Steel Hardness Conversion Calculator — HRC, HV, HB, HRB, and UTS per ASTM E140

Hardness testing is one of the most widely used mechanical property measurements in engineering — fast, non-destructive on bulk material, and closely correlated to tensile strength and wear resistance in steels. Yet the four major scales in everyday use (Rockwell C, Vickers, Brinell, Rockwell B) measure fundamentally different quantities and cannot be converted exactly between one another. The conversion tables in ASTM E140-12b provide standardised empirical correlations for wrought carbon and alloy steels; this calculator implements those tables, adds approximate UTS estimation per the Brinell–tensile strength relationship, and checks results against key code hardness limits including NACE MR0175/ISO 15156 sour service and ASME Section IX weld HAZ requirements.

The Four Major Hardness Scales: Principles and Valid Ranges

Each hardness scale measures the resistance of a material to permanent indentation, but the indenter geometry, applied load, and measurement methodology differ substantially between scales. These differences are the fundamental reason why conversions are empirical rather than exact.

Vickers Hardness (HV)

The Vickers test uses a square-based diamond pyramid indenter with a 136° face angle. A defined load (from 1 gf to 100 kgf) is applied for 10–15 seconds, and the diagonal lengths of the resulting square indentation are measured optically. Vickers hardness is calculated as:

HV = 1.854 × F / d²

Where:
  F  = applied load (kgf)
  d  = mean diagonal of indentation (mm)
  1.854 = geometric constant for 136° pyramid

Load suffix conventions:
  HV5    = 5 kgf load       (standard desktop tester)
  HV10   = 10 kgf load      (standard for HAZ testing per NACE / ISO 9015-1)
  HV0.3  = 300 gf load      (microhardness, case depth profiles)
  HV0.05 = 50 gf load       (thin coatings, individual phases)

Valid range: HV 1 – 2000+ (single continuous scale)
Advantages: wide range, thin sections, precise positioning, case depth profiling

The Vickers scale is the only scale that covers the full hardness range from very soft (annealed aluminium, HV 15) to extremely hard (cemented carbide, HV 1800) without a scale change. This makes it the preferred laboratory reference scale and the scale used for microhardness testing of case-hardened layers, welds, and HAZ profiling. For a full treatment of all hardness testing methods including equipment calibration and test procedure requirements, see the dedicated guide.

Rockwell Hardness (HRC, HRB, HRA)

The Rockwell test measures the depth of permanent penetration under a defined load. A minor load (10 kgf) is first applied to seat the indenter, the depth is zeroed, then the major load is applied and removed, and the residual penetration depth (after minor load re-engagement) is measured directly — no optical measurement is required. This makes Rockwell the fastest hardness test method for production quality control.

Rockwell C (HRC):
  Indenter: 120° diamond Brale cone
  Minor load: 10 kgf;  Major load: 150 kgf total
  HRC = 100 − (h / 0.002 mm)      [each 0.002 mm penetration = 1 HRC unit]
  Valid range: HRC 20–67
  Applicable: through-hardened steels, tool steels, case-hardened parts

Rockwell B (HRB):
  Indenter: 1/16" (1.588 mm) steel ball
  Minor load: 10 kgf;  Major load: 100 kgf total
  HRB = 130 − (h / 0.002 mm)
  Valid range: HRB 0–100
  Applicable: soft steels, brass, aluminium, annealed metals

Rockwell A (HRA):
  Indenter: 120° diamond Brale cone
  Minor load: 10 kgf;  Major load: 60 kgf total
  HRA = 100 − (h / 0.002 mm)
  Valid range: HRA 60–85
  Applicable: cemented carbides, case-hardened surfaces, thin sheet

Brinell Hardness (HBW)

The Brinell test presses a 10 mm tungsten carbide ball (HBW) into the test surface under a 3000 kgf load for 10–15 seconds. The hardness is calculated from the diameter of the residual indentation:

HBW = (2F) / (π × D × (D − √(D² − d²)))

Where:
  F  = applied load (kgf) = 3000 kgf for standard steel test
  D  = ball diameter (mm) = 10 mm standard
  d  = mean indentation diameter (mm), measured with calibrated optical scale

