Hardenability (Jominy) Calculator
The Jominy end-quench test produces a hardness profile that decays with distance from the quenched end as martensite fraction decreases. A simple exponential model HRC(x) = H_min + (H_max - H_min) * exp(-x / lambda) approximates many common steel hardenability curves, where H_max is the hardness at the quenched end, H_min is the fully annealed hardness (approximately 20 to 25 HRC for medium-carbon steels), and lambda is the hardenability length constant. Enter H_max (HRC at J1/16 = 1), H_min (asymptotic hardness), the hardenability constant lambda (mm), and a distance x to estimate HRC at that position.
Jominy hardenability model
HRC(x) = H_min + (H_max - H_min) * exp(-x / lambda)
Where H_max is the maximum (quench-end) hardness, H_min is the annealed base hardness, lambda is the hardenability length constant (mm), and x is the distance from the quenched end (mm). This is a simplified exponential approximation; the actual Jominy curve of a specific steel grade must be measured per ASTM A255.
Using Jominy data for heat treatment selection
By comparing Jominy curves for candidate steels against the required minimum hardness at the critical cross-section location, engineers select the grade with the least hardenability that still meets the specification. Excessive hardenability increases distortion risk, quench crack risk, and alloy cost. The ASTM A255 test provides Jominy H-band data (minimum and maximum hardness limits for each grade) enabling specification conformance testing.
Hardenability and Jominy test: frequently asked questions
What is the Jominy end-quench test?
The Jominy end-quench test (ASTM A255) measures hardenability by water-quenching one end of a standard 25 mm diameter bar and measuring Rockwell C hardness at 1/16-inch intervals from the quenched end. The hardness profile reveals how deeply a steel can be hardened.
What does hardenability mean in practice?
Hardenability describes how deeply and uniformly a steel can be hardened by quenching. High hardenability means hardness is maintained deeper into large sections. It is primarily controlled by alloying elements (Mn, Cr, Mo, Ni) and carbon content. Hardenability is not the same as maximum hardness, which depends only on carbon content.
How is the Jominy distance related to cooling rate?
Each Jominy distance corresponds to a specific cooling rate. The quenched end cools fastest (equivalent to a still water quench). At increasing distances from the quenched end, cooling rates slow progressively, simulating the interior of larger bars and different quenching media.
What is the ideal critical diameter (D_I)?
The ideal critical diameter D_I is the diameter of a bar that would harden completely to 50% martensite at its center under an ideal (infinite-severity) quench. It provides a single number to compare hardenability across steels. High-hardenability steels for large shafts or dies require D_I values of 100 mm or more.
Can the Jominy curve predict hardness in an actual part?
Yes, approximately. By correlating Jominy distance to equivalent cooling rates at specific locations in round bars of different diameters under different quench severities, the Jominy curve predicts as-quenched hardness throughout the cross-section. Charts from ASM or ASTM A255 facilitate this conversion.
Official sources
- ASTM A255, "Standard Test Methods for Determining Hardenability of Steel": astm.org.
- ASM International, "ASM Handbook Vol. 4A: Steel Heat Treating Fundamentals and Processes": asminternational.org.
- NIST, "Hardenability of Carbon and Alloy Steels": nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.