Vickers Hardness Calculator (HV from force and indentation diagonals)

Understanding the Vickers hardness calculator — concept and principle

The Vickers test presses a square diamond pyramid into a material and measures the two diagonals of the square dent it leaves. This calculator turns the test force and diagonal readings into the Vickers hardness number (HV), and also gives the contact area, the indentation depth and the difference between the two diagonals as a quality check.

A 10 kgf load leaving a 0.304 mm mark means about 201 HV.

How it is calculated

d = (d₁ + d₂) ÷ 2

Contact area A = d² ÷ (2 sin 68°)

HV = F(kgf) ÷ A ≈ 1.8544 × F(kgf) ÷ d²

With F in newtons: HV = 0.102 × 2F sin 68° ÷ d² ≈ 0.1891 × F ÷ d²

Depth ≈ d ÷ (2√2 × tan 68°) ≈ d ÷ 7

d in mm; F in kgf or N (1 kgf = 9.80665 N).

The principle

Hardness here means resistance to permanent indentation. The diamond has 136° between opposite faces, so each face meets the axis at 68°. Because the shape is always the same, a softer material simply gives a larger dent, and the sloping area of contact can be calculated from the diagonal alone. Dividing the force by that area gives a pressure-like number in kgf/mm², which is the historical definition of HV. The geometric similarity of the pyramid means HV is nearly independent of test force over a wide range, unlike some other hardness scales.

Worked example

Default inputs: force 10 kgf, d₁ = 0.302 mm, d₂ = 0.306 mm.

Mean diagonal d = (0.302 + 0.306) ÷ 2 = 0.304 mm.
Area = 0.304² ÷ (2 × 0.92718) = 0.092416 ÷ 1.85437 = 0.04984 mm².
HV = 10 ÷ 0.04984 = 200.7, shown as 201 (written 201 HV10).
Depth = 0.304 ÷ 7.0 = 0.0434 mm = 43.4 µm.
Force = 10 × 9.80665 = 98.07 N; diagonal difference = 0.004 ÷ 0.304 = 1.3 %.

Each point is the calculator re-run with only “Diagonal d₂ (mm, 0 = none)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Diagonal d₂ (mm, 0 = none)	Vickers hardness (HV)
0.0765	518
0.153	358
0.23	263
0.306	201
0.383	158
0.459	128
0.612	89

How to read the result

Report the hardness with the test force, for example 201 HV10. Annealed copper and aluminium alloys are typically well below 150 HV, structural steels around 120–200 HV, and hardened tool steels several hundred HV. A large difference between the two diagonals suggests the surface was tilted, the material is directional or the indent was distorted. The specimen should be at least 1.5 times the diagonal thick, and indents should be spaced well apart.

Common mistakes

Using a single diagonal when the dent is not square.
Mixing kgf and N in the formula.
Testing too thin a specimen, which makes the anvil affect the result.
Placing indents too close together or near an edge.

Keep in mind: Converting HV to other hardness scales or to tensile strength uses empirical tables that depend on the material. For acceptance testing follow ISO 6507 or ASTM E384 procedures and calibrated equipment.

Frequently asked questions

Why is the diamond angle 136°?

It was chosen to give values comparable to Brinell hardness for many metals, where the ball impression diameter is about 0.375 of the ball diameter.

What is microhardness?

Vickers testing at low forces (often below 1 kgf), used for thin layers and small features.

Does the test force change HV?

Ideally very little, but at low forces surface preparation and measurement error matter more.

What does HV10 mean?

A Vickers hardness measured with a 10 kgf test force.

Sources: ISO 6507-1, Metallic materials — Vickers hardness test — Part 1: Test method

Checked 9 Nov 2026. ISO 6507-1:1997, Metallic materials — Vickers hardness test — Part 1: Test method, Table 2 (HV = 0.102 × 2F sin(136°/2)/d² ≈ 0.1891 F/d², F in N, d = mean of d₁ and d₂ in mm; preview of the standard).

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