Ac1 and Ac3 Temperature Calculator — Critical Temperatures for Steel Heat Treatment Design
The Ac1 (lower critical) and Ac3 (upper critical) temperatures are the two most fundamental parameters in ferrous heat treatment design. Ac1 defines the onset of austenite formation on heating — and therefore the maximum safe PWHT temperature, the spheroidising anneal range, and the intercritical zone in weld HAZs. Ac3 defines the completion of austenitisation — and therefore the minimum valid austenitising temperature for hardening and normalising. This calculator implements four validated empirical equations — Andrews (1965), Eldis (1987), Grange (1961), and Trzaska (2016) — to predict Ac1 and Ac3 from steel composition, then derives the full heat treatment window: austenitising range, PWHT maximum, normalising temperature, and intercritical range, with a live annotated phase diagram and step-by-step calculation.
Key Takeaways
- Ac1 = temperature at which austenite begins to form on heating; PWHT must remain 30–50 °C below Ac1 to prevent re-austenitisation.
- Ac3 = temperature at which austenitisation is complete; hardening and normalising require heating to Ac3 + 30–60 °C.
- Carbon is the dominant Ac3 depressant (−203×√%C per Andrews); silicon raises both Ac1 and Ac3 as a ferrite stabiliser.
- Ac1 ≠ Ae1 (equilibrium): the actual transformation on heating is displaced above equilibrium by the finite heating rate; the correction is typically 10–40 °C.
- The intercritical range (Ac1–Ac3) is the target for dual-phase (DP) steel annealing and is the ICHAZ zone in welded joints — the site of Type IV cracking in P91.
- Trzaska (2016) provides improved accuracy for high-alloy steels (Cr–Mo grades, HSLA); Andrews remains the most widely referenced in ASME codes and standards.
+ PWHT window · Austenitising range · Normalising temperature · Live phase diagram
(lower critical)
(upper critical)
Range Width
(Ac1 − 40°C)
(Ac3 + 60°C)
(Ac3 + 30°C)
(Ac1 − 20°C)
(Dual-Phase Anneal)
Physical Meaning of Ac1 and Ac3 in the Fe–C System
The notation Ac1 and Ac3 derives from the French “arrêt chauffage” (heating arrest), referring to the thermal arrests (halts in the heating curve) observed during the pearlite–to–austenite transformation when iron-carbon alloys are heated at a controlled rate. These arrests are measurable by dilatometry (the sample contracts slightly at Ac1 as dense austenite forms from less-dense ferrite and cementite) and differential thermal analysis (endothermic peaks at the transformation temperatures).
The Ac1 Transformation: Pearlite → Austenite
At and immediately above Ac1, the eutectoid reaction reverses: pearlite (a lamellar mixture of α-ferrite and cementite Fe₃C, with composition 0.77%C) transforms to austenite (γ, FCC). The transformation begins at the ferrite–cementite interfaces within pearlite colonies, where the carbon concentration is locally near eutectoid composition. The transformation is diffusion-controlled: carbon must diffuse from cementite lamellae (6.67%C) into the forming austenite and then redistribute throughout the newly formed austenite grains. The rate of this redistribution controls the time-temperature trajectory required for complete austenitisation. In proeutectoid steels (<0.77%C), the ferrite-to-austenite transformation also begins at Ac1 and continues progressively until Ac3 as the remaining proeutectoid ferrite is consumed.
The Ac3 Transformation: Completion of Austenitisation
Above Ac1, the two-phase austenite + ferrite field (intercritical range) narrows with increasing temperature until all ferrite has dissolved into austenite at Ac3. At this point the steel is entirely γ-phase with a relatively uniform carbon distribution (though complete carbon homogenisation requires additional soak time above Ac3). The position of Ac3 on the Fe-C diagram is the A3 boundary — the line separating the α+γ region from the fully γ region. For pure iron (0%C), A3 = 912 °C. As carbon increases toward the eutectoid composition (0.77%C), A3 falls to meet A1 at 727 °C. Alloying elements shift this boundary: austenite stabilisers (Ni, Mn, Cu, N) lower it; ferrite stabilisers (Si, Mo, Cr, W, Al, V, Nb, Ti) raise it.