Valid range: HBW 60–739 (practical upper limit for WC ball)
Advantages:
  — Large indent (3–5 mm diameter) averages heterogeneous microstructure
  — Well-suited to castings, forgings, coarse-grained materials
  — Indent permanently visible for re-measurement or documentation
Disadvantages:
  — Cannot be used on finished surfaces (large indent)
  — Cannot measure thin sections or case-hardened layers
  — Slow (requires optical measurement after indentation)

ASTM E140 Conversion Method and Limitations

ASTM E140-12b (Standard Hardness Conversion Tables for Metals) provides tabulated conversions between all major hardness scales for several material categories. Table 2 covers non-austenitic steels (carbon and alloy steels) and is the basis for the conversions in this calculator. The table was derived from extensive experimental measurement programmes correlating simultaneously measured hardness values on the same specimens in multiple scales.

Polynomial Regression Equations Used in This Calculator

HV → HRC (valid HV 226–900, wrought carbon/alloy steel):
  HRC = −78.506 + 0.3494×HV − 0.0002506×HV²  (fitted to ASTM E140 Table 2)

HV → HBW (valid HV 80–740):
  HBW = −0.001388×HV² + 1.2115×HV − 21.11   (fitted to ASTM E140 Table 2)

HV → HRB (valid HV 80–226):
  HRB = 40.614 + 0.1804×HV + 0.001356×HV²   (fitted, lower hardness range)

HV → HRA (valid HV 226–900):
  HRA = 52.80 + 0.07168×HV − 0.0000267×HV²

UTS estimate (wrought steel, HBW 100–400):
  UTS (MPa) = 3.45 × HBW
  UTS (ksi)  = 0.500 × HBW

All input scales are first converted to HV using inverse relationships,
then all outputs are derived from HV as the common reference scale.

Inverse conversions (input → HV):
  HRC → HV: HV = 1041.43/(67.0−HRC) − 4.72   (approximation, valid HRC 20–65)
  HBW → HV: HV = 1.0563×HBW + 3.20            (linear, valid HBW 60–600)
  HRB → HV: HV = (HRB − 40.614)/0.1804         (simplified linear, valid HRB 40–100)
  HRA → HV: solved numerically from HRA equation above

NACE MR0175 / ISO 15156 Hardness Limits

The most practically important code hardness limit in the oil and gas and pressure equipment industries is the NACE MR0175/ISO 15156 maximum hardness for carbon and low-alloy steel in sour service (H₂S-containing environments). The limit is 22 HRC, with the following equivalences across scales per ASTM E140:

NACE MR0175 / ISO 15156 Part 2 — Carbon and Low-Alloy Steel Hardness Limit:

  Maximum hardness:  22 HRC  ≡  248 HV10  ≡  237 HBW

  Which scale to use:
  — Base metal (large section): HRC or HBW acceptable
  — Weld HAZ (narrow zone): HV10 required (ISO 9015-1 / ASTM E384)
    Small indent allows precise positioning within HAZ sub-zones
    HV10 load (10 kgf) produces ~0.10–0.15 mm indent diagonal — adequate for
    ~0.5 mm wide CGHAZ in most structural steels
  — Production quality control on pipe and fittings: HRC or HB per purchaser spec

  Conversion path for reporting:
    HV10 measurement on weld cross-section → Convert to HRC using ASTM E140
    Record BOTH values: "248 HV10 (≡ 22 HRC per ASTM E140)"

  Common mistake: applying Rockwell C directly to HAZ
    — The HRC indent is ~1.5 mm deep and samples an area ~4–5 mm wide
    — This is too large to isolate the narrow CGHAZ and ICHAZ sub-zones
    — Report HV10 as primary measurement; HRC equivalent as reference only

The 22 HRC limit applies to the base metal, weld metal, and all HAZ sub-zones (CGHAZ, FGHAZ, ICHAZ) in butt welds, fillet welds, and partial penetration welds. For duplex stainless steel and austenitic stainless steel, Part 3 of ISO 15156 specifies different hardness limits (typically 28–36 HRC depending on alloy and condition) and different test requirements. The relationship between HAZ hardness and hydrogen-induced cracking is explained in detail in the linked article.

