Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. In one (spatial) dimension, the law can be written in various forms, where the most common form (see) is in a molar basis:
where
*  is the diffusion flux, of which the dimension is the amount of substance per unit area per unit time.  measures the amount of substance that will flow through a unit area during a unit time interval.
*  is the diffusion coefficient or diffusivity. Its dimension is area per unit time.
*  is the concentration gradient
*  (for ideal mixtures) is the concentration, with a dimension of amount of substance per unit volume.
*  is position, the dimension of which is length.
 is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes–Einstein relation. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of . For biological molecules the diffusion coefficients normally range from 10 to 10 m/s.
In two or more dimensions we must use , the del or gradient operator, which generalises the first derivative, obtaining
where  denotes the diffusion flux vector.
The driving force for the one-dimensional diffusion is the quantity , which for ideal mixtures is the concentration gradient.