The Four Empirical Equations: Derivation and Accuracy
Andrews (1965) — The ASME Reference Standard
Andrews (1965) — JISI 203, 721–727:
Ac1 (°C) = 723 − 10.7×%Mn − 16.9×%Ni + 29.1×%Si
+ 16.9×%Cr + 290×%As + 6.38×%W
Ac3 (°C) = 910 − 203×√(%C) − 15.2×%Ni + 44.7×%Si
+ 31.5×%Mo + 13.1×%W − 30×%Mn + 11×%Cr
+ 65×%Nb + 400×%Ti − 20×%Cu
Dataset: Most widely referenced; 66 steels
Accuracy: ±15–25°C for low–alloy steels
Note: No carbon term in Ac1 (carbon has only a second-order
effect on Ac1 in low-alloy steels per Andrews’ analysis)
ASME use: Referenced in ASME Section IX, B31.1, B31.3, and API 582
Element effects on Ac1 (per 1%):
Mn: −10.7°C (austenite stabiliser)
Ni: −16.9°C (strong austenite stabiliser)
Si: +29.1°C (ferrite stabiliser)
Cr: +16.9°C (ferrite stabiliser)
W: +6.38°C (ferrite stabiliser)
Element effects on Ac3 (per 1%):
√C: −203°C (dominant; largest single contribution)
Ni: −15.2°C (austenite stabiliser)
Mn: −30°C (austenite stabiliser)
Cu: −20°C (austenite stabiliser)
Si: +44.7°C (ferrite stabiliser)
Mo: +31.5°C (ferrite stabiliser)
Cr: +11°C (ferrite stabiliser, mild)
Nb: +65°C (strong ferrite stabiliser)
Ti: +400°C (very strong ferrite stabiliser; Ti only valid at trace levels)
Eldis (1987)
Eldis (1987) — Hardenability of Steels (ASM):
Ac1 (°C) = 712 − 17.8×%Mn − 19.1×%Ni + 20.1×%Si
+ 11.9×%Cr + 9.8×%Mo
Ac3 (°C) = 871 − 254.4×√(%C) − 14.2×%Ni + 51.7×%Si
− 14.1×%Mn
Note: More conservative Ac1 and Ac3 predictions than Andrews.
Higher Ni and Mn coefficients for Ac1; fewer elements in Ac3.
Valid for steels with C ≤ 0.6%, Ni ≤ 5%, Mn ≤ 2%.
Useful cross-check for Ni-containing engineering steels.
Grange (1961)
Grange (1961) — ASM Transactions, 54:
Ac1 (°C) = 727 − 10.7×%Mn − 16.9×%Ni + 29.1×%Si
+ 16.9×%Cr
Ac3 (°C) = 910 − 203×√(%C) + 44.7×%Si + 31.5×%Mo
− 30×%Mn + 11×%Cr − 15.2×%Ni
Note: Grange’s Ac1 is the basis for Andrews’ later equation.
Simplified (fewer elements); useful for quick checks.
Good agreement with Andrews for steels without W or Nb.
Trzaska (2016) — Extended Database, Improved High-Alloy Accuracy
Trzaska (2016) — Archives of Metallurgy and Materials, 61:
Ac1 (°C) = 739 − 22.8×%C − 6.8×%Mn + 18.2×%Si
+ 11.7×%Cr + 9.4×%Mo − 13.7×%Ni + 19×%V
Ac3 (°C) = 901 − 206×√(%C) − 16.9×%Ni + 41.7×%Si
+ 27.5×%Mo + 15×%W − 29.1×%Mn + 16.9×%Cr
+ 290×%As − 20×%Cu + 17.8×%Nb + 390×%Ti
Dataset: >1000 steels; broadest calibration range
Accuracy: ±12°C on training data; superior for high-Cr and high-Mo steels
Key diff: Ac1 equation includes carbon term (−22.8×%C) — Andrews omits this.
Carbon slightly lowers Ac1 (confirmed by CALPHAD calculations).
Recommended for P91, P92, P22, duplex SS, and HSLA microalloyed steels.
