Avrami Equation Calculator
With k = 0.01 and n = 2.5, 42.8229 % of the material has transformed after 5 time units.
n ≈ 3–4 for nucleation and growth in 3D; about 1–2 for growth from fixed sites.
42.8229158358213 %
Full answer, then cut to fewer decimals (not rounded):
- 42.8229158358213 %
- 42.822915835821 %
- 42.82291583582 %
- 42.8229158358 %
- 42.822915835 %
- 42.82291583 %
- 42.8229158 %
- 42.822915 %
- 42.82291 %
- 42.8229 %
- 42.822 %
- 42.82 %
- 42.8 %
- Half-transformation time t₀.₅
- 5.449167835
- Rate of transformation ≈ 1/t₀.₅
- 0.1835142595
Step-by-step solution
- y = 1 − exp(−k tⁿ) = 1 − exp(−0.01 × 5^2.5) = 0.4282291584
Avrami Equation Formula
y = 1 − exp(−k tⁿ)
n Avrami exponent; t₀.₅ = (ln 2 / k)^(1/n)
Worked Example
A transformation with k = 0.01 and n = 2.5 after 5 time units:
- y = 1 − exp(−k tⁿ) = 1 − exp(−0.01 × 5^2.5) = 0.4282291584
Rate of transformation ≈ 1/t₀.₅: 0.1835142595
GATE tip
The rate of transformation is often defined as 1/t₀.₅ and follows an Arrhenius law; this links TTT curves to activation energies.
More Kinetics and Diffusion Calculators
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Arrhenius Equation Calculator
k = A e^(−Eₐ/RT)
ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)
Example: A process with A = 10¹³ and Eₐ = 150 kJ/mol at 800 K: Rate constant k = 1607.67.
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Diffusion Calculator
(Cₓ − C₀)/(Cₛ − C₀) = 1 − erf(x / (2√(Dt)))
D = D₀ exp(−Q/RT); diffusion distance ~ √(Dt)
Example: Carburising 0.2 % C steel at 950 °C with a 1.2 % C surface for 10 hours: Concentration at depth Cₓ = 0.774281 wt%.
Frequently asked questions
How do I find n and k from data?
Plot ln[ln(1/(1 − y))] against ln t: the slope is n and the intercept ln k.
Why is the curve sigmoidal?
Transformation starts slowly while nuclei form, speeds up as they grow, then slows as growing regions impinge on one another.
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). Avrami Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/avrami-equation-calculator/
IEEE
Scientific Converters, "Avrami Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/avrami-equation-calculator/