Why hardness scales do not convert exactly
Each hardness test measures resistance to a specific indenter under a specific load, and reports a number defined by its own equation. Brinell presses a 10 mm ball with 3,000 kgf and divides load by the curved area of the dent. Vickers presses a 136° diamond pyramid and divides load by the area of the square impression. Rockwell C presses a 120° diamond cone and reports the depth difference between a minor and a major load, on an inverted arbitrary scale. Rockwell B does the same with a 1/16 in ball.
Because they load different volumes of material to different depths and report different physical quantities, there is no derivation that turns one into another. What exists is measurement: thousands of specimens tested on several scales, correlated, tabulated and published as ASTM E140. Those tables are what every conversion chart, including this one, is built from.
The consequence is that a conversion carries real uncertainty, typically a few points of HRC. It also depends on the material. E140 gives separate tables for non-austenitic steels, austenitic stainless, nickel and high-nickel alloys, cast iron and copper alloys, and the numbers differ meaningfully between them. This calculator implements the non-austenitic steel correlation, which covers carbon steels, alloy steels and tool steels. Applying it to 304 stainless or to grey iron will give an answer, and that answer will be wrong.
How the conversion is actually done
This page uses Vickers as a pivot scale, for a practical reason: HV is defined continuously from soft annealed steel at about 84 HV up to fully hardened tool steel at 940 HV, using one indenter geometry throughout. Rockwell C and Rockwell B each cover only part of that span, and Brinell tops out where the ball begins to flatten.
So a reading is first mapped onto Vickers, then mapped out to every other scale. Between the published anchor points the calculator interpolates linearly. The anchors are sampled at 5-point intervals of Rockwell C over the hardened range and at 20-point intervals of Brinell over the soft range, so interpolated values between anchors carry slightly more uncertainty than the anchors themselves.
Each scale's own defining formula is worth knowing, because it explains the limits. Vickers is HV = 1.8544 F / d², with load in kgf and the mean diagonal in mm; because the pyramid is geometrically similar at all depths, HV is nearly independent of load. Brinell is HB = 2F / (πD(D − √(D² − d²))), and as the material gets harder the impression gets small enough that measuring its diameter accurately becomes the limiting factor, which is why standard Brinell stops in the region of 650 HB even with a carbide ball.
Rockwell has no area calculation at all — it reports indentation depth on an inverted scale, which is why it is fast and why it saturates. Above about 100 HRB the ball indenter deforms and the reading stops responding; below about 20 HRC the diamond cone barely penetrates differently between specimens. Those are the reasons this calculator returns nothing rather than a number outside those ranges.
The tensile estimate uses the long-established rule that ultimate tensile strength in psi is roughly 500 times the Brinell number, equivalently about 3.4 times HB in MPa. It applies to steels and is normally quoted up to around 400 HB; beyond that it progressively overstates strength, because heavily hardened steels fail before reaching the strength their hardness would imply.
Worked example: converting a 45 HRC shaft
A quenched and tempered 4140 shaft measures 45 HRC on a bench tester, and the drawing specifies Brinell. Work it through the anchors.
- Find the Vickers pivot. The correlation gives 45 HRC = 446 HV directly at an anchor point, so no interpolation is needed.
- Map Vickers to Brinell. The paired anchor is 446 HV = 421 HB. That is the number to record against the drawing.
- Estimate tensile strength. 500 × 421 = 210,500 psi = 210.5 ksi, or 210.5 × 6.895 = 1,451 MPa.
- Check the caveat. 421 HB is above the 400 HB point where the 500 × HB rule starts to overstate, so treat 210 ksi as an upper estimate and expect the certified tensile to come in somewhat below it.
Now take an intermediate reading. A part measures 47 HRC, which falls between the 45 and 50 anchors at 446 and 513 HV. Interpolating: 446 + (513 − 446) × (47 − 45) ÷ (50 − 45) = 446 + 67 × 0.4 = 472.8 HV. Mapping that back onto Brinell between the 421 and 481 anchors: 421 + (481 − 421) × (472.8 − 446) ÷ (513 − 446) = 421 + 60 × 0.4 = 445 HB. The linear step is what the calculator performs, and it is why a converted value should be quoted to no more precision than the input justifies — 445 HB, not 445.0 HB.
What a hardness number tells you, and what it does not
Hardness is fast, cheap and non-destructive, which is why it is the workhorse of incoming inspection and heat treatment control. It correlates well with tensile strength in steel, reasonably with wear resistance, and inversely with machinability. A 4140 shaft at 28–32 HRC machines readily; the same part at 45 HRC needs carbide and rigid setups; above 55 HRC most shops grind rather than cut.
Typical values give context. Hot-rolled mild steel arrives around 120–150 HB. Normalised medium-carbon steel runs 170–220 HB. Quenched and tempered 4140 lands anywhere from 28 to 50 HRC depending on tempering temperature. Case-hardened gear teeth reach 58–62 HRC at the surface with a soft core. Fully hardened and lightly tempered tool steels sit at 60–65 HRC, and file-hard is around 65.
