How is the Brinell hardness calculated?

The test load is divided by the area of indentation which is a circle with radius equal to half the diameter of the impression. The formula for calculating Brinell Hardness Number (BHN) is BHN = 2P / [π x D x (D - √(D² - d²)] where P is the load in kgf, D is the diameter of the ball and d is the average diameter of indentation in mm. If the load is 3000kgf, the diameter of the ball is 10mm and the indentation left behind is 5.00mm then BHN = 143. The values for calculating BHN must be averaged by measuring the indentation in two perpendicular directions.

What is the minimum required Brinell hardness for steel to be considered good?

This is completely dependent on the steel grade and heat treatment. Low carbon low alloy steels typically have a hardness of 120 to 180 HBW, while normalised medium carbon and alloy steels are around 150 to 220. Hardened and tempered grades like 4140 or 4340 can reach values from 250 to 400, while hardened tool steel is above 500. At about 450 the steel ball will start deforming so a tungsten carbide penetrator must be used.

Why must the ratio of load to diameter be kept constant?

Only if the load increases proportionally to the square of the diameter of the ball can the geometry of the indentation and resulting values be compared. Standards ISO 6506 and ASTM E10 specify an exponent of 0.102 F/D² for each material group. For steel it is 30, for cast iron and copper alloys 10, for light metals 5 and for lead and tin 1. If the test is performed outside this exponent, the results do not correspond to published tables.

Is the brinell hardness test a destructive test?

On the finished, precise surface these workpieces cannot be used because they leave permanent depressions of two to six millimetres. In practice they are cast together with production lots or heat-treated, used as test bodies or later machined and removed, or tested on unimportant surfaces of large forged parts or castings.

Can the Brinell hardness be converted to tensile strength?

For carbon and low alloy steels an approximate conversion is possible. The maximum tensile strength will be approximately 3.45 megapascals per Brinell hardness point or about 500 psi per point. So a steel with a value of 200 HBW would have a tensile strength of approximately 690 MPa. This rule is empirical and does not apply to cast irons, cold work alloys or non-ferrous metals. For these materials published tables sorted by material group are the only reliable way.

Brinell Hardness Number Calculator

Your Brinell test

Indenter ball diameter (D)

Applied test force (P)

Indentation diameter (d)

Brinell hardness number (HBW)

Material class

Dwell time

Estimate tensile strength from the hardness

Fill in any two of the force, the indentation diameter and the hardness number, and the third one appears in the field you left blank. Start with the ball diameter, which the calculator always needs.

Please input values into the fields

Test report and standard check

Ball diameter in millimetres
Standard force for this ball and class: kgf

A finished Brinell result is written as HBW ball/force/dwell = hardness, for example HBW 10/3000/15 = 143. Fill the test in above and your own designation appears here.

Pick the material class above and the calculator shows the force the standard expects for the ball you are using.

How the number is worked out

The whole test is one division: force over area.

The area is not the circle you see from above, it is the curved surface of the spherical cap the ball pressed out. That surface is pi times the ball diameter times the depth, and the depth follows from the chord geometry of the dent, which is where the square root in the formula comes from.

Because the number is a force divided by an area, it is really a pressure. Reported in kilogram-force per square millimetre it looks like a bare number, which is why Brinell values are usually written without units at all.

The Brinell hardness test measures the resistance of a metal to indentation. A hard ball is pressed into the surface with a known load, held for a specific time and then removed. The diameter of the resulting impression is then measured using a microscope.

The smaller the impression, the greater is the resistance of the material and the higher the value; the larger the impression, the more easily the material can be deformed and the lower the value.

This method was proposed by Johan August Brinell in 1900. It is still used today because it can be applied to materials of any size or shape. The indentation diameter is a few millimeters, which allows many grains to be covered and averaged with one measurement, making it suitable for castings and forgings.

What this test actually measures:

When a sphere is pressed onto a flat surface, it creates an indentation that is also spherical but flatter. In the Brinell test, the load is distributed over the curved surface of this spherical cap, rather than the area of a circle as seen from above.

This choice leads to a root in the expression and explains why the result gives a value similar to pressure. Regardless of the designation, the ratio of force to area is a pressure.

If the pressure is given in kilograms per square millimetre, this value corresponds to the hardness level. Therefore, Brinell hardness values are mostly noted as pure numbers without a unit.

