Hardness of materials: what it is, scales and HRC, HB and HV conversion chart

Hardness is a material's resistance to localized plastic deformation, such as a scratch or an indentation on the surface. It is measured by scratching (Mohs scale), by indentation (Brinell, Rockwell, Vickers, Knoop, Shore) or by rebound (Leeb). The number only means something together with its scale: a steel at 60 HRC is equivalent to about 697 HV and 654 HB (ASTM E140). "Hardness 60" with no scale tells you nothing.

Hardness is one of the most widely used mechanical properties of materials in industry, because it is quick to measure, barely damages the part and is related to strength and wear resistance. In this guide you will find the types of hardness, the scales and their formulas, the Mohs scale, an HRC × HV × HB conversion table with tensile strength, what 60 HRC means, the hardness of 1020, 1045 and 4140 steels and of tool steels, and the difference between hardness, strength and toughness. The step-by-step procedure for each test is in the article hardness testing.

The photo below shows, on an enlarged model of a steel block, the three indentation shapes that appear throughout the text: the spherical cap of the Brinell ball, the Rockwell cone and the Vickers pyramid. The shape of the indenter determines what each test measures, and that is why the numbers on the different scales do not match.

What is hardness

Callister and Rethwisch, in the textbook Materials Science and Engineering, define hardness as a measure of a material's resistance to localized plastic deformation, for example a small indentation or a scratch. The key word is localized: a hardness test deforms only one point on the surface, unlike the tensile test, which deforms the entire test specimen until it fractures.

One detail sets hardness apart from properties such as the modulus of elasticity: hardness is not a fundamental property of the material. The number depends on the method: indenter shape, applied load, dwell time and what is measured (diameter, diagonal or depth of the indentation). That is why there is no exact formula to convert one scale into another. Conversion is done with empirical tables, obtained from tests, such as those in ASTM E140 and ISO 18265.

In practice, high hardness means the surface resists scratching, indentation and abrasive wear. That is why cutting tools, dies, bearings and gears are specified by hardness, while parts that must absorb impact are specified with a maximum hardness limit.

Types of hardness: scratch, indentation and rebound

Hardness measurement methods fall into three families, according to the phenomenon they measure: scratching, the indentation left by an indenter, or the rebound of a body striking the surface.

Scratch hardness is the oldest. One material is harder than another if it can scratch it. The Mohs scale, from 1812, ranks ten minerals this way. It is simple and useful in the field, but it only gives the order, not how much harder one material is than another.

Indentation hardness is the one industry uses. A standardized indenter (ball, cone or pyramid) is pressed into the surface with a known load and the indentation is measured. The smaller or shallower the indentation, the harder the material.

Rebound hardness measures how much energy comes back after impact: a hard material deforms little and returns more energy. Leeb testers are portable, are used on parts too large to bring to the lab, and ASTM E140 itself includes a table to convert Leeb values into Brinell, Vickers and Rockwell for steels.

The table summarizes the three families, their scales and where they are used:

Type of hardness	What is measured	Scales	Typical use
Scratch	Which material scratches which	Mohs, pencil hardness	Minerals, gemstones, paints and coatings
Indentation	Size or depth of the indentation made by an indenter under load	Brinell, Rockwell, Vickers, Knoop, Shore	Metals, polymers and rubbers: this is the engineering family
Rebound	Energy or return velocity of a body striking the surface	Leeb, Shore scleroscope	Portable hardness testers and large parts

Hardness scales and their formulas

Each indentation scale combines an indenter, a load and a measured quantity: the indentation diameter, the diagonal or the depth. Below are the main scales, with the formula for each and the material it works best on; at the end of the section, a table brings them all together.

Brinell hardness (HB)

The Brinell test presses a 10 mm ball into the part, with 3,000 kgf for steel, and measures the diameter of the cap it leaves. Hardness is the force divided by the area of the cap:

HBW = 0.102 × 2F / [πD(D − √(D² − d²))]

with F in newtons, D the ball diameter and d the mean indentation diameter, both in mm. The constant 0.102 (equal to 1/9.80665) converts newtons to kilogram-force, because the scale was born in kgf/mm². The large indentation is an advantage in heterogeneous materials, such as cast iron and forgings, because it averages over many grains. Current notation uses HBW: the ball is made of hard metal (tungsten carbide with cobalt, hence the W); the old steel ball has been dropped from the standard. The symbol is followed by the ball diameter and the load: 229 HBW 10/3000 is a hardness of 229 measured with a 10 mm ball and 3,000 kgf.

