Vickers Hardness Number Calculator: HV Formula and Conversions
Enter the applied load and the mean indentation diagonal to calculate the Vickers Hardness Number (HV). Choose any two of the three variables (force, diagonal, HV) and solve for the third. Results include surface hardness in MPa, approximate Brinell and Rockwell C conversions, and estimated tensile strength. The step-by-step panel shows every calculation with your live values.
Formula
Worked example
A 10 kgf load leaves an indentation with diagonals of 0.48 mm and 0.52 mm on a steel specimen. Mean diagonal d = (0.48 + 0.52) / 2 = 0.50 mm. HV = 2 x 10 x sin(68°) / 0.50^2 = 2 x 10 x 0.92718 / 0.25 = 74.17. The result is reported as 74.2 HV10 (load appended to scale). Surface hardness: 74.2 x 9.807 = 727.6 MPa.
What is the Vickers hardness test?
The Vickers hardness test was developed in 1921 by engineers Robert Smith and George Sandland at Vickers Ltd as an alternative to the Brinell method. It uses a square-based diamond pyramid indenter with a face-to-face angle of 136 degrees, pressed into the specimen surface for 10 to 15 seconds under a defined load. After the load is removed, the diagonals of the square indentation are measured under an optical microscope and averaged. The Vickers Hardness Number (HV) is then the load divided by the contact area of the indentation, expressed in kgf/mm^2. Because the same indenter geometry is used at all loads, the test is truly universal: one machine and one formula cover anything from soft annealed copper at 40 HV to cemented carbide at over 1500 HV. Standard test loads range from 1 kgf (HV1) to 100 kgf (HV100), and sub-kilogram loads (the microhardness range, 0.01 to 1 kgf) are used for thin coatings, individual grains, and heat-affected zones in welds.
How to use this calculator and which mode to choose
The calculator has three solve modes. The default mode (HV from F and d) is the most common: enter the load you applied and the average diagonal you measured to get the Vickers hardness. Use the Force mode when you have a calibration target (a known HV) and want to find the load that produces a specific indent size on that material, which is useful in test-machine setup. Use the Diagonal mode to predict how large an indentation will be for a given load on a material of known hardness before you run the test, helping you pick a load that keeps the indentation within the measurable range of your microscope. Regardless of mode, the results panel also shows the hardness in MPa (multiply HV by 9.807), an approximate Brinell equivalent, an approximate Rockwell C equivalent where valid (above 200 HV for steel), and an estimated tensile strength via the Tabor relation (UTS approx 3.3 x HV in MPa). These conversions are approximate: for critical specifications always report the directly measured scale.
The formula and its derivation
The Vickers hardness formula follows directly from the definition: hardness equals force per unit contact area. For a square pyramid indenter with a face-to-face angle of 136 degrees, the half-angle at each face is 68 degrees. The surface area of the four triangular faces of the indentation is d^2 / (2 sin(68 degrees)), where d is the mean diagonal. Dividing the load F (in kgf) by this area in mm^2 gives:
HV = 2 F sin(68°) / d^2 ≈ 1.8544 F / d^2
The constant 1.8544 is a rounded form of 2 sin(68°) = 1.85440..., and is the value used by most references and standards. To convert to SI units (Pa), multiply HV by the gravitational acceleration g = 9.80665 m/s^2 x 10^6 to reach MPa, or simply HV x 9.80665 gives MPa directly when HV is in kgf/mm^2. The result is always reported with the test load appended: "450 HV30" means 450 HV obtained with a 30 kgf load, following ISO 6507-1.
Hardness conversions and their limitations
No single universal conversion formula exists between hardness scales, because each test measures a slightly different physical response (projected area vs contact area, different indenter geometries, different depth-to-width ratios). ISO 18265 and ASTM E140 publish empirical conversion tables for specific material families, most importantly non-austenitic steels. For steels in the range 200 to 900 HV, the conversions to Rockwell C and Brinell given here are reasonable engineering estimates, accurate to within about 5 percent for carbon and alloy steels. They are less reliable for stainless steels, cast irons, non-ferrous alloys and ceramics. The Brinell test (HBW with a 10 mm tungsten carbide ball) is not used above about 650 HB because the indenter deforms; Vickers is the preferred method for materials harder than that. For copper, aluminium and other non-ferrous metals, compare only within the same scale or use the appropriate Rockwell superficial scales.