Formula for Brinell hardness:

If load is given in kilograms and both diameters are given in millimeters:

\text{HBW} = \frac{2P}{\pi D \left( D - \sqrt{D^{2} - d^{2}} \,\right)}

Here P is the applied load, D is the diameter of the ball and d is the average indentation diameter.

In order to use Newtons you need to divide by the standard gravitational constant. The symbol .102 appears on other pages for this reason. If you divide 1 by 9.80665 it equals .10197.

\text{HBW} = 0.102 \times \frac{2P_{N}}{\pi D \left( D - \sqrt{D^{2} - d^{2}} \,\right)}

This tool uses the exact value of 9.80665 and not a rounded off value for 0.102. Hence the results are about 0.03% lower than those on sites that use this simplified value.

The denominator itself is twice the curved surface area of the indentation, so it's worth looking at that value separately.

A = \frac{\pi D \left( D - \sqrt{D^{2} - d^{2}} \,\right)}{2}\qquad h = \frac{D - \sqrt{D^{2} - d^{2}}}{2} \qquad A = \pi D h

The depth h is a value that actually has some use. The thickness of the test piece should be at least eight times the depth of the indentation. Otherwise, what will be measured is not the test piece itself but the backing material ("anvil").

Example calculation:

A plate of low carbon steel is tested with a 10mm diameter tungsten carbide ball and a load of 3000kgf for 15 seconds. The indentation measured horizontally is 5.00mm.

Start by doing the calculations in parentheses. Squaring both diameters and then subtracting 25 from 100 gives you 75, and the square root of 75 is 8.660mm.

So the value inside the brackets is 1.340 mm (the difference between 10 and 8.660). Multiplying this by pi and D, then dividing by two gives a curved surface area of 21.04 square millimeters.

If the load is divided by this area, a value of 142.6 results, with 3000 being divided by 21.04. The result for this steel plate is HBW 10/3000/15 = 143, which falls within the normal range for low carbon steels of 120 to 180.

How to measure results of Brinell hardness test:

A pure number such as HB 178 alone does not represent a complete result. This is because the readings can vary even for the same material if test conditions are different. The test conditions are also stated in standard form.

For example, let's take 600 HBW 1/30/20. The 600 is the hardness, HBW means that a tungsten carbide ball was used, 1 is the diameter of the ball in millimeters, 30 is the load (in kilograms) and 20 is the duration of impact (in seconds).

If the test duration is between 10 and 15 seconds, it's usually omitted as this is the standard set time. The letters are also important. HBW stands for a tungsten carbide ball while older HBS stood for steel ball.

The reason why the rule of thumb "load - diameter" makes most comparisons invalid.

The load cannot be chosen arbitrarily. The larger the ball, the greater the depression. To ensure that the values obtained have the same meaning, the load must be increased proportionally to the square of the diameter of the ball.

The value that must be kept constant is the load diameter exponent which is expressed as 0.102 F/D² where F is the force in Newtons. This actually corresponds to the division of the load expressed in kilogram-force by the square of the ball diameter expressed in millimeters.

\frac{0.102 \, F}{D^{2}} = \frac{P_{\text{kgf}}}{D_{\text{mm}}^{2}}= \text{constant for a material class}

If a load of 500 kgf is applied to steel material and a ball with a diameter of 10 mm is used, the exponent will be 5 which does not correspond to the value of 30 required by the standard. The obtained value is the result of an actual measurement on a particular object but it does not match any published table.

Index	Typical materials	Force on a 10 mm ball	On a 5 mm ball
30	Steel, nickel and titanium alloys, harder cast iron	3000 kgf	750 kgf
10	Softer cast iron, copper and copper alloys	1000 kgf	250 kgf
5	Pure copper, harder aluminium alloys	500 kgf	125 kgf
2.5	Aluminium and magnesium alloys	250 kgf	62.5 kgf
1.25	Bearing metals and soft castings	125 kgf	31.25 kgf
1	Lead, tin and their alloys	100 kgf	25 kgf

The calculation tool shows the resulting exponent from the entered data as well as the required load for the selected material class. This allows inconsistencies to be recognized before results are recorded.

Why does the depth have to be between 0.24 and 0.60, in relation to the diameter of the ball?

The standard does not allow for recesses that are narrower than .24 or wider than .60 relative to the ball diameter, due to sensitivity issues.

As you approach the narrow edge, the hardness curve approaches a vertical line. At an indentation of 2.5 mm, measurement errors in the range of one tenth of a millimeter can lead to deviations of several tens of points. Therefore, the measured value no longer reflects the metal itself but is influenced by the microscope.

