Fick Flux Calculator

Model molecular transport using Fick's first law. Enter two points or a known concentration gradient. Get flux, direction, and molar flow in seconds here.

Calculator Inputs

Choose how the gradient is defined.
Used for molar flow: Ṅ = J·A.
Mass units need molar mass.
g/mol
Example: NaCl is 58.44 g/mol.
Used for x positions and gradient scaling.
Optional temperature dependence.
Typical liquids: 10⁻¹¹ to 10⁻⁹ m²/s.
m²/s
kJ/mol
Model: D = D0 · exp(−Ea / (R·T)).
Gradient is computed as (C2 − C1) / (x2 − x1).
If auto, your value is interpreted as (conc unit)/(distance unit).
Reset

Formula used

Fick's first law in one dimension relates diffusive flux to the concentration gradient:

  • Flux: J = -D\,\frac{dC}{dx}
  • Two-point gradient: \frac{dC}{dx} \approx \frac{C_2 - C_1}{x_2 - x_1}
  • Molar flow rate: \dot{N} = J\,A
  • Optional temperature model: D = D_0\,e^{-E_a/(RT)}

Sign convention: a positive gradient (C increases with x) produces flux toward −x.

How to use this calculator

  1. Select the method: Two-point or Direct gradient.
  2. Pick units for concentration, distance, and area.
  3. If you use g/L or g/m³, enter the solute molar mass.
  4. Either enter D directly, or enable Arrhenius and fill D0, Ea, and temperature.
  5. Press Calculate to view flux and molar flow above the form.
  6. Use Download CSV or Download PDF for reports.

Example data table

Scenario D (m²/s) C1 (mol/L) C2 (mol/L) x1 (m) x2 (m) Area (m²) Flux J (mol/(m²·s)) Molar flow (mol/s)
Salt diffusing in water 1.0e-9 1.0 0.2 0 0.01 0.01 8.0e-8 8.0e-10
Steeper gradient 2.0e-9 0.5 0.0 0 0.002 0.005 5.0e-7 2.5e-9

These examples assume a linear gradient between the two points.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.