Carburizing Case Depth Calculator

Screen gas-carburizing total case depth from time at temperature with the Harris √t relation — and the furnace time a target case depth costs — at the three classic carburizing temperatures.

Materials 4 inputs 4 results

Inputs

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Carburizing temperature

Time at temperature (t)

Target total case depth (d_t)

Results

Default result

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Total case depth(d)

1.796mm

Pass

d = K·√t — the total (visual) case.

Also computed

Effective case (est.)(d_eff)1.257mm

Effective case (to 50 HRC) runs roughly 2/3-3/4 of total; confirm by microhardness traverse, not by this screen.

Customary screening estimate ≈ 0.7 × total; the 50 HRC effective case is what drawings usually specify.

Time for target depth(t_req)2.48h

(d_t / K)² — note the square: doubling depth quadruples time.

Rate constant used(K)0.635mm/√h

Method notes 4 notes

Harris √t screening for gas carburizing of plain-carbon and low-alloy steels at carbon-saturation atmosphere. Boost/diffuse cycles, carbon potential control, alloy content (Cr, Mo raise hardenability but slow diffusion little; Ni dilutes), and quench practice all move real results.
Total case = depth to base-carbon; effective case = depth to 50 HRC after quench. Drawings usually call the effective case — quote the heat treater the drawing value and the steel grade.
The √t law means the last tenth of a millimeter is the expensive one: doubling depth quadruples furnace time.
Vacuum/low-pressure carburizing and carbonitriding follow different kinetics; use supplier data there.

Gas-carburizing case depth follows the Harris square-root-of-time relation d = K*sqrt(t), with K about 0.533/0.635/0.762 mm per root-hour at 1650/1700/1750 F. Effective case (to 50 HRC) runs roughly 0.7x total. This calculator screens depth from a cycle, the furnace time a target depth costs, and shows why doubling depth quadruples time.

How to use this calculator

Pick the temperature. The three presets carry the classic Harris constants; 1700 °F / 927 °C is the workhorse setpoint.
Enter the cycle time. Hours at temperature (boost + diffuse) gives the expected total case and the ~0.7× effective estimate.
Or work backward. Enter the drawing's case depth as the target to get the furnace time it costs — remembering the √t square.
Confirm with the heat treater. Quote the steel grade and the EFFECTIVE case requirement; atmosphere control and quench practice set the final result.

How it works

Carburizing is controlled diffusion: carbon dissolves into hot austenite from the furnace atmosphere and walks inward. Diffusion depth grows with the square root of time, and the Harris relation packages that with temperature-dependent rate constants:

d_total = K·√t K ≈ 0.533 / 0.635 / 0.762 mm/√h at 1650 / 1700 / 1750 °F

Temperature buys speed (each 50 °F step is roughly +20% rate) at the cost of more distortion and grain-growth risk; time buys depth at a square-root crawl. The calculator runs both directions — depth from a cycle, and the cycle a target depth costs.

Around the same drawing callout: the hardness conversion chart maps the 50 HRC effective-case threshold to other scales, the soak time calculator covers the through-heating before the clock starts, and the carbon equivalent calculator screens the weldability questions that follow carburized parts around.

Worked example

Verified against the live calculator

A pinion carburized 8 h at 1700 °F (927 °C):

d = 0.635 × √8 = 1.80 mm total ≈ 1.26 mm effective (≈0.071 / 0.050 in)

Suppose the drawing calls 1.0 mm total case: the required time is (1.0/0.635)² = 2.5 h. Now the square at work — a 2.0 mm case at the same temperature needs (2.0/0.635)² = 9.9 h: twice the depth, four times the furnace time. Moving to 1750 °F cuts that to (2.0/0.762)² = 6.9 h, the trade every heat treater prices daily.

Frequently asked questions

How do you calculate carburizing case depth?

With the Harris square-root-of-time relation: total case depth = K·√t, where t is hours at temperature and K depends mainly on temperature — about 0.635 mm/√h (0.025 in/√h) at the common 1700 °F / 927 °C setpoint. Eight hours gives √8 × 0.635 ≈ 1.8 mm of total case.

What is the difference between total and effective case depth?

Total case is the full depth of carbon enrichment; effective case is the depth where hardness still meets 50 HRC after quench — what drawings usually specify. Effective runs roughly 2/3 to 3/4 of total; this screen estimates 0.7× and a microhardness traverse confirms it.

Why does case depth grow with the square root of time?

Carbon enters by diffusion, and diffusion depth scales with √(D·t). The practical consequence is brutal: doubling the case depth quadruples the furnace time, which is why deep cases dominate heat-treat cost and why drawings should not specify more case than the contact stress analysis needs.

Does steel alloy change carburizing depth?

Less than people expect — carbon diffusion in austenite is similar across plain-carbon and low-alloy carburizing grades, so the Harris constants screen well for 8620, 9310, 4320 and friends. What alloy changes strongly is hardenability (how deep the quench converts that carbon into hardness) and distortion behavior.

Method & assumptions

Harris √t screening for conventional gas carburizing of carburizing-grade steels at carbon-saturation atmosphere; boost/diffuse scheduling, carbon-potential control and part geometry move real results.
Total case from the relation; effective case (50 HRC) estimated at 0.7× as a customary screening ratio — specify and verify effective case by microhardness traverse per the drawing standard.
Hardenability (alloy + quench) determines whether the enriched depth actually hardens; thin sections and oil vs. press quench change the outcome.
Vacuum/low-pressure carburizing, carbonitriding and nitriding follow different kinetics — supplier data governs there.