Typical Vickers hardness ranges by material
| Material | Typical HV range | Notes |
|---|---|---|
| Commercially pure aluminium | 15-40 HV | Soft, easily indented |
| Annealed copper | 40-80 HV | Very ductile |
| Mild steel (as-rolled) | 100-170 HV | Structural grade |
| Stainless steel 304 (annealed) | 140-200 HV | Austenitic, work-hardens |
| Carbon steel (normalized) | 150-230 HV | Typical for medium-carbon grades |
| Cast iron (grey) | 180-300 HV | Brittle; carbide inclusions vary readings |
| Alloy steel (quenched and tempered) | 300-600 HV | Dependent on carbon and alloy content |
| High-speed tool steel (hardened) | 600-900 HV | e.g. M2, T1 grades |
| Cemented tungsten carbide | 1200-1600 HV | Composite; tested with Vickers or Knoop |
| Diamond | ~8000 HV | Hardest known natural material; reference only |
Approximate HV ranges for common engineering materials. Exact values depend on alloy composition and heat treatment.
Frequently asked questions
What does the number after HV mean, for example HV10?
The number after HV is the test load in kilogram-force. HV10 means the hardness was measured with a 10 kgf load. Standard loads are 1, 2, 5, 10, 30, 50 and 100 kgf. Reporting the load is mandatory under ISO 6507-1 because results from different loads can differ slightly, especially on materials that are not homogeneous. Always compare HV numbers measured at the same load.
How do I measure the diagonal if it is too small to see clearly?
Vickers indentations at low loads (below 5 kgf) can be smaller than 0.1 mm and require a calibrated filar eyepiece or digital image analysis system on a metallurgical microscope. For microhardness testing (loads below 1 kgf), a minimum magnification of 400x is typical. Ensure the surface is polished to at least a 1 µm finish and that the specimen is flat and firmly clamped, because any tilt introduces asymmetric diagonals that raise measurement uncertainty.
Why does Vickers use 136 degrees and not some other angle?
The 136-degree face-to-face angle was chosen so that the Vickers number at mid-range loads would match the Brinell number (with a 10 mm ball at 3000 kgf) on the same steel. This compatibility was by design in the 1920s when the Brinell test was already the accepted standard. The geometry also ensures that the ratio of indentation depth to diagonal is nearly constant, making the scale truly load-independent for most metals.
Can I use this calculator for ceramics or coatings?
Yes, the formula is the same, but interpreting results requires care. Ceramics often show cracking at the indentation corners, which biases the diagonal measurement. Thin coatings require the load to be low enough that the indentation depth is less than one-tenth of the coating thickness (the ten-percent rule), otherwise the substrate contributes to the result. For coatings thinner than about 10 µm, use even lower loads and consider the Berkovich nano-indentation test instead.
How accurate is the tensile strength estimate from HV?
The Tabor relation (UTS in MPa approximately 3.3 x HV) works well for low- and medium-alloy steels in the range 200 to 600 HV, with typical errors of 10 to 15 percent. It is much less reliable for cast irons (which are brittle and fail differently), cold-worked metals, high-alloy steels, and all non-ferrous alloys. Treat this as a first estimate only. For design-critical applications, measure tensile strength directly from a machined test piece.
What is the difference between Vickers and Knoop hardness?
Both are microindentation tests that use a diamond pyramid, but the Knoop indenter is elongated (rhomboid cross-section, length-to-width ratio about 7:1) and produces a much shallower indentation for the same load. Knoop is preferred for brittle materials such as ceramics and glass (less cracking) and for anisotropic materials where directionality matters. Vickers gives a more symmetric impression and is easier to relate to other scales, so it is the more widely used of the two.
What load should I choose for a typical steel part?
For bulk hardness of a steel component, 10 to 30 kgf (HV10 or HV30) is the usual choice. These loads produce indentations between 0.3 and 0.7 mm for common engineering steels, which are easy to measure accurately. Use smaller loads (HV1 or HV0.3) for thin hardened layers such as case-hardened or nitrided surfaces, weld heat-affected zones, or when testing individual microstructural constituents such as martensite plates.
Sources
- ISO 6507-1:2023, Metallic materials - Vickers hardness test - Part 1: Test method (International Organization for Standardization)
- ASTM E92-23, Standard Test Methods for Vickers Hardness and Knoop Hardness of Metallic Materials (ASTM International)
- ASTM E140-12b(2019), Standard Hardness Conversion Tables for Metals (HV, HRC, HRB, Brinell)