What Is the Vickers Hardness Number?
The Vickers Hardness Number (VHN or HV) measures how strongly a material resists being permanently dented. A lab presses a small diamond, shaped like a square-based pyramid, into the material's surface under a precisely controlled force, then measures the diagonal of the tiny indentation left behind under a microscope.
The trick is that the same diamond shape and the same formula work whether you're testing soft aluminum or hardened tool steel, which is why Vickers hardness is used so widely across manufacturing, materials science, and quality control.
The Vickers Hardness Formula
[
HV = 1.8544 \times \frac{F}{d^2}
]
Where:
- HV is the Vickers Hardness Number
- F is the force applied to the indenter, in kilogram-force (kgf)
- d is the average diagonal length of the indentation, in millimeters
Squaring the diagonal converts a length measurement into an area, since the indentation is roughly a small square. The constant 1.8544 comes from the geometry of the diamond indenter itself — its faces meet at a 136° angle, and 1.8544 equals 2 × sin(68°), which turns the raw force-over-area ratio into true pressure over the pyramid's actual surface area.
Worked Example
Say a test applies 30 kgf of force and leaves an indentation with an average diagonal of 0.3 mm:
[
HV = 1.8544 \times \frac{30}{0.3^2} = 1.8544 \times \frac{30}{0.09} \approx 618.1 \text{ HV}
]
A result around 618 HV is consistent with a hardened tool steel — for comparison, mild steel typically sits closer to 120–200 HV, while soft aluminum alloys often fall below 50 HV.
Why the Diagonal Matters So Much
Because the diagonal is squared, small measurement errors have an outsized effect on the final number. Halving the diagonal quadruples the calculated hardness, so labs measure both diagonals of the indentation under magnification and average them before plugging the value into the formula — a habit worth copying whenever you're checking a test result by hand.
Typical Vickers Hardness Ranges
| Material | Typical VHN |
|---|---|
| Soft aluminum alloys | 15 – 50 HV |
| Mild (low-carbon) steel | 120 – 200 HV |
| Hardened tool steel | 500 – 800 HV |
| Tungsten carbide | 1,500 – 2,200 HV |
| Diamond | ~10,000 HV |
Quick Recap
- HV = 1.8544 × force (kgf) ÷ diagonal² (mm), using the average of both indentation diagonals.
- The 1.8544 constant comes directly from the 136° angle of the diamond indenter.
- Small errors in the diagonal measurement are squared, so measure carefully and average both diagonals.
- Use the calculator above to turn a force and diagonal reading into an instant HV value.
If you're comparing hardness test methods, the Brinell hardness number calculator uses the same force-over-area idea with a hardened steel ball instead of a diamond pyramid.