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Brinell Hardness Calculator

Brinell hardness number (BHN/HBW) from load, ball & indent

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How to use

  1. 1.Choose your load unit (kgf or N), then enter the applied test force F.
  2. 2.Enter the indenter ball diameter D in millimetres (typically 10, 5, 2.5, or 1 mm).
  3. 3.Enter the measured indentation diameter d in millimetres — the Brinell hardness number (BHN/HBW) updates in real time.

About Brinell Hardness Calculator

The Brinell hardness number is BHN = 2F / (πD(D − √(D² − d²))). Enter your applied load F, the indenter ball diameter D, and the measured indentation diameter d, and this calculator returns the value instantly — no sign-up, everything runs in your browser. If your load is recorded in newtons, switch the unit toggle to N and the tool divides by 9.80665 (1 kgf = 9.80665 N) before applying the formula, matching the 0.102 factor in ASTM E10 and ISO 6506.

How the Brinell test works: a hardened or tungsten-carbide ball of diameter D is pressed into a metal surface under a fixed load F for a set dwell time. The load is typically held for a dwell time of 10 to 15 seconds so the metal fully deforms. The ball then leaves a round impression, and you measure its diameter d (usually the mean of two perpendicular readings) with a microscope. Harder material resists the ball, so the indentation is smaller; softer material yields a wider one. Brinell hardness is defined as the load divided by the curved surface area of that spherical impression, which is exactly what the formula above computes. Modern results carry the HBW suffix (Hardness, Brinell, tungsten carbide indenter); older tests using a hardened steel ball were written HBS or simply HB.

What each parameter means: F is the test force, historically in kilogram-force (kgf) and today often in newtons; D is the ball diameter, commonly 10, 5, 2.5, or 1 mm; d is the diameter of the residual indent in millimetres. A key physical constraint is d < D — the impression can never equal or exceed the ball diameter, so this calculator rejects any d ≥ D (which would also force a negative value under the square root) and flags zero or negative entries.

Where it is used: Brinell testing suits castings, forgings, and coarse-grained or non-homogeneous metals because the large indent averages out local variation, unlike the tiny impressions of Rockwell or Vickers. It is widely applied to steel, cast iron, aluminium, copper alloys, and bearing metals for incoming inspection, heat-treatment verification, and quality control. Typical Brinell values span roughly 20 HBW for soft lead and tin, around 30 to 90 HBW for pure aluminium and copper, 120 to 250 HBW for mild and medium-carbon steels, and 400 to 650 HBW for hardened tool steels and bearing races. To keep results comparable, labs hold the load-to-diameter ratio 0.102F/D² constant for a given material class. Use this tool to convert measured indentation diameters into hardness values, to double-check a manual calculation, or to explore how load and ball size change the reading before running a physical test.

Frequently asked questions

What is the Brinell hardness formula?
The Brinell hardness number is BHN = 2F / (πD(D − √(D² − d²))), where F is the applied load in kgf, D is the ball diameter, and d is the indentation diameter (both in mm). It equals the load divided by the curved surface area of the spherical impression, as defined in ASTM E10 and ISO 6506.
What units do F, D, and d use?
F is the applied force. The classic formula uses kilogram-force (kgf); if you have newtons, toggle to N and the tool divides by 9.80665 first (the 0.102 factor). D and d are both in millimetres: D is the ball diameter and d is the measured indent diameter.
Why must the indentation diameter d be smaller than the ball diameter D?
The ball only presses part-way into the metal, so its round impression is always narrower than the ball itself. If d ≥ D the impression would be impossible, and D² − d² turns negative, making the square root undefined. This calculator rejects any d that is zero, negative, or not smaller than D.
How is Brinell hardness different from Rockwell and Vickers?
Brinell uses a large ball and a big indentation, which averages out surface variation — ideal for castings, forgings, and coarse-grained metals. Rockwell measures indentation depth directly for a fast dial reading, while Vickers uses a diamond pyramid for very hard or thin materials. They report on different scales and are not directly interchangeable without conversion tables.
How do I choose the test load?
Load is picked so the load-to-diameter ratio 0.102F/D² stays constant for a material class — for example 30 for steel and cast iron, 10 for copper alloys, and 2.5–5 for soft metals like aluminium. Keeping this ratio fixed makes readings comparable across different ball sizes.

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