Goldschmidt's tolerance factor (from the German word Toleranzfaktor) is an indicator for the stability and distortion of crystal structures. It was originally only used to describe the perovskite ABO<sub>3</sub> structure, but now tolerance factors are also used for ilmenite.
Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure.
The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926.
The Goldschmidt tolerance factor () is a dimensionless number that is calculated from the ratio of the ionic radii:
In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation:
The perovskite structure has the following tolerance factors (t):