A Diffusion Ellipsoid is completely represented by the Diffusion Tensor, D. FA is calculated from the eigenvalues () of the diffusion tensor. The eigenvectors  give the directions in which the ellipsoid has major axes, and the corresponding eigenvalues   give the magnitude of the peak in that direction.
with  being the mean value of the eigenvalues.
An equivalent formula for FA is
which is further equivalent to:
where R is the "normalized" diffusion tensor:
Note that if all the eigenvalues are equal, which happens for isotropic (spherical) diffusion, as in free water, the FA is .   The FA can reach a maximum value of  (this rarely happens in real data), in which case D has only one nonzero eigenvalue and the ellipsoid reduces to a line in the direction of that eigenvector. This means that the diffusion is confined to that direction alone.