This Vickers hardness number calculator uses the size of the indentation to return the hardness of a material. There are several scales used to measure hardness, including the Brinell hardness, Rockwell hardness, Meyer hardness, and the Vickers hardness test — the focus of this tool.
The Vickers hardness scale, named after the company where it was developed in 1921, is an alternative to the Brinell hardness test. It is relatively easy to use because, unlike Brinell, the result does not depend on the diameter or size of the indenter. Read on to understand how to calculate the Vickers hardness number once you have completed the indentation experiment.
Vickers hardness test
Hardness tests measure the resistance of a material against plastic deformation. To perform these tests — be it Brinell, Rockwell, or Vickers — an indenter is pressed onto the surface of the specimen with a specific force F for a time interval of, say, 10–15 s. During this interval, the material undergoes plastic deformation that you measure after unloading the specimen.
The indentation shape depends on the type of test. For a Vickers hardness test, you use a diamond indenter with an angle of 136° between opposite faces, which leaves a square pyramid-shaped indentation. The two diagonals of the indentation are measured and averaged. Once you know the mean diagonal, you can use the Vickers hardness formula to find its value.
ISO 6507. You can find the test conditions, guidelines, and formula for calculating the Vickers hardness number in the international standard BS EN ISO 6507-1: Metallic materials — Vickers hardness test.
Vickers hardness number
The Vickers hardness number, HV, is a function of the normal force in kgf (kilogram-force) F, the mean diagonal in mm d, and the surface area of the indentation. The Vickers hardness number in kgf/mm² is given by:
HV = Force ÷ Area = 2F · sin(α/2) ÷ d²
where:
- F — applied normal force (in kgf);
- d — mean diagonal of the indentation (in mm); and
- α — angle of the indenter, commonly taken as α = 136°.
For the standard 136° diamond pyramid, the term 2 sin(α/2) equals approximately 1.8544, so the formula simplifies to HV ≈ 1.8544 × F / d².
Tensile strength and converting HV to MPa
To convert the Vickers hardness number to MPa, multiply the HV value by the acceleration due to gravity, g = 9.80665 m/s². So the hardness H in MPa is:
H (MPa) = HV × g = HV × 9.80665
As a rough rule of thumb for steels, the ultimate tensile strength can be estimated as UTS (MPa) ≈ 3.2 × HV. This calculator shows that estimate for convenience, but you should treat it only as a guide.
Using the Vickers hardness number calculator
To calculate the Vickers hardness number with this tool:
- Select your measurement system — Metric (N, mm) or American / Imperial (lbf, in).
- Enter the test force, F, applied to the indenter.
- Insert the mean diagonal of the indentation, d.
- The indenter angle defaults to 136°; change it only if you use a non-standard pyramid.
- Optionally set the dwell time (load duration) used in the standard designation.
The calculator returns the Vickers hardness number HV, the hardness in MPa and GPa, the indentation surface area, an estimated ultimate tensile strength, and the standard ISO 6507-1 designation.
Example: Using the Vickers hardness number calculator
Determine the Vickers hardness number for a specimen tested with a force of 294.2 N (≈ 30 kgf) that leaves a square indentation with a mean diagonal of 0.5 mm.
- Enter the test force, F = 294.2 N (= 30 kgf).
- Insert the mean diagonal, d = 0.5 mm.
- Keep the indenter angle at α = 136°.
The Vickers hardness number (HV) is then calculated:
HV = 1.8544 × 30 ÷ 0.5²
HV ≈ 222.5 (≈ 2182 MPa)
Vickers hardness of common materials
The following table lists approximate Vickers hardness numbers for some common materials:
| Material | Vickers hardness (HV) |
|---|---|
| Pure aluminium (annealed) | ~ 15 – 25 |
| Pure copper | ~ 40 – 50 |
| Mild / low-carbon steel | ~ 120 – 180 |
| Austenitic stainless steel | ~ 200 – 350 |
| Hardened tool steel | ~ 600 – 900 |
| Tungsten carbide | ~ 1500 – 2400 |
| Diamond | ~ 8000 – 10000 |
FAQs
What is the Vickers hardness test?
The Vickers hardness test presses a square-based diamond pyramid (136° between faces) into a material under a known load. The hardness number is the ratio of the load to the surface area of the resulting indentation, calculated from the mean of its two diagonals.
Why is the angle 136° used?
The 136° angle was chosen so that Vickers hardness values would closely match Brinell hardness values for the same materials at low hardness levels, making the two scales broadly comparable.
What is the difference between Vickers and Brinell hardness?
Both are indentation tests, but Vickers uses a diamond pyramid and a single continuous scale for all materials, while Brinell uses a hardened ball. Vickers is independent of the load for a given material and is well suited to very hard materials and micro-hardness measurements.
How do I convert HV to MPa or GPa?
Multiply HV by g = 9.80665 to obtain the hardness in MPa, then divide by 1000 for GPa. For example, HV 222.5 corresponds to about 2182 MPa or 2.18 GPa.
Can I use this calculator in imperial units?
Yes. Choose the American / Imperial system to enter the force in pounds-force (lbf) and the diagonal in inches; the calculator converts internally and returns the standard Vickers number along with the area and tensile-strength estimate in imperial units.