What hardness does not tell you is toughness, ductility, or fatigue behaviour. Two steels at 45 HRC can have very different impact energies depending on alloy and tempering route, and tempering in the embrittlement range can produce a part that is perfectly hard and dangerously brittle. Hardness also says nothing about depth: a case-hardened part reads high at the surface and low a millimetre down, which is exactly the point of case hardening but means a single surface reading describes only the surface.
Two measurement cautions matter more than the conversion arithmetic. First, the reading must be taken on a properly prepared, flat, adequately supported surface at least two and a half indentation diameters from any edge, and three from any previous indentation. Second, the specimen must be thick enough that the indentation does not affect the far side — roughly ten times the depth for Rockwell. A thin part on a hard anvil reads high, and no conversion table can rescue that.
Approximate hardness equivalents for non-austenitic steels
| Rockwell C | Vickers HV | Brinell HB | Approx. tensile (ksi) | Approx. tensile (MPa) | Typical condition |
|---|---|---|---|---|---|
| 20 | 238 | 226 | 113 | 779 | Normalised medium-carbon steel |
| 25 | 266 | 253 | 127 | 872 | Q&T alloy steel, high temper |
| 30 | 302 | 286 | 143 | 986 | 4140 tempered around 620 °C |
| 35 | 345 | 327 | 164 | 1127 | General machinery shafting |
| 40 | 392 | 371 | 186 | 1279 | Highly stressed shafting |
| 45 | 446 | 421 | 211 | 1451 | Q&T alloy steel, low temper |
| 50 | 513 | 481 | 241 | 1658 | Tool steel, tempered |
| 55 | 595 | 560 | 280 | 1930 | Die steel working hardness |
| 60 | 697 | 654 | 327 | 2255 | Case-hardened surface, bearing races |
| 65 | 832 | 739 | 370 | 2548 | Fully hardened tool steel |
Rockwell C is not defined below 20; use Rockwell B or Brinell there. Tensile estimates above 400 HB extrapolate the 500 × HB rule and overstate strength.
Ways a hardness conversion goes wrong
- Using the steel table on a different material. ASTM E140 publishes separate correlations for austenitic stainless, nickel alloys, cast iron and copper alloys. The numbers differ materially, and using the wrong table is the single most common error.
- Converting a case-hardened surface reading into a bulk property. A 60 HRC case over a 25 HRC core is not a 60 HRC part. Superficial Rockwell scales exist precisely for thin cases, and their conversions are different again.
- Quoting converted values as measured values. A specification that calls for Brinell should be verified with a Brinell test. A converted number is evidence, not a certificate, and many quality systems will not accept it.
- Testing too close to an edge or a previous indentation. The material must be able to flow around the indenter. Keep at least two and a half indentation diameters from an edge and three from a prior dent.
- Testing a part too thin for the load. If the indentation influences the far face, the anvil is being measured too. Rockwell needs roughly ten times the indentation depth in thickness.
- Reading Rockwell outside its scale. Rockwell B saturates near 100 and Rockwell C loses resolution below 20. Readings there are not merely hard to convert, they are unreliable measurements.
- Treating the tensile estimate as a certified value. The 500 × HB rule is an approximation for steel with roughly ten percent scatter, and it degrades above 400 HB. Use it to sanity-check, not to design.
Key terms
- HBW
- Brinell hardness measured with a tungsten carbide ball, now the standard designation. Older results using a steel ball were written HBS and are limited to about 450 HB.
- Superficial Rockwell
- Rockwell scales using a 15, 30 or 45 kgf major load instead of 60, 100 or 150. Used for thin sections, cases and coatings, with their own conversion tables.
- Non-austenitic steel
- Carbon, alloy and tool steels with ferritic, pearlitic, bainitic or martensitic structure. The scope of the correlation used on this page.
- Knoop hardness
- A microhardness test using an elongated diamond pyramid, used for very thin layers and brittle materials where a Vickers impression would crack.
Where hardness data feeds the rest of the shop
The tensile strength this page estimates is a direct input elsewhere. Forming force in sheet metal scales with ultimate tensile strength, so an unlabelled coil whose hardness you can measure becomes usable in the press brake tonnage calculator. Base metal strength governs the plate-side check in the fillet weld strength calculator, and hardness is the fastest way to place unlabelled stock into a strength band. And where a joint's cooling rate matters, the welding heat input calculator quantifies the energy that determines what hardness the heat-affected zone ends up with — hardness testing across a weld is the standard way of confirming a procedure did not produce brittle martensite.
Machining decisions follow hardness closely. Cutting speed for a given tool material falls sharply as workpiece hardness rises, which is why speed and feed tables are indexed by hardness band rather than by alloy. A 4140 part at 200 HB and the same part at 45 HRC are effectively two different materials on the machine.
Hardness also underpins the classic wear and fatigue rules of thumb. Rolling contact fatigue life in bearings improves with hardness up to about 60 HRC and falls above it as toughness drops. Endurance limit in steel is often approximated as half the tensile strength up to about 200 ksi, above which it plateaus — another reason the tensile estimate above 400 HB deserves scepticism. For the elastic behaviour that sits underneath all of it, the stress and strain calculator handles stress, strain and Young's modulus, and notably the modulus barely changes with hardness at all: a 20 HRC steel and a 60 HRC steel have essentially the same stiffness.