula (Machinery’s Handbook 29th Ed., p. 505) is HBW = 2P / (πD(D − √(D² − d²))), where P is the applied load in kgf, D is the ball diameter in mm, and d is the measured indentation diameter in mm. For the standard test (10 mm ball at 3000 kgf), a 3.5 mm indentation gives HBW ≈ 302. Enter your values in the calculator above to compute it directly.
What is the Brinell hardness formula?
The Brinell formula is HBW = 2P / (πD(D − √(D² − d²))). HBW is the Brinell hardness number (dimensionless). P is the test load in kilogram-force (kgf). D is the diameter of the indenter ball in millimeters. d is the mean diameter of the resulting indentation, also in millimeters. The “W” in HBW designates a tungsten carbide ball per current ASTM E10 and ISO 6506; older literature using a hardened steel ball wrote the same number as HB or BHN. The algebraic form is identical.
What is the difference between HB, HBW, and BHN?
All three are the same Brinell hardness number from the same formula — they differ only in indenter material and era of literature. BHN (Brinell Hardness Number) and HB are the historic designations using a hardened steel ball. HBW designates a tungsten carbide ball, which is the current ASTM E10 / ISO 6506 standard indenter. Per MH29 p. 505, a steel ball may be used up to BHN 450, a Hultgren ball up to BHN 500, and a carbide ball up to BHN 630. Above BHN 630 the Brinell test is not recommended — use Rockwell C or Vickers instead.
What test load and ball should I use for Brinell testing?
Per MH29 p. 505, the standard test uses a 10 mm ball with three primary loads matched to the material’s expected hardness range. Use 3000 kgf for steels and cast irons with expected BHN 160 to 600. Use 1500 kgf for medium-hardness materials with expected BHN 80 to 300. Use 500 kgf for soft non-ferrous metals with expected BHN 26 to 100. For very soft metals (lead, tin, soft aluminum), loads of 250, 125, or even 100 kgf are sometimes used. The aim is to keep the resulting indentation between 2.50 mm and 4.75 mm — readings outside that window are less repeatable.
How do I convert Brinell hardness to tensile strength?
For steels only, Machinery’s Handbook 29th Ed. (p. 509) gives two approximate linear relations: tensile strength in psi equals BHN × 515 when BHN is 175 or less, and BHN × 490 when BHN is above 175. For example, BHN 200 corresponds to roughly 98,000 psi (676 MPa). MH29 explicitly notes this relationship does not apply to non-ferrous metals except certain aluminum alloys, and the linear approximation breaks down above BHN 500 (where MH29 prints standard-ball values in parentheses as out of normal range). The calculator displays the estimated tensile strength alongside HBW when applicable.
How accurate is a Brinell test?
Brinell readings are most repeatable when the indentation falls in the 2.50–4.75 mm window MH29 specifies for the standard 10 mm ball (p. 505); impressions outside that window are less repeatable. Accuracy depends on a flat, clean, well-supported surface, a square indenter, and careful measurement of the indentation diameter — read as the mean of two diameters 90° apart under a low-power microscope per ASTM E10. For thin sections, surface treatments, or case-hardened layers, Rockwell Superficial or Vickers is preferred because the Brinell impression is too deep.
Related Calculators
- Hardness Conversion Calculator — Convert Brinell to Rockwell C, Rockwell B, Vickers, or Shore Scleroscope
- Stainless Steel Grades Chart — Yield, tensile, and typical hardness for common stainless grades
- Density of Metals Chart — Specific gravity and density for steel, aluminum, copper, brass, titanium
References
- Oberg, E. et al. Machinery’s Handbook, 29th Edition, Industrial Press, 2012, p. 505. Brinell Hardness Test — algebraic BHN formula, standard load/ball pairings, target indentation-diameter range, and ASTM E10-66 ball-material limits.
- Oberg, E. et al. Machinery’s Handbook, 29th Edition, p. 509. Relation Between Hardness and Tensile Strength — for steels, TS (psi) = BHN × 515 (BHN ≤ 175) or BHN × 490 (BHN > 175).
- ASTM E10 — Standard Test Method for Brinell Hardness of Metallic Materials. Current edition of the standard cited by MH29.
- ISO 6506-1 — Metallic materials: Brinell hardness test (Part 1: Test method). International equivalent of ASTM E10.
Data last verified: June 2026
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