Rockwell hardness (HRC and HRB)

Rockwell measures depth, not size. The indenter goes down with a preload, receives the total load, returns to the preload, and the tester reads the permanent depth h. Rockwell is not a single scale but a family: each letter (A, B, C and others) indicates a combination of indenter and load. The C scale, the one for hardened steels, uses a 120° diamond cone, a 10 kgf preload and a 150 kgf total load:

HRC = 100 − h/0.002 (h in mm)

Each HRC point corresponds to 0.002 mm of depth. The reading is taken directly from the dial, with no microscope, which is why Rockwell is the standard on the shop floor and in heat treatment inspection. The B scale (HRB = 130 − h/0.002) uses a 1/16" ball and a 100 kgf total load, for mild steels, brass and copper alloys. Always write the scale letter: 60 HRC and 60 HRB are completely different materials.

The photo shows a benchtop Rockwell hardness tester on the C scale: the diamond cone comes down onto a cylindrical steel part resting on the tester's anvil.

Vickers hardness (HV) and microhardness

Vickers uses a square-based diamond pyramid with a 136° angle between opposite faces. The indentation is a diamond (rhombus) shape, and the mean d of its two diagonals is measured:

HV = 0.1891 × F / d² (F in N, d in mm)

The great advantage is that a single scale covers everything from lead to hard metal, because the indentation geometry is the same at any load. The number after HV is the load in kgf: 348 HV30 was measured with 30 kgf.

Knoop (HK) is a variant of Vickers. The diamond pyramid is elongated and leaves a long, narrow indentation, with the long diagonal about seven times the short one; only the long diagonal is measured. For the same load, the Knoop indentation is shallower than the Vickers one, which makes it suitable for very thin layers and for brittle materials such as ceramics.

With small loads (microhardness), Vickers and Knoop measure carburized and nitrided cases and coatings, phase by phase. For this, the sample is cut, mounted and polished as in metallography, with a metallographic cutting machine and a grinding and polishing machine, and the indentation is measured under the microscope. The photo shows a Vickers indentation under the microscope on polished and etched steel: the diamond is small compared with the grains, and the two diagonals are measured in the eyepiece or on the image.

Shore hardness

The Shore durometer (ASTM D2240) is for rubbers and plastics. A spring-loaded indenter sinks into the material and the reading goes from 0 to 100. The A scale is for rubbers and soft elastomers, the D scale for rigid plastics. Shore cannot be converted to Brinell or Rockwell.

Which scale to use

In short: Brinell for heterogeneous and soft materials, Rockwell for quick inspection of heat-treated steel, Vickers for anything that requires precision and thin layers, Knoop for very thin layers and ceramics, Shore for rubbers and plastics. The table brings together the indenter, load, measured quantity and notation of each scale:

Scale	Indenter and load	What is measured	Notation example	Typical materials
Brinell (HBW)	10 mm hard metal ball, 3,000 kgf for steel	Indentation diameter	229 HBW 10/3000	Annealed and normalized steels, cast iron, forgings
Rockwell C (HRC)	120° diamond cone, 10 kgf preload, 150 kgf total load	Permanent depth	60 HRC	Hardened steels, from 20 to 70 HRC
Rockwell B (HRB)	1/16" ball, 100 kgf total load	Permanent depth	84 HRB	Mild steels, brass, copper alloys
Vickers (HV)	Square-based diamond pyramid, 136° angle	Mean of the diagonals	348 HV30	Any metal, from lead to hard metal; thin layers
Knoop (HK)	Elongated diamond pyramid	Long diagonal	HK 0.1	Microhardness of thin layers and ceramics
Shore A and D	Calibrated spring-loaded indenter	Depth, reading from 0 to 100	70 Shore A	Rubbers (A) and rigid plastics (D)

The step-by-step procedure for each test, the precautions regarding minimum thickness and edge distance, and the procedure standards (ASTM E10-23, E18-25 and E92-26) are in the article hardness testing.

Mohs scale

The Mohs scale was created by the German mineralogist Friedrich Mohs in 1812. It ranks ten minerals from 1 to 10: each one scratches all those with a lower number and is scratched by those with a higher number.

Mohs	Mineral	Everyday reference (approximate)
1	Talc	Scratched by a fingernail
2	Gypsum	Scratched by a fingernail (fingernail ≈ 2.5)
3	Calcite	Copper coin ≈ 3 to 3.5
4	Fluorite	Scratched by a steel nail
5	Apatite	Steel blade or nail ≈ 5.5
6	Orthoclase (feldspar)	Glass ≈ 5.5 to 7, depending on the source
7	Quartz	Scratches glass
8	Topaz
9	Corundum
10	Diamond

The caveat with the Mohs scale is that it is ordinal: it gives the order, not the proportion. In Vickers, quartz (Mohs 7) is about 1,200 HV, alumina, which has the same chemistry as corundum (Mohs 9), reaches 2,500 HV, and diamond (Mohs 10) is about 10,000 HV, according to the Open University table. Diamond is roughly 8 times harder than quartz, and the last step of the scale, from 9 to 10, alone is worth about 4 times. That is why engineering does not use Mohs to specify metals.