As you approach the wide rim, the ball penetrates too deeply and the material bulges around the edge so that the geometry of a simple spherical cap no longer describes the actual contour. The upper graph shows this curve for the ball used and the load applied. The steep rise on the left side illustrates all of the reasons mentioned.

Reverse calculation of test

If one of the three fields is left blank, the tool will calculate the value for that field. This solves two common problems on site.

Firstly it is about the expected size of indentation. For a shaft made from 4140 steel that has been hardened and tempered to a target hardness of 300 HBW, and tested with a ball having a diameter of 10 mm and a load of 3000 kgf, the area must be 10 square millimeters (calculated as 3000 divided by 300).

By reverse calculation of the geometric relationships, the indentation should be 3.51 mm. A significantly larger indentation means that hardening or annealing has not reached the expected state.

d = \sqrt{D^{2} - \left( D - \frac{2P}{\pi D \cdot \text{HBW}} \right)^{2}}

The second problem concerns the question of which load should be used. For an aluminium component of type 6061-T6, a measurement value of 1.90 mm was achieved with a ball diameter of 5 mm and a result of 95 HBW, resulting in a load of 280 kgf according to the conversion formula.

P = \frac{\text{HBW} \times \pi D \left( D - \sqrt{D^{2} - d^{2}} \,\right)}{2}

It is useful to know this. The standard load for aluminum with a ball diameter of 5 mm is 250 kgf, so the load in this test was about twelve percent higher.

Typical Brinell Hardness Values

Hardness is not a property that can be determined by the material name alone. Heat treatment can give steel materials a wide range of hardness points and cold working changes all materials.

Material	Approximate hardness
Lead	5 HBW
Pure aluminium	15 HBW
Copper	35 HBW
AW-6060 aluminium	75 HBW
Brass	55 to 200 HBW
Mild steel, AISI 1018 or 1020	120 to 180 HBW
Annealed alloy steel	150 to 220 HBW
4140 or 4340, quenched and tempered	250 to 400 HBW
Hardened tool steel	500 to 700 HBW
Glass	around 1550 HBW

When the value exceeds about 450, the hardened steel ball begins to flatten under load, leading to invalid results. In this case a tungsten carbide ball must be used. The current method according to ISO 6506-1 uses tungsten carbide balls for the whole process. The "W" in HBW stands for this use.

Use of hardness instead of tensile strength.

For carbon and low alloy steels there is a reasonably high correlation between tensile strength and hardness which makes them practically valuable.

\text{UTS} \approx 3.45 \times \text{HBW} \;\; \text{MPa} \qquad \text{UTS} \approx 500 \times \text{HBW} \;\; \text{psi}

Thus a steel plate with an HBW value of 143 would be approximately equivalent to 493 MPa or about 71500 psi. These two constants are consistent with each other since 3.45 MPa can be converted into 500 psi.

This relationship is empirical and has a very limited range of application. It does not apply to cast iron, severely cold worked alloys or any non-ferrous metals. So this should be considered as a method for material classification rather than proof of conformity.

Comparison of Brinell, Rockwell and Vickers hardness tests

All three methods press something onto the surface of an object, with the thing being pressed differing and the method of measurement following.

Test	Indenter	What is measured	Best for
Brinell	1 to 10 mm carbide ball	Dent diameter, optically	Castings, forgings, coarse-grained metal
Rockwell	Diamond cone or small ball	Depth of penetration	Fast production checks on finished parts
Vickers	Diamond pyramid	Dent diagonals, optically	Thin sections, coatings, the whole hardness range

There are conversion relationships between the various hardness scales, and ASTM E140 publishes corresponding conversion tables. However, these conversion relationships are material dependent. A misclassification of alloy based on a single table entry can result in differences of five to ten points on the Rockwell-C scale.

What to do if a hardness test is not satisfactory?

Impressions are permanent and several millimeters wide so they are not a suitable method for inspecting the surface of finished products. In practice test specimens are used which have been cast or heat treated with actual parts. It is also possible to check end areas that will be machined away later, or surfaces no one can see.

Positioning is also critical. The distance between the center of a depression and one of its edges should be at least twice the radius, while the distance to the next depression should be at least three times the diameter. Otherwise, free surfaces or neighboring areas with cold hardening can lead to erroneous measurement results.

