Diffusion Penetration Calculator
Calculate concentration inside a semi-infinite medium after a maintained surface-concentration step.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the one-dimensional semi-infinite constant-diffusivity solution with a suddenly maintained boundary value.
C(x,t)=Cinitial+(Csurface−Cinitial) erfc(x/(2√Dt))
Worked example
At x=0 concentration is the surface value. With x=0.1 mm, D=10⁻⁹ m²/s and t=10 s, the boundary-step fraction is erfc(0.5)≈0.479500122.
Assumptions and input details
Uniform semi-infinite initial medium, no advection, reaction, binding, moving boundary or variable D. Positive elapsed time; sufficiently deep values can numerically reach the initial concentration. Not a biological exposure or material-processing recommendation.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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