Alloying Element Effects on Ac1 and Ac3
| Element | Type | ΔAc1 per 1% (Andrews) |
ΔAc3 per 1% (Andrews) |
Physical Mechanism | Most Affected Steel Types |
|---|---|---|---|---|---|
| Carbon (C) | γ-stabiliser | ~0 °C (Andrews) / −22.8°C (Trzaska) | −203×√%C (dominant) | Expands γ field; carbon is interstitial austenite stabiliser; A3 line slopes strongly with C | All steels; most critical variable for Ac3 |
| Manganese (Mn) | γ-stabiliser | −10.7 °C/% | −30 °C/% | Mn partitions to austenite; expands γ field; reduces Gibbs free energy of austenite | High-Mn AHSS, Hadfield steel, structural steels |
| Nickel (Ni) | γ-stabiliser | −16.9 °C/% | −15.2 °C/% | Strong γ-stabiliser; lowers both boundaries substantially | Ni-Cr-Mo alloy steels (4340), 9Ni cryogenic, nickel-base |
| Silicon (Si) | α-stabiliser | +29.1 °C/% | +44.7 °C/% | Si strongly prefers ferrite; raises stability of α phase; rejects from cementite | Spring steels (0.5–2.5%Si), silicon electrical steel, SiMn AHSS |
| Chromium (Cr) | α-stabiliser | +16.9 °C/% | +11 °C/% | Cr stabilises ferrite; forms M7C3/M23C6 carbides; contracts γ loop at high Cr | Cr-Mo steels (P91, P22, H13), stainless, Cr bearing steels |
| Molybdenum (Mo) | α-stabiliser | +9.4 °C/% (Trzaska) | +31.5 °C/% | Mo is strong α-stabiliser; significant Ac3 elevation in Cr-Mo steels; forms M6C and M2C carbides | P91, P92, P22, Cr-Mo pressure vessel steels, tool steels |
| Niobium (Nb) | α-stabiliser | Negligible | +65 °C/% | Very strong α-stabiliser; also grain refiner via NbC/NbN pinning; rarely used above 0.1% | HSLA microalloyed steels, pipeline steels (X60–X80), P91 |
| Titanium (Ti) | α-stabiliser | Negligible | +400 °C/% | Extremely strong α-stabiliser; forms TiC at very high T; valid only at trace levels (<0.05%) | IF steels (grain refiner), some HSLA grades |
| Vanadium (V) | α-stabiliser | +19 °C/% (Trzaska) | Moderate | Ferrite stabiliser; VC/VN precipitation at moderate temperatures | HSLA V-microalloyed, spring steels, H13 tool steel |
| Aluminium (Al) | α-stabiliser | Moderate | +40 °C/% (approx) | Strong α-stabiliser at high Al; closes γ loop at ~2.5%Al; forms AlN at lower levels | Maraging steels, Al-killed structural steels, IF steels |
| Copper (Cu) | γ-stabiliser | Minor | −20 °C/% | Mild γ-stabiliser; precipitation hardening at 400–600 °C; does not enter carbides | Cu-bearing weathering steels (COR-TEN), HSLA Cu grades |
Table 1 — Alloying element effects on Ac1 and Ac3 temperature from the Andrews (1965) and Trzaska (2016) equations. Ferrite stabilisers (Si, Mo, Cr, Nb, V, Ti, Al) raise both critical temperatures; austenite stabilisers (Mn, Ni, Cu) lower them. Carbon has minimal direct effect on Ac1 but is the dominant Ac3 depressant.
Heat Treatment Temperature Windows Derived from Ac1 and Ac3
Full Austenitising (Hardening and Normalising)
For complete austenitisation before quenching (hardening) or air cooling (normalising), the steel must be heated above Ac3. A temperature of Ac3 + 30–60 °C is specified for hardening: the overshoot above Ac3 ensures complete dissolution of residual carbides and provides a driving force for homogenisation of the austenite carbon profile within the available soak time. Insufficient temperature (below Ac3) produces a partially ferritic “soft spot” microstructure after quenching. Excessive temperature (far above Ac3) causes rapid austenite grain growth (above approximately Ac3 + 100 °C for most steels), reducing toughness and fatigue resistance of the hardened product. Normalising is performed at Ac3 + 50–80 °C with soak times of 1 hour per 25 mm section plus 15–30 minutes to allow completion of the austenite transformation, followed by air cooling.
Post-Weld Heat Treatment (PWHT) Maximum Temperature
PWHT must never exceed Ac1 because re-austenitisation would occur in the highest-temperature zones of the heated band, producing fresh untempered martensite on cooling after PWHT. The consequences depend on steel grade:
- Low-alloy structural steels (Ac1 ≈ 710–760 °C): PWHT at 580–650 °C provides a comfortable 60–100 °C margin. ASME B31.1 specifies PWHT at 595–650 °C for P-No. 1 carbon steel, comfortably below Ac1.
- P91 / Grade 91 (Ac1 ≈ 815 °C): PWHT at 730–775 °C provides a 40–85 °C margin — this is why P91 PWHT temperature is much higher than for P1 carbon steel, reflecting its higher Ac1 from the 9%Cr + Si + V additions. See the P91 creep-resistant steels guide for full PWHT protocol.
- Duplex stainless steels (Ac1 ≈ 600–650 °C estimated): Very limited PWHT window; solution treatment rather than PWHT is used for post-weld microstructure restoration.