Hardness conversion table: HRC, HV, HB and tensile strength

The table below is the most searched-for item on this topic. The values are those of ASTM E140 for non-austenitic steels (carbon, low-alloy and tool steels, in the forged, annealed, normalized or quenched and tempered condition), as transcribed in Mitutoyo Bulletin 2059. Tensile strength is as tabulated by the same source, from 32 to 58 HRC.

HRC	HV	HB (10 mm, 3,000 kgf)	Approx. tensile strength (MPa)
65	832	739	not tabulated
62	746	688	not tabulated
60	697	654	not tabulated (estimates of 2,200 to 2,500)
58	653	615	2,330
56	613	577	2,158
54	577	543	2,013
52	544	512	1,882
50	513	481	1,758
48	484	455	1,641
46	458	432	1,524
44	434	409	1,434
42	412	390	1,338
40	392	371	1,255
38	372	353	1,179
36	354	336	1,110
32	318	301	1,007
30	302	286	not tabulated
20	238	226	not tabulated

How to use the table. Find the row for the scale you measured and read the other columns; for intermediate values, interpolate between neighboring rows. Three limits always apply:

• Only for non-austenitic steels. Austenitic stainless steel, aluminum, copper and nickel alloys have their own tables in E140. Using the steel table on them gives the wrong number.
• Typical uncertainty is ±5% between 20 and 60 HRC. It is an empirical conversion, not a measurement.
• Below 20 HRC, do not use HRC. The scale loses resolution; measure in HB or HRB. Above about 450 HB, Brinell is only valid with a hard metal ball (HBW).

The chart shows why you cannot convert with a simple rule of three: the curve is not a straight line. Between 20 and 40 HRC, each HRC point is worth about 8 HV; between 56 and 65 HRC, about 24 HV.

What is the difference between HRC and HB?

HB (Brinell) measures the diameter of the indentation made by a large ball; HRC (Rockwell C) measures the depth of the indentation made by a diamond cone, as shown in the scales section above. Since they are different quantities, there is no formula between the two, only the empirical table: 40 HRC ≈ 371 HB, 50 HRC ≈ 481 HB. In the converter below, choose the scale you measured and read the others.

What does 60 HRC mean

60 HRC is a high-hardness hardened steel. Per ASTM E140, it is equivalent to about 697 HV and 654 HBW. By the definition of the C scale, the permanent depth of the indentation was (100 − 60) × 0.002 = 0.080 mm; a part at 20 HRC would leave 0.160 mm.

This hardness is found in cold-work tool steels such as D2 (VC131 from Villares Metals, a Brazilian steelmaker, used between 58 and 63 HRC), in dies and cutting knives, and on the surface of induction-hardened 1045 steel shafts, which reach 54 to 60 HRC. Tensile strength is not tabulated in this range: estimates go from about 2,200 to 2,500 MPa, and at this hardness steel is brittle, so the value measured in tension is uncertain. What 60 HRC guarantees is resistance to wear and to edge deformation, not toughness.

Hardness of steels: 1020, 1045, 4140, 4340 and tool steels

The question "what is the hardness of steel X?" only has an answer once you know the heat treatment condition. The same 1045 steel ranges from about 170 HB as rolled to 60 HRC on a hardened surface.

Each treatment works differently. Quenching forms martensite and takes the steel to the maximum hardness its carbon content allows. Tempering trades part of that hardness for toughness, and the higher the temperature, the more the hardness drops. Annealing and normalizing leave the steel soft, in the Brinell range. Carburizing, nitriding and induction hardening harden only the surface and keep the core tougher. Work hardening, by cold deformation, also raises hardness without any heat treatment. The overview is in heat treatment of metals.

The chart below shows the effect of tempering on 4140 steel: oil quenched it reaches 54-58 HRC, and the hardness drops from 52-54 HRC, tempered at 205 °C, to 26-30 HRC, tempered at 650 °C.

