Contact Mechanics · Hardness scales

Hardness scales and conversions: Vickers, Knoop, Brinell, Rockwell

Each scale divides a force by a different area, so one metal gets five different numbers.

Why does one metal get a different number on each hardness scale?

Five standard indenters press into one metal.

One ideal pressure for all five, so HK reads 1.08 × HV and Brinell differs from the E140 table. Bottom strip: one scale.
Material
ScaleIndentNumber
Mean pressure H
Tabor: flow stress ≈ H/3

Try it: Tool steel: Vickers 52 µm, Brinell 2.25 mm. Copper: no valid HRC.

Can you convert Vickers to Rockwell or Brinell?

ASTM E140 tables pair the scales, one table per material group.

Section through the part, true scale.
Solid: steel. Dashed: cartridge brass. Grey: outside the steel tables.
Part
Vickers pit depth
Rockwell reading
Brinell HBW (E140)
Rockwell pit depth

Try it: Hard coating: the 1.4 µm pit passes the 0.3 µm limit. HV0.01 and 5 µm: 0.44 µm, under the limit.

Why does Knoop hardness change when you rotate the indenter on a crystal?

Turn the Knoop diamond on the (001) face of a cubic crystal.

Grey outline: the same indent with no anisotropy.
HK against angle: four lobes, repeating every 90°.
Knoop hardness HK0.05
Long diagonal L
Long axis along
Max / min over a turn

Try it: drag from 0° to 45°: HK falls from 275 to 225 and the diamond grows.

What to take away

Different areas

HV and HB use the surface area; HK and HIT the projected area. HV ≈ 0.0945 HIT (MPa).

Tables fit one material

Use the steel table only for steels, and none for thin coatings.

Direction matters

On one grain, Knoop hardness changes with the direction of the long axis.

More detail: formulas, assumptions and limits

The five formulas

Vickers (ISO 6507-1): square pyramid, 136° between faces. HV = 0.102 × 2F sin68°/d2 = 0.1891 F/d2 with F in N and d the mean diagonal in mm. The area is the sloping surface of the pit, d2/1.8544. Depth is d/7.00.

Knoop (ISO 4545-1, ASTM E384): rhombic pyramid, 172.5° and 130°, long diagonal L = 7.11 × short diagonal and about 30.5 × depth. HK = 14.229 F/L2 with F in kgf and L in mm, or 1.451 F/L2 with F in N. It uses the projected area 0.07028 L2.

Berkovich (ISO 14577-1): three-sided pyramid, face angle 65.27° from the axis. Projected area A = 24.5 h2, the same as Vickers at equal depth. HIT = F/A, usually in GPa.

Brinell (ISO 6506-1): hard ball of diameter D. HBW = 0.102 × 2F/(πD(D − √(D2 − d2))), the force over the curved area of the cap. The page uses D = 10 mm with 0.102F/D2 = 30 for steels and 10 for copper and aluminium. Valid when 0.24D < d < 0.6D and HBW ≤ 650.

Rockwell (ISO 6508-1): 98.07 N preload sets zero, 1471 N total load for C (120° diamond cone, 0.2 mm tip radius), then back to the preload. h is the lasting extra depth. HRC = 100 − h/0.002 mm. Scale B uses a 1.5875 mm ball, 980.7 N and HRB = 130 − h/0.002 mm.

Surface area against projected area

For the Vickers pyramid the projected area is d2/2 and the surface area is d2/1.8544, so their ratio is sin68° = 0.927. So HV × 9.807 MPa = 0.927 HIT, which gives HV = 0.0945 HIT with HIT in MPa (ISO 14577-1). Real HIT uses the contact depth under load, so measured pairs scatter around this line.

What the first widget assumes

Every indenter meets the same mean pressure H, found from the preset's Vickers value: H = HV × 9.807/0.927. This is the ideal plastic case, with no elastic spring-back, no pile-up and no work hardening. Real metals break it: a ball strains the metal about 0.2 d/D and a Vickers pyramid about 8% (Tabor), so a work-hardening metal gives a ball reading that changes with load. That is one reason no single table fits all metals.

Two results come from this ideal model and are not real data. Knoop uses the projected area, so here HK = HV/0.927 = 1.08 HV at every hardness. Brinell divides the same force by the curved cap area, so the page's HBW is not the E140 value: for the Q&T steel it gives 413 HBW where E140 lists 371, and for the tool steel 742 HBW, above the 650 limit, where E140 lists 654. Read the Brinell and Knoop numbers in widget 1 as what one ideal pressure gives, and the E140 numbers in widget 2 as measured pairs. The presets use typical handbook values (about 50 HV for annealed copper, 107 HV for 6061-T6, 131 HV for annealed low-carbon steel, 392 and 697 HV for steels at HRC 40 and 60).

The Rockwell numbers are not computed from contact mechanics: for steels the page reads HRC or HRB from the E140 steel tables and shows the depth that number means. For copper and aluminium it shows no number, because the steel tables do not apply.

