Lever Rule Calculator
An alloy at 35 wt% B, with α of 20 wt% and β of 60 wt% on the tie line, is 62.5 % α and 37.5 % β by mass.
62.5 %
- Fraction of β, Wβ
- 37.5 %
Step-by-step solution
- Wα = (Cβ − C₀) ÷ (Cβ − Cα) = (60 − 35) ÷ (60 − 20) = 0.625
- Wβ = 1 − Wα = 0.375 (the "opposite arm" of the lever)
Lever Rule Formula
Wα = (Cβ − C₀) / (Cβ − Cα)
Fe–C: eutectoid 0.76 wt% C, ferrite 0.022, cementite 6.7 wt% C
Worked Example
An alloy of 35 wt% B between α at 20 wt% and β at 60 wt%:
- Wα = (Cβ − C₀) ÷ (Cβ − Cα) = (60 − 35) ÷ (60 − 20) = 0.625
- Wβ = 1 − Wα = 0.375 (the "opposite arm" of the lever)
GATE tip
Use mass percentages consistently: the lever rule gives mass fractions when compositions are in wt%, and mole fractions when they are in at%.
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Frequently asked questions
Why the “opposite arm”?
The fraction of a phase is the length of the tie line on the far side of C₀ divided by its full length, like a balanced lever.
How much pearlite is in a 0.4 % C steel?
Just below 727 °C, (0.4 − 0.022)/(0.76 − 0.022) = 51 % pearlite and 49 % pro-eutectoid ferrite.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Lever Rule Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/lever-rule-calculator/
IEEE
Scientific Converters, "Lever Rule Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/lever-rule-calculator/