Diffusion Coefficient (Fick & Stokes-Einstein) Calculator

Calculate the diffusion coefficient using multiple methods.

Select a method and enter the known values below. Leave the field you want to calculate empty.

Diffusion Coefficient Calculator Examples

See how to use the calculator for different scenarios.

Fick's Law Example

Fick's Law Example

Calculate D when J = 0.002 mol/(m²·s) and dC/dx = 10 mol/m³/m.

Diffusion Flux (J): 0.002

Concentration Gradient (dC/dx): 10

Distance (x): undefined m

Time (t): undefined s

Temperature (T): undefined

Viscosity (η): undefined Pa·s

Particle Radius (r): undefined m

Boltzmann Constant (kB): undefined

Calculation Method: Fick's Law

Distance Unit:

Time Unit:

Dimension:

Viscosity Unit:

Radius Unit:

Diffusion Coefficient Unit: m²/s

Stokes-Einstein Example

Stokes-Einstein Example

Calculate D for a particle with r = 1e-9 m in water at 298 K (η = 0.001 Pa·s).

Diffusion Flux (J): undefined

Concentration Gradient (dC/dx): undefined

Distance (x): undefined m

Time (t): undefined s

Temperature (T): 298

Viscosity (η): 0.001 Pa·s

Particle Radius (r): 1e-9 m

Boltzmann Constant (kB): 1.380649e-23

Calculation Method: Stokes-Einstein Equation

Distance Unit:

Time Unit:

Dimension:

Viscosity Unit: Pascal seconds (Pa·s)

Radius Unit: Meters (m)

Diffusion Coefficient Unit: m²/s

Experimental (1D) Example

Experimental (1D) Example

Calculate D when x = 0.01 m, t = 3600 s, 1D diffusion.

Diffusion Flux (J): undefined

Concentration Gradient (dC/dx): undefined

Distance (x): 0.01 m

Time (t): 3600 s

Temperature (T): undefined

Viscosity (η): undefined Pa·s

Particle Radius (r): undefined m

Boltzmann Constant (kB): undefined

Calculation Method: Experimental (x²/2t or x²/4t)

Distance Unit: Meters (m)

Time Unit: Seconds (s)

Dimension: 1D (D = x²/2t)

Viscosity Unit:

Radius Unit:

Diffusion Coefficient Unit: m²/s

Experimental (2D) Example

Experimental (2D) Example

Calculate D when x = 0.005 m, t = 1800 s, 2D diffusion.

Diffusion Flux (J): undefined

Concentration Gradient (dC/dx): undefined

Distance (x): 0.005 m

Time (t): 1800 s

Temperature (T): undefined

Viscosity (η): undefined Pa·s

Particle Radius (r): undefined m

Boltzmann Constant (kB): undefined

Calculation Method: Experimental (x²/2t or x²/4t)

Distance Unit: Meters (m)

Time Unit: Seconds (s)

Dimension: 2D (D = x²/4t)

Viscosity Unit:

Radius Unit:

Diffusion Coefficient Unit: m²/s

Other Titles
Understanding Diffusion Coefficient (Fick & Stokes-Einstein) Calculator: A Comprehensive Guide
Master the science and math behind diffusion coefficient calculations.

What is Diffusion Coefficient?

  • Definition and Importance
  • Fick's Law
  • Stokes-Einstein Equation
The diffusion coefficient (D) quantifies how fast a substance spreads out in another medium. It is a key parameter in chemistry, biology, and engineering.
Fick's Law and Stokes-Einstein
Fick's Law relates diffusion flux to concentration gradient, while Stokes-Einstein connects D to temperature, viscosity, and particle size in liquids.

Common Diffusion Examples

  • Calculating D for oxygen in water.
  • Estimating D for dye in agar gel.

Step-by-Step Guide to Using the Calculator

  • Input Selection
  • Calculation Methods
  • Interpreting Results
Select the calculation method: Fick's Law, Stokes-Einstein, or Experimental. Enter the required values for your chosen method. The calculator will compute D and show step-by-step details.
Example Workflow
For Fick's Law, enter flux and concentration gradient. For Stokes-Einstein, enter temperature, viscosity, and radius. For Experimental, enter distance, time, and dimension.

Step-by-Step Examples

  • Calculating D for a protein in water using Stokes-Einstein.
  • Finding D for a solute in a gel using the experimental method.

Real-World Applications of Diffusion Coefficient

  • Biology and Medicine
  • Material Science
  • Environmental Engineering
Diffusion coefficients are used to model oxygen transport in tissues, pollutant spread in water, and material processing in industry.
Industry and Research
Engineers and scientists use D to design processes, predict outcomes, and understand natural phenomena.

Industrial & Research Examples

  • Modeling drug delivery in the body.
  • Predicting pollutant spread in rivers.

Common Misconceptions and Correct Methods

  • Unit Conversions
  • Choosing the Right Method
  • Experimental Errors
A common mistake is using incorrect units for distance, time, or viscosity. Always check your units and input values carefully.
Tips for Accurate Calculations
Use the calculator's tooltips for guidance and double-check all input values and units.

Common Mistakes

  • Entering cm instead of m for distance.
  • Using cP instead of Pa·s for viscosity.

Mathematical Derivation and Examples

  • Fick's Law Formula
  • Stokes-Einstein Equation
  • Experimental Calculation
Fick's Law: D = -J / (dC/dx). Stokes-Einstein: D = kB T / (6 π η r). Experimental: D = x²/(2t) for 1D, x²/(4t) for 2D, x²/(6t) for 3D.
Worked Example
For a dye diffusing 0.01 m in 1 hour: D = (0.01)²/(23600) = 1.39e-8 m²/s (1D). For a nanoparticle in water: D = 1.380649e-23298/(6π0.001*1e-9) = 2.18e-9 m²/s.

Mathematical Examples

  • Calculating D for a dye in water using Fick's Law.
  • Using Stokes-Einstein for a nanoparticle.