Science & Lab Tools
Diffusion Coefficient Calculator
Calculate the diffusion coefficient to measure how quickly molecules move through a medium
Reviewed by the calculator.uk.com Team · Last reviewed 5 August 2026 · Our methodology
Enter values to calculate the diffusion coefficient
Related to Diffusion Coefficient Calculator
The Diffusion Coefficient Calculator uses the Stokes-Einstein equation to determine how quickly molecules move through a medium. This fundamental equation in physical chemistry relates the diffusion coefficient to temperature, viscosity, and particle size. The calculator provides results in both SI (m²/s) and CGS (cm²/s) units for broad applicability across different scientific fields.
The Stokes-Einstein Equation
D = (k * T) / (6 * π * η * r) where: - D is the diffusion coefficient - k is the Boltzmann constant (1.380649 × 10⁻²³ J/K) - T is the absolute temperature in Kelvin - η (eta) is the dynamic viscosity of the medium - r is the radius of the diffusing particle
Key Parameters
- Temperature affects molecular motion - higher temperatures increase diffusion rates - Viscosity represents the medium's resistance to flow - higher viscosity decreases diffusion - Particle radius influences mobility - smaller particles diffuse more quickly
The diffusion coefficient (D) quantifies the rate of molecular movement through a medium. Understanding this value helps predict molecular behavior in various systems, from biological processes to industrial applications. The magnitude of D provides insights into transport phenomena and reaction kinetics.
Typical Values
- Small molecules in water (20°C): ~10⁻⁹ m²/s - Proteins in water: ~10⁻¹¹ m²/s - Large particles in solution: ~10⁻¹³ m²/s Higher values indicate faster diffusion, while lower values suggest slower molecular movement.
Applications
- Drug delivery systems: Predicting medication distribution - Chemical engineering: Designing separation processes - Biology: Understanding cellular transport - Materials science: Developing new materials
1. What factors affect the diffusion coefficient?
The main factors are temperature (higher temperatures increase diffusion), viscosity of the medium (higher viscosity decreases diffusion), and particle size (smaller particles diffuse faster). Environmental conditions like pressure and concentration gradients can also influence diffusion rates.
2. Why are there different unit systems (SI and CGS)?
Different fields traditionally use different unit systems. SI units (m²/s) are the international standard and commonly used in engineering, while CGS units (cm²/s) are often used in chemistry and biological sciences. Our calculator provides both for convenience and cross-disciplinary work.
3. How accurate is the Stokes-Einstein equation?
The Stokes-Einstein equation is highly accurate for spherical particles in laminar flow conditions. It works best for dilute solutions where particles are much larger than solvent molecules. For non-ideal conditions (non-spherical particles, concentrated solutions), the equation provides a good approximation but may need correction factors.
4. Can this calculator be used for all types of diffusion?
This calculator is specifically designed for molecular diffusion in liquids based on the Stokes-Einstein equation. While it's widely applicable, it may not be suitable for other types of diffusion like surface diffusion, grain boundary diffusion, or diffusion in gases, which follow different physical laws.
5. What is the scientific source for this calculator?
The Stokes-Einstein relation applied here comes from Albert Einstein's 1905 paper on Brownian motion, which combined statistical mechanics with George Stokes' earlier fluid-drag work to connect a particle's diffusion coefficient to its size, the solvent's viscosity, and temperature. It's one of the foundational results linking microscopic random motion to macroscopically measurable diffusion, still taught in physical chemistry and biophysics. The calculator uses the current SI-defined value of the Boltzmann constant in the underlying calculation.