The table lists typical hardness values by steel and heat treatment condition:

Steel	Condition	Typical hardness	Source
SAE 1020	Rolled or annealed	111 HB (about 64 HRB)	AZoM
SAE 1020	Carburized	above 65 HRC in the case; soft core	AZoM
SAE 1045	Hot rolled or normalized	170 to 210 HB	AZoM
SAE 1045	Quenched and tempered at 550-650 °C	26 to 35 HRC	Huaxia Steel
SAE 1045	Quenched and tempered at 400-500 °C	35 to 45 HRC	Huaxia Steel
SAE 1045	Quenched and tempered at 100-200 °C (Ø 10 mm bar)	57 to 58 HRC	Lucefin (C45E)
SAE 1045	Induction surface hardening	54 to 60 HRC at the surface	AZoM
SAE 4140	Annealed	197 HB	AZoM
SAE 4140	Oil quenched, untempered	54 to 58 HRC	ASM Handbook (via UTEC)
SAE 4140	Tempered from 205 °C to 650 °C	from 52-54 to 26-30 HRC	ASM Handbook (via UTEC)
SAE 4140	Commercial pre-hardened (quenched and tempered) bar	28 to 32 HRC	Nifty Alloys
SAE 4340	Annealed	217 HB	AZoM
D2 / VC131	Quenched and tempered	58 to 63 HRC	Villares Metals; GGD Metals
High-speed steel (M2, M42)	Quenched and tempered	63 to 68 HRC	Aobo Steel

The values are typical ranges: they vary with the part cross section, the quenching medium and the actual carbon content. What the engineering drawing specifies, and inspection checks, is the final range, for example "4140 quenched and tempered, 28 to 32 HRC".

Which steel has the highest hardness?

Among steels, the hardest are high-speed steels (63 to 68 HRC) and powder metallurgy tool steels, which approach 70 HRC. Beyond that it is no longer steel: cemented carbide (tungsten carbide with cobalt) has 1,500 to 2,500 HV, and technical ceramics go even higher.

Hardness, strength and toughness are not the same thing

Hardness and tensile strength correlate in steels, because both reflect resistance to plastic flow. Three relationships are used in practice:

Relationship	Expression	Source
Callister's rule	UTS (MPa) ≈ 3.45 × HB	Callister and Rethwisch
Pavlina and Van Tyne	UTS = −99.8 + 3.734 × HV; yield = −90.7 + 2.876 × HV (MPa)	J. Mater. Eng. Perform. 17 (2008) 888-893
Mitutoyo table (E140)	tabulated value from 32 to 58 HRC	Bulletin 2059

The three do not agree, and that is the point. An example: a batch of quenched and tempered 4140 shafts measured 40 HRC, that is, 392 HV and 371 HB. The table gives 1,255 MPa, Callister's rule 3.45 × 371 = 1,280 MPa, and Pavlina −99.8 + 3.734 × 392 = 1,364 MPa. That is about 8% difference between them. To confirm the ultimate tensile strength, a tensile test is run on a 10 mm diameter test specimen (78.5 mm² area): the expected breaking force is between 98.6 and 107.1 kN. A 50 kN universal testing machine cannot break this specimen, and even a 100 kN machine is at its limit; the 100 to 200 kN dual-column model, in the 150 or 200 kN version, breaks it with margin to spare, and the software plots the complete stress-strain curve. Hardness is the screening; the design value comes from the tensile test.

Hardness and toughness usually move in opposite directions. Toughness is the energy a material absorbs before fracturing. Diamond has about 10,000 HV and a fracture toughness of only 3.4 MPa√m; glass and ceramics are hard and break all at once. In steel, tempering at a low temperature keeps hardness high and reduces the energy absorbed in the impact test; tempering at a high temperature does the opposite. A cutting tool is specified by hardness; a crane hook, by toughness.

Hardness and stiffness are also different things. The modulus of elasticity of steel is around 200 GPa whether annealed or hardened: heat treatment takes 4140 from 197 HB to over 50 HRC and barely changes its stiffness. A hardened part does not deflect less than an annealed one under the same elastic load; it only withstands more before deforming permanently.

Hardness of other materials

In Vickers, almost all materials can be placed on the same scale. The chart, on a logarithmic scale, runs from tin (5 HV) to diamond (10,000 HV), with the types of materials shown by color.

High-hardness materials. At the top of the scale are technical ceramics: alumina, silicon carbide, cubic boron nitride and diamond. Their hardness comes from ionic and covalent bonds, which allow almost no plastic deformation; the price is brittleness, which is why they serve as abrasives, cutting tools and coatings, not as parts subjected to impact. Among metals, hardness depends more on the alloy and the treatment than on the base metal. In stainless steel, austenitic grades (such as 304) do not harden by quenching, only by cold working, and stay in the low range; martensitic grades (such as 420) are hardenable and reach the range of hardened steels. The titanium alloy Ti-6Al-4V is chosen for its strength-to-weight ratio and corrosion resistance, but its hardness is that of a medium steel, not a tool steel.