Tabor's rule

For metals that no longer work-harden much, the mean pressure under a sharp indenter is about 3 times the flow stress: H ≈ 3σ, with σ taken at about 8% strain for Vickers (Tabor 1951). Compare with a tensile curve.

Knoop anisotropy model

The page uses HK(θ) = HK0(1 + a cos 4θ) with HK0 = 250 and θ measured from [100]. This has the fourfold symmetry of a (001) cubic face. The page puts the maximum along <100> and the minimum along <110>; both this choice and the size a are illustrative. Which direction is harder, and by how much, depends on the crystal, its slip systems and the load (Garfinkle and Garlick 1967 map it for several metals). Daniels and Dunn (1949) first mapped this effect in silicon ferrite and zinc, and linked it to slip on the active slip systems; Brookes, O'Neill and Redfern (1971) turned that idea into the effective resolved shear stress model. The long diagonal is L = √(14.229 F/HK) at F = 0.05 kgf.

On this site: Making the number · When it lies · Scratch hardness · Reading a tensile curve · Grain orientation

Questions people ask

How do I convert Vickers hardness to GPa?

Multiply HV by 9.807 and divide by 1000: 1 HV = 9.807 MPa. That is the force over the surface area of the pit. To compare with nanoindentation hardness HIT, which uses the projected area, divide again by 0.927: HV 500 is 4.90 GPa over the surface area and about 5.29 GPa as HIT.

How accurate is converting HRC to HV?

For carbon and alloy steels, E140 values are useful estimates, but the standard itself calls every conversion approximate. Heat treatment, surface condition and cold work move the real pairs. Report the measured scale and mark a converted value as converted.

When should I use Knoop instead of Vickers?

Knoop pits are long and shallow: about 30 times longer than deep, against 7 for Vickers. That suits thin layers, brittle materials that crack under Vickers, and direction-dependent hardness. The number is less reliable for very small indents because the short diagonal is hard to read.

Why can't I use Rockwell C on soft metals?

HRC is defined from about 20 to 70. In a soft metal the cone goes so deep that the reading falls below 20 and loses meaning. Use a scale with a ball and a lower load, such as HRB or HRF, and do not convert to HRC.

How do I measure the hardness of a thin coating?

Keep the indent shallow: a common guide is a depth under one tenth of the coating thickness. Deeper indents feel the substrate. For coatings of a few micrometres this usually means nanoindentation (ISO 14577-4) rather than Vickers or Rockwell.

Can I get yield strength from hardness?

Roughly. Tabor's rule says H ≈ 3σ, with σ the flow stress near 8% strain. It works best for cold-worked metals. For annealed metals that harden a lot, it gives a stress well above the yield strength.

References

Show the 12 references
  1. ISO 6507-1:2023, Metallic materials. Vickers hardness test. Part 1: Test method. International Organization for Standardization, Geneva.
  2. ISO 4545-1:2023, Metallic materials. Knoop hardness test. Part 1: Test method. International Organization for Standardization, Geneva.
  3. ISO 6506-1:2014, Metallic materials. Brinell hardness test. Part 1: Test method. International Organization for Standardization, Geneva.
  4. ISO 6508-1:2023, Metallic materials. Rockwell hardness test. Part 1: Test method. International Organization for Standardization, Geneva.
  5. ISO 14577-1:2015, Metallic materials. Instrumented indentation test for hardness and materials parameters. Part 1: Test method; and ISO 14577-4:2016, Part 4: Test method for metallic and non-metallic coatings.
  6. ASTM E140-12b(2019)e1, Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, Scleroscope Hardness, and Leeb Hardness. ASTM International. Table 1 (nonaustenitic steels, C range), Table 2 (B range), Table 4 (cartridge brass).
  7. ASTM E384-22, Standard Test Method for Microindentation Hardness of Materials. ASTM International.
  8. D. Tabor, The Hardness of Metals, Clarendon Press, Oxford (1951).
  9. F. W. Daniels and C. G. Dunn, The effect of orientation on Knoop hardness of single crystals of zinc and silicon ferrite, Transactions of the ASM 41, 419 to 442 (1949).
  10. M. Garfinkle and R. G. Garlick, A stereographic representation of Knoop hardness anisotropy, NASA Technical Note D-4226, Lewis Research Center (1967).
  11. C. A. Brookes, J. B. O'Neill and B. A. W. Redfern, Anisotropy in the hardness of single crystals, Proceedings of the Royal Society of London A 322, 73 to 88 (1971). doi:10.1098/rspa.1971.0055
  12. ASM International, ASM Handbook vol. 2, Properties and Selection: Nonferrous Alloys and Special-Purpose Materials (1990): typical hardness of annealed copper and 6061-T6.
Cite this page: Tripathy, Manisha. “Hardness Scales and Conversions Lab.” untethered atom, 2026, https://untetheredatom.com/indentation/hardness-scales-and-conversions.
BibTeX 
@misc{tripathy2026hardnessscales,
  author = {Tripathy, Manisha},
  title  = {Hardness Scales and Conversions Lab},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/indentation/hardness-scales-and-conversions}},
  note   = {Interactive web tool}
}
Last updated 28 September 2026.