Iron-Carbon Phase Diagram Calculator: Lever Rule, Pearlite and Critical Temperatures
Phases, lever rule fractions and critical temperatures for a steel or cast iron from the carbon content and temperature.
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How this calculator works
Enter the carbon content and a temperature. The calculator names the type of steel or cast iron, gives the critical temperatures A1 (727 degrees C), A3 for a hypoeutectoid steel and Acm for a hypereutectoid steel, and tells you which phases are present at your temperature.
It finds the fraction of each phase by the lever rule. After slow cooling to room temperature, it gives the fraction of pearlite and of the proeutectoid ferrite or cementite, and for cast iron the primary phase and ledeburite.
The diagram lines are drawn as straight lines between the key points, which is close but not exact. Use the full diagram for design. These are equilibrium results for very slow cooling.
Formulas used
- W_{pearlite} = \frac{C_0 - 0.022}{0.77 - 0.022}\ (C_0 < 0.77)
- W_{Fe_3C} = \frac{C_0 - 0.022}{6.67 - 0.022}
- W_\alpha = \frac{C_\gamma - C_0}{C_\gamma - C_\alpha}
Worked example
With the default numbers in the calculator above:
- Type: medium-carbon steel, hypoeutectoid
- Lower critical temperature A1 (austenite starts to form on heating): 727 °C
- Upper critical temperature A3 (all austenite above it): 815.90 °C (a straight-line estimate)
- Phases below A1 (ferrite and cementite), by the lever rule: Ferrite 94.31 %, cementite 5.69 %
- Pearlite after slow cooling: 50.53 % pearlite
- Proeutectoid ferrite (the ferrite that formed before the pearlite): 49.47 % ferrite
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Temperature 800 °C.
- Type: medium-carbon steel, hypoeutectoid
- Lower critical temperature A1 (austenite starts to form on heating): 727 °C
- Upper critical temperature A3 (all austenite above it): 815.90 °C (a straight-line estimate)
- Phases: austenite (gamma) and ferrite (alpha): Ferrite 14.61 %, austenite 85.39 %
Common questions
What is the eutectoid?
The composition and temperature where austenite turns into pearlite on cooling: 0.77 percent carbon at 727 degrees C.
What is the difference between steel and cast iron?
Steel has less than 2.11 percent carbon, and cast iron has more.
Does it work for fast cooling?
No. Quenching gives martensite, and faster cooling gives bainite or finer pearlite, which are not on the equilibrium diagram.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Callister, Materials Science and Engineering (iron-iron carbide diagram); ASM Handbook, Alloy Phase Diagrams.
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