Diffusion Calculator

Carburising a 0.2 % C steel at 950 °C with 1.2 % C at the surface for 10 hours raises the carbon at 0.5 mm depth to 0.774281 wt%.

Calculate:

Concentration at depth (Fick’s second law, erf)Time to reach a concentration at a depthDiffusion coefficient D = D₀ e^(−Q/RT)

D₀ (m²/s):

Carbon in γ-iron: D₀ = 2.3 × 10⁻⁵ m²/s, Q = 148 kJ/mol.

Activation energy Q (kJ/mol):

Temperature:

Surface concentration Cₛ (wt%):

Initial concentration C₀ (wt%):

Depth x:

Time t:

Concentration at depth Cₓ =

0.774280880856048 wt%

Precision

Full answer, then cut to fewer decimals (not rounded):

0.774280880856048 wt%
0.77428088085604 wt%
0.7742808808560 wt%
0.774280880856 wt%
0.77428088085 wt%
0.7742808808 wt%
0.774280880 wt%
0.77428088 wt%
0.7742808 wt%
0.774280 wt%
0.77428 wt%
0.7742 wt%
0.774 wt%
0.77 wt%
0.7 wt%

Diffusion coefficient D: 1.100294422 × 10⁻¹¹ m²/s
z = x/(2√(Dt)): 0.3972229229
erf(z): 0.4257191191
Diffusion length √(Dt): 0.6293695193 mm

Step-by-step solution

D = D₀e^(−Q/RT) = (1.100294422 × 10⁻¹¹) m²/s
(Cₓ − C₀)/(Cₛ − C₀) = 1 − erf(x/2√(Dt)), z = 0.3972229229
Cₓ = 1.2 − 1 × erf(0.3972229229) = 0.7742808809 wt%

Diffusion Formula

(Cₓ − C₀)/(Cₛ − C₀) = 1 − erf(x / (2√(Dt)))

D = D₀ exp(−Q/RT); diffusion distance ~ √(Dt)

Worked Example

Carburising 0.2 % C steel at 950 °C with a 1.2 % C surface for 10 hours:

D = D₀e^(−Q/RT) = (1.100294422 × 10⁻¹¹) m²/s
(Cₓ − C₀)/(Cₛ − C₀) = 1 − erf(x/2√(Dt)), z = 0.3972229229
Cₓ = 1.2 − 1 × erf(0.3972229229) = 0.7742808809 wt%

z = x/(2√(Dt)): 0.3972229229 · erf(z): 0.4257191191 · Diffusion length √(Dt): 0.6293695193 mm

GATE tip

When the target is halfway between C₀ and Cₛ, erf(z) = 0.5 and z ≈ 0.477, so x ≈ 0.95√(Dt). Many questions are built around this.

More Kinetics and Diffusion Calculators

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.

Open the arrhenius equation calculator →
Avrami Equation Calculator

y = 1 − exp(−k tⁿ)

n Avrami exponent; t₀.₅ = (ln 2 / k)^(1/n)

Example: A transformation with k = 0.01 and n = 2.5 after 5 time units: Fraction transformed y = 42.8229 %.

Open the avrami equation calculator →

Frequently asked questions

Why does case depth go with √t?

The erf argument is x/(2√(Dt)), so the same concentration is reached at a depth proportional to √t: doubling the depth takes four times as long.

Why carburise in austenite?

Carbon is far more soluble in FCC austenite (up to about 2 wt%) than in BCC ferrite, and diffuses quickly at 900–950 °C.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

Cite this page

APA

Scientific Converters. (2026, October 15). Diffusion Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/diffusion-calculator/

IEEE

Scientific Converters, "Diffusion Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/diffusion-calculator/