Hardness–Tensile Strength Relationship

The Brinell–tensile strength correlation is one of the most widely used empirical relationships in materials engineering. It arises from the physical similarity between the hardness test and a constrained plastic flow process: both the hardness indentation and the tensile necking region involve triaxial stress states and large plastic strains, and both are dominated by the flow stress of the material.

Primary relationship (Tabor, 1951):
  UTS (MPa) = C × HBW
  UTS (ksi)  = C_imp × HBW

  For wrought carbon and alloy steels (HBW 100–400):
    C = 3.45    → UTS (MPa) = 3.45 × HBW       (ASTM E140 Annex A)
    C_imp = 0.500 → UTS (ksi) = 0.500 × HBW

  Accuracy:  ±10–15% for within-class steels
  Range:     HBW 100–400 → UTS 345–1380 MPa

Why the relationship works for steel:
  — Both UTS and hardness scale with carbon content and work hardening rate
  — Hardness ∝ flow stress at ~8% plastic strain
  — UTS ∝ maximum flow stress before necking (Considère criterion)
  — For steels with similar work-hardening exponents, ratio ≈ constant

Where it FAILS (do not use for these materials):
  Grey cast iron:        C ≈ 1.3–1.6 (lower — graphite flakes affect indent)
  Austenitic stainless:  C ≈ 3.4–3.8 (similar range but higher scatter)
  Aluminium alloys:      C ≈ 0.27–0.35 (much lower — different modulus)
  Copper alloys:         C ≈ 0.45–0.55 (different deformation mechanism)
  Case-hardened surfaces: NOT valid — indent averages case + core

Alternative for different steels:
  Low-alloy structural (normalised): UTS ≈ 3.3 × HBW
  Cold-worked stainless 304:         UTS ≈ 3.1 × HBW
  High-strength Q+T (HBW > 350):    Use Vickers + direct tensile testing

Comprehensive Hardness Conversion Reference Table

Hardness Testing in Practice: Inspection and QC Applications

Hardness Testing of Welds and HAZ

Post-weld hardness testing verifies that the weld metal and HAZ have not exceeded the maximum hardness specified by the applicable code or material specification. ISO 9015-1 specifies weld hardness testing procedures for arc-welded joints; it requires a traverse of Vickers HV10 indentations across the weld cross-section including weld metal, HAZ, and base metal, at defined spacings. The maximum hardness location in the CGHAZ (coarse-grained HAZ) typically occurs approximately 0.5–1.0 mm from the fusion line; the traverse spacing must be fine enough to capture this peak. For NACE sour service qualification, API 1104 and ISO 15614-1 specify the number of traverses, indent spacing, and acceptance criteria.

Portable Hardness Testing (Leeb / Rebound)

For in-service inspection of pressure vessels, storage tanks, and structural components where bench testing is impossible, portable Leeb (rebound) hardness testers are standard. The instrument fires a spring-loaded tungsten carbide ball against the surface and measures the ratio of rebound to impact velocity (Leeb value HL). Built-in conversion algorithms translate HL to HRC, HV, or HBW per ASTM A956 / ISO 16859. Key practical requirements for reliable results:

• Surface finish Ra ≤ 3 μm (grind or polish to this level if rougher)
• Material thickness ≥ 10 mm, or backed solidly to prevent vibration
• At least 5 individual readings, discard outliers, use the mean
• Use the correct material group setting in the instrument (steel, cast iron, aluminium, etc.)
• Never use results from curved surfaces without applying the curvature correction factor from the instrument manual

Case Depth Verification by Hardness Traverse

The effective case depth after carburising, nitriding, or induction hardening is defined as the depth at which hardness drops to a specified value — typically 550 HV for carburised steel per ISO 2639 (effective case depth), or 50% above the core hardness for induction-hardened components. Vickers microhardness traverses (HV0.3 or HV0.5) from the surface toward the core are the standard method. The traverse spacing must be ≤ 0.1 mm in the case layer to accurately determine the depth at which the hardness threshold is crossed. For the metallurgical context of case hardening processes and their effects on microstructure and hardness profiles, the martensite formation and quenching and tempering guides provide the relevant background.

Frequently Asked Questions

Recommended References and Tools

Further Reading