Measuring Hardness of Materials; Brinell, Vickers, Knoop and Rockwell Hardness Tests

Materials science is a very important branch of engineering and there are lots of notions in materials engineering to cope with. To select the proper material for an engineering application, it is very important to know and calculate these parameters related to materials. One of these parameters is the hardness of materials. 

What is the Hardness of Materials?

From the engineering viewpoint, the hardness of material means the resistance to local deformation when a load or localized stress is applied. It is a very important parameter to compare different materials’ strength values. Also, the hardness of materials is correlated with the corrosion characteristics and the corrosion resistance of materials can be compared with the hardness values of materials. 

The hardness of materials can be measured with different methods. In this article, we will elaborate on the different methods of hardness tests and we provide the calculators for the users. 

How the Hardness of Materials are Measured?

All the hardness measurement methods depend on the same characteristics. Specific shapes made from specific materials are applied on the surfaces of materials with specific loads and kgs, and the local indentation is measured. 

Different hardness tests are; the Brinell hardness method, Vickers hardness method, Knoop hardness method, and Rockwell hardness method. 

Brinell Hardness Measurement Method 

Brinell hardness test is carried out on test specimen.

In the Brinell hardness measurement method, a 10mm diameter steel or tungsten-carbide ball is applied to the curved surface of the material specimen with different kilograms of pressure. Most used kilograms are 500, 1500, and 3000 kg. In general, a round localized deformation occurred. The diameter of this localized deformation is measured and put into the equation. 

In this equation, ‘D’ is the diameter of the Brinell hardness test ball, and ‘d’ is the diameter of the indentation that occurred on the surface of the material specimen. The units of them are in ‘millimeters’. 

In most cases, the Brinell hardness tests that were carried out with a tungsten-carbide test ball can be more precise because lower deformation occurs on the test ball compared with a steel one. 

Vickers Hardness Test

In the Vicker’s hardness tests, the shape of the test indenter is a diamond pyramid. After the application om the test specimen, the diagonal length is measured and put inside the HV formula; 

In this formula again, ‘L’ is the diagonal length of the indentation, and ‘P’ is the applied load in kilograms. In general, 1-120 kilograms of loads are used in the Vickers hardness test. The tip angle of the pyramid is 136 degrees. 

Knoop Hardness Test


Image Source: Steven R. Schmid, Bernard J. Hamrock, Bo O. Jacobson – Fundamentals of Machine Elements, 3rd Ed., Pg: 64

Like in the Vickers hardness tests, a diamond pyramid shape is used as an indenter. But the ratio between the two diagonals is different. The ratio between the small diagonal and the long diagonal is 7.11 and the ratio between the height of the pyramid and the small diagonal is 4.0. 

In general, 0.025 to 5 kilograms of loads are applied in Knoop hardness tests. 

The long diagonal is put into the Knoop hardness formula below; 

In this formula, ‘P’ is the applied kilograms and the ‘L’ is measured long diagonal of the indentation. 

Knoop hardness tests are generally carried out for small brittle specimens and indentation sizes are very small. Because of it, the kilograms that are used in Knoop hardness tests are very low. 

Rockwell Hardness Test

In Rockwell hardness tests, a diamond cone or steel balls are used. The primary angle of the diamond cone is 120 degrees. And the diameter of the steel ball is 1/16 or 1/8 inches. 

According to the type of the used indenter is changed, the Rockwell test and the formulations changes. 

If the diamond cone is used, Rockwell hardness tests are: 

  • HRA: 60 kilograms of pressure is used.
  • HRC: 150 kilograms of pressure is used.
  • HRD: 100 kilograms of pressure is used.

The formulation of these Rockwell tests; 

HR = 100-t500

where ‘t’ is the indentation height in millimeters.

If the 1/16 in. of diameter steel ball is used in Rockwell hardness tests; 

  • HRB: 100 kilograms of pressure is used.
  • HRF: 60 kilograms of pressure is used.
  • HRG: 150 kilograms of pressure is used.

If the 1/8 in. of diameter steel ball is used in Rockwell hardness tests; 

  • HRE: 100 kilograms of pressure is used.

The formulation of these Rockwell tests; 

HR = 130-t500

where ‘t’ is the indentation height in millimeters.

Hardness Test Calculator 

As a team, we prepared a calculator that you can easily calculate these hardness tests without any difficulty. 

Brinell Hardness Calculator


Vickers Hardness Calculator


Knoop Hardness Calculator






The use of the calculator above is very simple. First of all, you need to select the type of Hardness test that you want to calculate. Then enter the values that you measuredç After that, click on the ‘Calculate!’ button. If you want to make another calculation, just click on the ‘Reset!’ button. 

For the Rockwell hardness calculator, you just need select which type of Rockwell hardness you want to calculate. 


The general logic of the hardness of materials is very simple like above. Hardness values are standardized with the test methods described above. They are very good tools to make a comparison between engineering materials.

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

Please take special care about the units when you are making calculations with the Hardness calculator above.

You can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanical Base!

Do not forget to leave your comments and questions below about the contact stress calculator of hardness tests. 

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