Brinell Hardness Number Calculator

Input mode: Chooses whether you enter two measured indentation diameters or one value that is already averaged.

Test force: The load applied during the Brinell test.

Force unit: The unit for Test force. If you choose kgf, the calculator converts it to newtons before solving.

Ball diameter (mm): Diameter of the spherical indenter ball.

Indentation diameter 1 (mm) and Indentation diameter 2 (mm): Two mark widths measured at right angles on the specimen surface [2].

Average indentation diameter: The diameter actually used in the hardness formula.

Brinell hardness (HBW): The main Brinell result. A higher value means the material resisted indentation more strongly.

Brinell hardness number (legacy name): The same result shown with the older BHN wording many users still search for.

Indented surface area: The curved contact area of the ball impression used in the calculation.

Diameter measurement uncertainty (mm): Your plus/minus reading uncertainty for the indentation diameter, used for the sensitivity check.

Sensitivity note: A short message explaining how much the hardness changes when the diameter shifts by the chosen uncertainty.

Mistake: Entering Test force in newtons while Force unit is set to kgf, or the other way around.
Fix: Match Force unit to the number you typed and verify Force used in calculation shows the expected value in N.

Mistake: Typing an Average indentation diameter (mm) that is equal to or larger than Ball diameter (mm) .
Fix: Enter a smaller indentation value. Valid Brinell geometry requires the indentation diameter to stay below the ball diameter.

Mistake: Using Two measured diameters mode but leaving Indentation diameter 2 (mm) blank.
Fix: Fill in both Indentation diameter 1 (mm) and Indentation diameter 2 (mm) , or switch Input mode to One average diameter .

Mistake: Re-entering a hand average that does not match the two measured values.
Fix: In Two measured diameters mode, let the calculator create Average indentation diameter automatically from the two inputs.

Mistake: Entering a negative or too-large Diameter measurement uncertainty (mm) and expecting sensitivity results anyway.
Fix: Use a value that is 0 or more, and small enough that the adjusted diameters still stay above 0 and below Ball diameter (mm) . Otherwise HBW at smaller indentation or HBW at larger indentation will show N/A.

Mistake: Reading Brinell hardness number (legacy name) as a different quantity from Brinell hardness (HBW) .
Fix: Treat them as the same hardness value with different naming. Use Brinell hardness (HBW) as the formal designation shown by the calculator.

• The calculator only works for valid Brinell geometry, so the indentation diameter used in the formula must be greater than 0 and smaller than the ball diameter.
• It assumes the entered force, ball diameter, and indentation measurement come from a properly performed Brinell test procedure. Poor surface preparation, bad optics, or reading the mark incorrectly can change the real result.
• When Force unit is kgf, the tool converts to newtons using 9.80665 N/kgf before calculating.
• The sensitivity check is only computed when Average indentation diameter minus the uncertainty stays above 0 and plus the uncertainty stays below Ball diameter (mm). Otherwise those outputs are shown as N/A.
• Brinell hardness (HBW) and Brinell hardness number (legacy name) are the same numeric hardness here; the second output is provided only because many users still search for BHN.
• Results can differ from a lab report if the test standard, ball material, dwell conditions, optical measurement method, or reporting rules differ from your setup.

Formula used

The calculator first determines the indentation diameter used in the math. In two-diameter mode, it averages the two measured values. In single mode, it uses the entered average directly.

d = (d1 + d2) / 2

If Test force is entered in kgf, it is converted to newtons using standard gravity.

F_N = F_kgf x 9.80665

The Brinell hardness equation then uses force in newtons, ball diameter D in mm, and average indentation diameter d in mm.

HBW = 0.102 x 2F_N / (pi x D x (D - sqrt(D^2 - d^2)))

The curved surface area of the indentation is also shown because hardness uses 0.102 times the force in newtons divided by that area.

A = pi x D x (D - sqrt(D^2 - d^2)) / 2

HBW = 0.102 x F_N / A

Worked mini-example

Suppose Test force is 3000 kgf, Ball diameter (mm) is 10, and the two measured diameters are 3.50 mm and 3.60 mm. The average indentation diameter is 3.55 mm.

d = (3.50 + 3.60) / 2 = 3.55 mm

The force conversion is:

F_N = 3000 x 9.80665 = 29419.95 N

Using the Brinell equation gives a hardness of about 293.303 HBW, and the corresponding indented surface area is about 10.231 mm^2.

Sensitivity check

If you enter Diameter measurement uncertainty (mm), the calculator recomputes hardness at a slightly smaller and slightly larger indentation diameter. This shows how much your hardness result moves when the diameter reading changes.

d_low = d - uncertainty

d_high = d + uncertainty

HBW_low_tol = HBW(d_low)

HBW_high_tol = HBW(d_high)

A smaller indentation gives a higher hardness, and a larger indentation gives a lower hardness. This is why careful diameter measurement matters.

Standards context

Brinell testing is standardized under ASTM E10, and Brinell calculations commonly use two perpendicular indentation readings and the HBW designation in current practice [1][2].

Assumptions behind the result

The math assumes a valid spherical indentation with 0 < d < D. If the indentation diameter is equal to or larger than the ball diameter, the geometry is invalid and the calculator blocks the result. The displayed value is a direct formula result, so reported lab values may differ slightly if a procedure uses different rounding or reporting rules.