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Ac1, Ac3 and Ms calculator

The austenitising window and the martensite-start temperature for a steel, from its composition, using the Andrews (1965) equations. It also tells you when your steel sits outside the range those equations were fitted to — which is the part most calculators leave out.

Composition

Weight percent. Leave an element blank if it is not present or not reported.

Load a typical composition

Austenitising window

Andrews (1965), composition in wt %

Ac1 — austenite starts—
Ac3 — fully austenitic—
Ms — martensite starts—
Typical austenitise (Ac3 + 30–70)—
Temper below (Ac1 − 30)—
—

Take this composition further. The same chemistry, with your route, heat treatment and section thickness, gives yield, tensile, hardness, elongation and fatigue life — each with its uncertainty, and a plain statement of where the model is weak. Open it in METALLAI with this composition →

How it is calculated

These are the expressions METALLAI uses internally, written out so you can check them. Two of the three are routinely mis-transcribed, so they are worth reading carefully.

Ac1 = 723 − 10.7·Mn − 16.9·Ni + 29.1·Si + 16.9·Cr + 290·As + 6.38·W Ac3 = 910 − 203·√C − 15.2·Ni + 44.7·Si + 104·V + 31.5·Mo + 13.1·W − 30·Mn − 11·Cr − 20·Cu + 700·P + 400·Al + 120·As + 400·Ti Ms = 539 − 423·C − 30.4·Mn − 17.7·Ni − 12.1·Cr − 7.5·Mo − 7.5·Si + 10·Co

Two things to notice

Source: K. W. Andrews, “Empirical formulae for the calculation of some transformation temperatures”, Journal of the Iron and Steel Institute 203 (1965) 721–727.

Validity envelope

Andrews fitted these to low-alloy steels. The commonly quoted envelope is:

ElementFitted up to (wt %)
Carbon0.6
Chromium2.5
Nickel5
Molybdenum1
Manganese2
Outside that envelope the equations still return a number, and it is an extrapolation. Try the 410 stainless preset above: at 12.5 % chromium the result is far outside the fit, and the calculator says so rather than quietly handing you a temperature. For tool steels, martensitic stainless, bearing steels and maraging grades, use the alloy datasheet or a dilatometry measurement — and note that many of those grades are deliberately austenitised well above Ac3 for carbide dissolution or secondary hardening, so Ac3 + 30 is not the right target anyway.

What the numbers are for

Tempering must stay below Ac1

Above Ac1 the steel re-austenitises, and on cooling that fresh austenite becomes untempered martensite — so instead of tempering the part you have re-hardened part of it. A margin of about 30 °C is normal, because the calculated Ac1 is itself an estimate.

Full austenitising sits above Ac3

Heating into the Ac1–Ac3 range gives a partly-ferritic structure and, after quenching, mixed hardness. Normal practice is Ac3 + 30 to +70 °C: high enough to be fully austenitic with a margin, low enough to avoid grain growth.

Ms tells you what you will retain

Carbon dominates Ms. A low Ms means the transformation may not complete before room temperature, leaving retained austenite — which is why high-carbon and high-alloy steels are sometimes given a sub-zero treatment. Martensite finish is roughly Ms − 215 °C.

Questions

What are Ac1 and Ac3?
On heating, Ac1 is where austenite starts to form and Ac3 is where the transformation completes and the steel is fully austenitic. Between them it is part ferrite, part austenite. Austenitising is run above Ac3; tempering must stay below Ac1.
How do you calculate Ac1 and Ac3 from composition?
With the Andrews (1965) empirical relations shown above, composition in weight percent and results in °C. Watch two things: Ac1 has no Mo term, and Ac3's Cr term is negative (−11 per wt %). Both are commonly mis-transcribed, and the Cr error grows with alloy content.
When do the Andrews equations stop being valid?
Outside roughly C ≤ 0.6, Cr ≤ 2.5, Ni ≤ 5, Mo ≤ 1, Mn ≤ 2. Tool steels, martensitic stainless, bearing steels and maraging grades all sit outside it. The formula still returns a smooth number, but it is an extrapolation — this calculator flags it instead of hiding it.
What is the Ms temperature?
The temperature at which austenite begins transforming to martensite on cooling. Ms = 539 − 423C − 30.4Mn − 17.7Ni − 12.1Cr − 7.5Mo. Carbon dominates. A low Ms means retained austenite at room temperature.
Why must tempering stay below Ac1?
Because above Ac1 the steel starts to re-austenitise, and that fresh austenite becomes untempered martensite on cooling. You end up with brittle as-quenched martensite in a part you believed you had tempered. Keep about 30 °C of margin.

A temperature is not a heat treatment

METALLAI takes the same composition plus your actual route and schedule and predicts yield, tensile, hardness, elongation and fatigue life — and refuses the combinations that cannot work, like a temper above Ac1.

Run the full prediction — free Carbon equivalent calculator