Low-hardness materials. Pure metals such as tin, lead, copper and aluminum are soft; aluminum gains hardness from alloying elements and from aging, which is why its alloys cover a wide range. Polymers sit below metals, and rubbers below everything: in them, low hardness is precisely what gives flexibility and impact absorption, and it is measured in Shore A, from about 20 to 80 for silicone rubbers depending on the formulation. Wood is also a low-hardness material, with values on the order of a few Brinell units.

The table summarizes the typical Vickers hardness of each family:

Material	Typical Vickers hardness
Polymers (PP, PVC, epoxy)	7 to 45 HV
Copper	40 HV
Aluminum alloys	25 to 140 HV
Low-carbon steel	140 to 280 HV
Austenitic stainless steel	180 to 400 HV
Titanium Ti-6Al-4V	320 to 380 HV
Soda-lime glass	490 HV
Tool steel	700 to 1,000 HV
Cemented carbide (WC)	1,500 to 2,500 HV
Silicon carbide	2,400 to 2,800 HV
Cubic boron nitride	about 4,500 HV
Diamond	about 10,000 HV

The numbers are orders of magnitude: each value depends on the alloy, the treatment and the test load. Polymers appear in Vickers only for comparison: in practice they are specified in Shore, and their tensile and compressive behavior is measured on universal testing machines of 2 to 10 kN.

Solved hardness exercises

1. Vickers. In an HV30 test (F = 30 kgf = 294.2 N), the measured diagonals were 0.398 mm and 0.402 mm. The mean is d = 0.400 mm and d² = 0.160 mm². So HV = 0.1891 × 294.2 / 0.160 = 348 HV30. From the table, it falls between 354 HV (36 HRC) and 318 HV (32 HRC), that is, about 35 HRC, with an estimated tensile strength of 1,200 MPa by Pavlina.

2. Brinell. 10 mm ball, 3,000 kgf load (29,420 N), indentation with d = 4.00 mm. First, √(D² − d²) = √(100 − 16) = 9.165 mm, so D − 9.165 = 0.835 mm. The area is πD × 0.835 = 26.23 mm². So HBW = 0.102 × 2 × 29,420 / 26.23 = 229 HBW 10/3000, and the tensile strength by Callister's rule is 3.45 × 229 ≈ 790 MPa.

3. Rockwell. The hardness tester recorded a permanent depth of 0.100 mm on the C scale. What is the hardness? HRC = 100 − 0.100 / 0.002 = 100 − 50 = 50 HRC, which from the conversion table is equivalent to 513 HV and 481 HB. Compare with the 0.080 mm of a 60 HRC part: the harder the part, the shallower the indentation.

4. Interpolating in the table. A shaft measured 45 HRC, a value not in the table. It lies halfway between 44 HRC (434 HV, 409 HB, 1,434 MPa) and 46 HRC (458 HV, 432 HB, 1,524 MPa), so you take the average of the neighboring rows: about 446 HV, 420 HB and 1,480 MPa of estimated tensile strength, with the ±5% uncertainty of the conversion itself.

Common mistakes about hardness

1. Giving the number without the scale. "Hardness 60" can be 60 HRC (tool steel), 60 HRB (brass) or 60 Shore A (rubber).
2. Converting with the wrong table. The steel table does not apply to austenitic stainless steel, aluminum or copper.
3. Using HRC below 20. Out of range; use HB or HRB. Annealed 4140 has 197 HB, not "13 HRC".
4. Stating a steel's hardness without its condition. Annealed, normalized or quenched and tempered changes everything.
5. Confusing hardness with toughness or stiffness. Glass is hard and brittle; hardened steel has the same modulus of elasticity as annealed steel.
6. Measuring a thin case with Rockwell. A carburized or nitrided case calls for Vickers or Knoop microhardness on a polished cross section.
7. Estimating the strength of steel above 58 HRC from the table. It is not tabulated, and the estimates differ by about 15%.

Hardness standards

• ASTM E140-12b(2019)e1: hardness conversion tables for metals (Brinell, Vickers, Rockwell, Knoop, scleroscope and Leeb).
• ISO 18265:2013: conversion of hardness values for metallic materials.
• ASTM E10-23, E18-25 and E92-26: Brinell, Rockwell, and Vickers and Knoop methods. In Brazil, the adoptions ABNT NBR ISO 6506-1:2019, 6508-1 and 6507-1.
• ASTM E110-14(2023): Rockwell and Brinell with portable hardness testers.
• ASTM D2240-15(2021): Shore hardness of rubbers and plastics.