Formula & Calculator
Vickers Hardness Number
Calculates hardness from the applied load and the diagonal length of the indentation left by a pyramidal diamond indenter.
Interpretation
HV = 1.854 × F/d². Hardness from a diamond indenter. F is load (kgf), d is diagonal length (mm). Used for a wide range of materials. Quick and non‑destructive testing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| HV | Vickers hardness number | kgf/mm2 |
| F | Applied test load | kgf |
| d | Average diagonal length of indentation | mm |
What it means
The Vickers hardness test uses a square‑based diamond pyramid indenter to measure hardness. The Vickers hardness number (HV) is calculated from the applied load F (in kgf) and the average diagonal d (in mm) of the indentation: HV = 1.854F/d². The constant 1.854 comes from the geometry of the indenter. This test is versatile because it can be used for soft and hard materials alike, and the indent size is small, making it suitable for thin sections and micro‑hardness testing. It is widely used in research, quality control, and failure analysis. Hardness is not a fundamental property but correlates with strength and wear resistance. Understanding HV is essential for material selection, heat treatment evaluation, and process control in manufacturing.
Worked example
Vickers Hardness – Two Examples
Real‑World| Parameter | Value |
|---|---|
| F | 30 kgf |
| d | 0.42 mm |
| Parameter | Value |
|---|---|
| F | 10 kgf |
| d | 0.25 mm |
Common mistakes
- Vickers hardness number (HV): HV = 1.854·F/d² – where F is the indenter load (kgf) and d is the average diagonal length of the indentation (mm).
- Force units: F in kgf (kilogram‑force) – if using Newtons, convert (1 kgf ≈ 9.807 N).
- Diagonal d: The average length of the two diagonals of the square indentation – in mm.
- Indenter: Diamond pyramid with a 136° included angle – the factor 1.854 accounts for the geometry.
- Application: Works for a wide range of materials – but avoid very small or very large loads that cause inaccuracies.
Applications
The Vickers hardness number (HV) is calculated from the applied load (F) and the diagonal length (d) of an indentation, HV = 1.854·F/d² (when d is in mm). Vickers hardness testing is widely used to characterise the hardness of metals, ceramics, and thin films. Engineers and quality control professionals use HV to assess material properties, to monitor heat treatment effectiveness, and to correlate hardness with tensile strength. The Vickers indenter (a diamond pyramid) is suitable for a wide range of materials and can be applied to small samples and surfaces. By measuring HV, materials scientists can quickly evaluate the mechanical performance of materials and ensure they meet specifications.
- Quality control and hardness testing in metal production
- Heat treatment process validation (hardness verification)
- Characterisation of coatings and surface treatments
- Microhardness testing of phases and microstructures
- Correlation of hardness with strength and wear resistance
Frequently Asked Questions
The Vickers hardness test uses a diamond indenter with a square‑based pyramid shape. The hardness number (HV) is calculated from the applied load (F, in kgf) and the diagonal length (d, in mm) of the indentation: HV = 1.854 · F / d². The constant 1.854 comes from the geometry of the indenter.
HV is expressed in kgf/mm². Sometimes it is quoted in MPa (multiply by 9.807). The test is often specified with the load, e.g., HV₁₀ means 10 kgf load.
Mixing diagonal length units (mm vs µm) without adjusting the constant accordingly. If diagonal length is in µm, the formula becomes HV = 1.854 × F × 10⁶ / d² (with d in µm).
The Vickers test is applicable to both hard and soft materials, and the indentation size can be varied by changing the load. The scale is continuous and independent of load (for a given material).
For steels, there is an empirical relationship: UTS (MPa) ≈ 3.45 × HV. This is useful for estimating strength without destructive testing.
Vickers uses a diamond indenter, which can test harder materials. The indentation is small, making it suitable for thin sections or surface layers. It also works on a wider range of materials.
It comes from the geometry of the Vickers pyramid (face angle 136°). The projected area of the indentation is related to the diagonal length by A = d² / (2 sin(68°)), and the constant is 1.854.
Using a microscope with a micrometre eyepiece. The indentation is a square; measure the two diagonals and take the average. The accuracy depends on the sharpness of the indentation edges.
- Requires a flat, polished surface.
- Indentation may be affected by the indentation size effect.
- Operator skill affects measurement accuracy.
- Not suitable for very thin coatings (use nanoindentation).
- Soft metals (e.g., aluminium): ~20‑50 HV.
- Structural steels: 150‑250 HV.
- Tool steels: 500‑800 HV.
- Ceramics: 1000‑2000 HV.