How is carburising case depth calculated?

Carburising case depth is estimated using Fick's second law of diffusion: the carbon concentration at depth x after time t is C(x,t) = Cs - (Cs - C0) × erf(x / 2√(D·t)), where Cs is the surface carbon potential, C0 is the core carbon content, D is the diffusion coefficient of carbon in austenite at temperature, and erf is the error function. Effective case depth (ECD) is conventionally defined as the depth where hardness reaches 550 HV (approximately 0.35% C).

What is the diffusion coefficient of carbon in austenite?

The diffusion coefficient of carbon in austenite (D) follows the Arrhenius equation: D = D0 × exp(−Q/RT), where D0 ≈ 0.2 cm²/s and Q ≈ 142 kJ/mol for carbon in gamma-iron. At 920°C, D ≈ 2.0 × 10⁻⁷ cm²/s; at 950°C, D ≈ 2.8 × 10⁻⁷ cm²/s. The diffusivity increases significantly with temperature, which is why carburising at higher temperatures produces faster case depth growth.

How long does it take to achieve 1 mm case depth?

For gas carburising at 920°C on a 0.2% C steel with 1.0% Cp, a 1.0 mm effective case depth (to 0.35% C) takes approximately 6–8 hours total cycle time (boost + diffuse). At 950°C the same depth takes approximately 4–6 hours. These are estimates based on Fick's law with ideal diffusion; actual times vary with steel alloy, grain size, and atmosphere control quality.

Can the diffusion calculator be used for nitriding?

Yes — the calculator supports nitrogen diffusion for gas nitriding, plasma nitriding, and ferritic nitrocarburising (FNC). Nitrogen diffusion in ferrite/martensite follows Fick's second law with different diffusivity constants than carbon in austenite. Nitriding diffusivity is significantly lower, which is why nitriding produces shallower case depths (typically 0.1–0.6 mm) over longer times (12–100+ hours) at lower temperatures (480–580°C).

Diffusion Calculator — Carburising Depth, Nitriding Case & Diffusion Time

Approximate Carburising Time to Achieve Effective Case Depth

Target ECD (mm)	900 °C	920 °C	950 °C	980 °C
0.30	1.5 hr	1.2 hr	0.8 hr	0.6 hr
0.50	4 hr	3 hr	2 hr	1.5 hr
0.75	8 hr	6 hr	4 hr	3 hr
1.00	14 hr	10 hr	7 hr	5 hr
1.50	32 hr	22 hr	15 hr	11 hr
2.00	56 hr	39 hr	27 hr	19 hr
ECD to 550 HV / 0.35% C. Times are boost+diffuse estimates for low-alloy carburising steels. Register free for exact calculations

Calculator Features

Case depth vs time prediction using Fick's second law
Carbon and nitrogen diffusion modes (carburising and nitriding)
Temperature-dependent diffusivity for common steel grades
Boost/diffuse cycle optimisation for target ECD
Carbon profile plot — surface to core concentration gradient
Comparison of nitriding routes: gas, plasma, and FNC

How It Works

Enter process parameters

Input carburising temperature, target carbon potential, steel core carbon, and target ECD.

Get case depth prediction

The calculator returns predicted case depth vs time and plots the carbon concentration profile.

Optimise the cycle

Adjust boost and diffuse periods interactively to achieve the target surface carbon and ECD.

Who Uses This Tool

Process Engineers

Developing new carburising or nitriding recipes for specific case depth requirements.

Heat Treatment Technicians

Estimating cycle times before production runs and verifying results against predictions.

Metallurgists

Modelling case profiles and investigating deviations from specified case depth in production.

Diffusion in Case Hardening Heat Treatments

Carburising and nitriding are diffusion-controlled processes — the rate of case depth growth is governed by Fick's second law of diffusion and the temperature-dependent diffusivity of carbon or nitrogen in steel. Understanding the diffusion kinetics allows process engineers to predict cycle times accurately, design boost/diffuse cycle ratios for target case profiles, and explain why results deviate from expectation.

Our diffusion calculator implements the Fick's law solution for a semi-infinite solid with constant surface concentration, using published diffusivity data for carbon in austenite and nitrogen in ferrite. It provides both the effective case depth prediction and the full concentration profile through the case, giving a complete picture of the hardening treatment.

Diffusion Calculator — Free

Predict case depth and optimise carburising and nitriding cycles. Free with a registered account.

Diffusion Calculator

Calculator Features

How It Works

Who Uses This Tool

Diffusion in Case Hardening Heat Treatments

Diffusion Calculator — Free

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