The indentations are measured in two perpendicular directions and the average is taken. At 5 mm impressions, a measurement error of one-tenth of a millimeter can lead to an error in hardness of about eight percent, which is far beyond what many would expect.

This tool uses the standard Brinell formulas and considers validity limitations per ISO 6506-1, but does not replace either the standard itself or calibrated instruments. Material acceptance decisions should be made on the basis of certified tests rather than estimates.

Frequently asked questions

How is the Brinell hardness calculated?: The test load is divided by the area of indentation which is a circle with radius equal to half the diameter of the impression. The formula for calculating Brinell Hardness Number (BHN) is BHN = 2P / [π x D x (D - √(D² - d²)] where P is the load in kgf, D is the diameter of the ball and d is the average diameter of indentation in mm. If the load is 3000kgf, the diameter of the ball is 10mm and the indentation left behind is 5.00mm then BHN = 143. The values for calculating BHN must be averaged by measuring the indentation in two perpendicular directions.
What is the minimum required Brinell hardness for steel to be considered good?: This is completely dependent on the steel grade and heat treatment. Low carbon low alloy steels typically have a hardness of 120 to 180 HBW, while normalised medium carbon and alloy steels are around 150 to 220. Hardened and tempered grades like 4140 or 4340 can reach values from 250 to 400, while hardened tool steel is above 500. At about 450 the steel ball will start deforming so a tungsten carbide penetrator must be used.
Why must the ratio of load to diameter be kept constant?: Only if the load increases proportionally to the square of the diameter of the ball can the geometry of the indentation and resulting values be compared. Standards ISO 6506 and ASTM E10 specify an exponent of 0.102 F/D² for each material group. For steel it is 30, for cast iron and copper alloys 10, for light metals 5 and for lead and tin 1. If the test is performed outside this exponent, the results do not correspond to published tables.
Is the brinell hardness test a destructive test?: On the finished, precise surface these workpieces cannot be used because they leave permanent depressions of two to six millimetres. In practice they are cast together with production lots or heat-treated, used as test bodies or later machined and removed, or tested on unimportant surfaces of large forged parts or castings.
Can the Brinell hardness be converted to tensile strength?: For carbon and low alloy steels an approximate conversion is possible. The maximum tensile strength will be approximately 3.45 megapascals per Brinell hardness point or about 500 psi per point. So a steel with a value of 200 HBW would have a tensile strength of approximately 690 MPa. This rule is empirical and does not apply to cast irons, cold work alloys or non-ferrous metals. For these materials published tables sorted by material group are the only reliable way.

Related calculators

Bolt Tensile Force CalculatorFind the tensile force (preload) on a bolt from its tensile stress and stress area with F = sigma times A. Solve for any value, set the stress from an ISO grade and preload target, and estimate the tightening torque.

Aerodynamic Drag CalculatorCalculate aerodynamic drag force with the drag equation. Solve for force, speed, area, density, or drag coefficient, plus dynamic pressure, power, and terminal velocity.

Force CalculatorCalculate force with Newton's second law F = ma, or solve for the mass or acceleration instead. Also finds the acceleration and force from a change in velocity, in any unit from newtons to pound-force.

Strouhal Number CalculatorCalculate the Strouhal number from vortex shedding frequency, characteristic length, and flow velocity with St = f L / U, and solve for any of the four. Check for vortex-induced resonance, estimate the cylinder value from the Reynolds number, and compare against typical Strouhal numbers.

Pipe Weight CalculatorCalculate the weight of a pipe from its outer diameter, wall thickness or inner diameter, length and material. Reports weight per metre and per foot, the metal area, the volume, and the weight when filled with fluid.

Belt Length CalculatorFind the length of a belt around two pulleys from the pulley diameters and center distance, or solve backward for the spacing, with open and crossed belt geometry and wrap angles.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

ISO 6506-1:2014 — Metallic materials, Brinell hardness test, Part 1: Test method
The governing standard: indenter, force scale, the load-diameter index, the 0.24 to 0.60 indentation window, dwell times and the reporting format.
Brinell scale (Wikipedia)
The formula, the HBW designation, the history of the test and typical hardness values for common materials.
Indentation hardness (Wikipedia)
How the indentation family of hardness tests relates to one another and why each measures a different aspect of plastic resistance.
Rockwell scale (Wikipedia)
The depth-based alternative used for production testing, and the material-specific nature of scale conversions.
Ultimate tensile strength (Wikipedia)
Background for the empirical hardness to tensile strength relation used for carbon and low-alloy steels.