Vickers Hardness Number Calculator

The Vickers Hardness Number (HV) is calculated using the formula: HV = (2F × sin(136°/2)) / (g × d²), which simplifies to HV = 1.8544 × F / d², where F is the applied force in kgf and d is the average diagonal length in millimetres. The constant 1.8544 comes from the indenter geometry — a square pyramid with a 136° face angle. g is the standard gravity factor (9.80665 m/s²) when working in SI units.

The standard Vickers hardness formula per BS EN ISO 6507 is: HV = 0.1891 × F / d², where F is in Newtons and d is the average diagonal in millimetres. Alternatively, in kgf units: HV = 1.8544 × F(kgf) / d(mm)². The factor 1.8544 is derived from the geometry of the 136° pyramidal indenter.

The square pyramid indenter with a 136° face angle produces geometrically similar impressions regardless of load, meaning the HV number remains constant across different test forces for a homogeneous material. Spherical indenters (like Brinell) suffer from load-dependent results because the ratio of indentation depth to contact area changes with load. This makes Vickers the preferred method for comparing hardness across a wide range of materials and loads.

Typical HV values vary widely: soft annealed copper sits around 40–80 HV, structural mild steel is roughly 120–180 HV, grey cast iron ranges from 180–300 HV, hardened carbon steel reaches 600–900 HV, and tungsten carbide can exceed 1500 HV. Pure iron is typically around 70–80 HV.

A common empirical approximation for steels is: Tensile Strength (MPa) ≈ HV × 3.3. This relationship holds reasonably well for carbon and low-alloy steels in the range of 100–400 HV but becomes less accurate for very hard or very soft materials, and should not be used for non-ferrous alloys without material-specific correction factors.

Variation between the two perpendicular diagonals of a Vickers indentation can be caused by surface anisotropy in the material (such as rolling texture or directional grain structure), surface roughness that disrupts the indentation symmetry, or optical measurement error. If the two diagonals differ by more than 5%, the test should typically be rejected and repeated on a better-prepared surface, per ISO 6507 guidance.

As a general rule, the sample thickness should be at least 10 times the indentation depth to avoid the hard backing effect influencing the result. For practical guidance, the thickness should be greater than 1.5 times the diagonal length. For micro-Vickers tests (low loads), thin coatings or surface layers can be measured, but careful load selection is necessary to confine the plastic zone within the layer of interest.

There is no universal mathematical formula to convert between Vickers (HV) and Rockwell (HRC or HRB) scales because they measure hardness differently. Approximate conversions are given in ASTM E140 and ISO 18265 tables. As a rough guide for steels: HRC 20 ≈ 226 HV, HRC 40 ≈ 392 HV, HRC 60 ≈ 746 HV. Always use the standard conversion tables for precise work rather than linear extrapolation.