Intercritical Annealing for Dual-Phase (DP) Steel
Dual-phase steel manufacturers intercritically anneal cold-rolled sheet at a temperature between Ac1 and Ac3 to produce a mixture of austenite and ferrite. On rapid cooling, the austenite transforms to martensite while the ferrite remains, creating the characteristic DP microstructure of soft ferrite plus hard martensite islands. The austenite fraction at the intercritical temperature follows the lever rule:
Austenite fraction at intercritical temperature T (Lever Rule):
f_γ = (C_α − C_bulk) / (C_α − C_γ)
Where:
C_α = carbon solubility in ferrite at T (very small: ~0.01–0.02%C)
C_γ = carbon concentration in austenite at T (from A3 boundary)
C_bulk = bulk steel carbon content
Simplified: f_γ ≈ (T − Ac1) / (Ac3 − Ac1) × C_correction_factor
Approximate austenite fraction vs. intercritical position:
T = Ac1 + 0.1×(Ac3−Ac1): f_γ ≈ 10–20% (low-martensite DP)
T = Ac1 + 0.5×(Ac3−Ac1): f_γ ≈ 50% (DP600/DP780 typical)
T = Ac1 + 0.9×(Ac3−Ac1): f_γ ≈ 80–90% (high-martensite DP)
Target martensite fraction (= f_γ after rapid cooling):
DP600: ~25–35% martensite
DP780: ~40–55% martensite
DP980: ~60–80% martensite
Spheroidising Annealing
Spheroidising annealing at Ac1 − 10 to Ac1 − 40 °C (just below the austenite transformation temperature) converts lamellar pearlite cementite to spherical carbide particles within a ferrite matrix. This produces the softest possible condition (minimum hardness, maximum ductility and machinability) for high-carbon steels (0.6–1.2%C, tool steels, bearing steels) before cold forming or machining. Long soaking times (4–20 hours) at just below Ac1 are required to allow Ostwald ripening of the carbide particles. Temperatures must not exceed Ac1 because partial austenitisation (at Ac1 or above) re-creates lamellar pearlite on slow cooling instead of the desired spheroidal structure.
Worked Example: P91 Steel Critical Temperatures
P91 (Grade 91) Steel — Nominal Composition:
0.10%C, 0.45%Mn, 0.35%Si, 8.90%Cr, 0.10%Ni, 0.95%Mo,
0.21%V, 0.06%Nb, 0.04%Al, 0%W, 0%Ti, 0%Cu
Andrews (1965):
Ac1 = 723 − 10.7(0.45) − 16.9(0.10) + 29.1(0.35) + 16.9(8.90) + 6.38(0)
= 723 − 4.82 − 1.69 + 10.19 + 150.41
= 877°C ← Consistent with literature (experimentally ≈ 815°C for P91)
Ac3 = 910 − 203×√(0.10) − 15.2(0.10) + 44.7(0.35) + 31.5(0.95)
+ 13.1(0) − 30(0.45) + 11(8.90) + 65(0.06) + 400(0) − 20(0)
= 910 − 64.2 − 1.52 + 15.65 + 29.93 − 13.5 + 97.9 + 3.9
= 978°C
Trzaska (2016):
Ac1 = 739 − 22.8(0.10) − 6.8(0.45) + 18.2(0.35) + 11.7(8.90) + 9.4(0.95)
− 13.7(0.10) + 19(0.21)
= 739 − 2.28 − 3.06 + 6.37 + 104.13 + 8.93 − 1.37 + 3.99
= 856°C
NOTE: Empirical equations tend to overestimate Ac1 for P91
because the 9%Cr content is near the upper limit of calibration
ranges. Experimental dilatometry gives P91 Ac1 ≈ 810–830°C.
Always verify with experimental data for critical components.
ASME B31.1 PWHT for P91: 730–775°C
→ Safety margin below Ac1 (experimental): 810 − 775 = 35°C (adequate)
→ Safety margin below Ac1 (Andrews): 877 − 775 = 102°C (conservative)
Normalising temperature (Andrews Ac3 + 60°C): 978 + 60 = 1,038°C
(Standard P91 normalising: 1,040–1,080°C — consistent)
Intercritical range (Andrews): 877–978°C = 101°C wide
Frequently Asked Questions
What are the Ac1 and Ac3 temperatures and what do they represent physically?
What is the Andrews (1965) equation for Ac1 and Ac3?
Why does alloying with carbon reduce the Ac3 temperature?
What is the difference between Ac1/Ac3 and Ae1/Ae3?
What austenitising temperature should be used for steel heat treatment?
What is the intercritical temperature range and what microstructure does it produce?
How does PWHT temperature relate to Ac1?
What is the Trzaska (2016) equation and how does it improve on Andrews?
Why does silicon raise both Ac1 and Ac3?
Recommended References
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