A reversible transformation of the unit-cell parameters and atomic coordinates of centrosymmetric perovskites ABX
3 into a Cartesian space is defined. Analytical expressions for the three vectors for the pseudocubic cell and three vectors for a BX
6 octahedron are derived for space groups Pbmn, Cmcm, Ibmm, P4/mbm, P4/nmc, I4/mcm and R
3
c. The following structural parameters may be derived from these vectors: up to six pseudocubic parameters defining octahedral geometry; length- and angle-based octahedral distortion parameters λ and σ; inclination angles of tilted octahedra, θ1, θ2 and θ3; angles of tilt of octahedra; AX
12:BX
6 polyhedral volume ratio, V
A
/V
B
; parameters η
A
and η
B
defining the relative contraction of inner AX
8 polyhedra and expansion of BX
6 octahedra due to octahedral tilting. The application of these parameters is demonstrated by reference to published crystal structures. The variation of η
A
and η
B
with temperature in the compositional series Sr
x
Ba1–x
SnO3 and Sr
x
Ba1–x
HfO3, as well as the temperature series of BaPbO3 and CaTiO3, is related to the sequence of phases Pbmn → Ibmm→ Pm
3
m. Stabilization of the Cmcm phase is likewise interpreted in terms of these two parameters for NaTaO3 and NaNbO3. The pressure evolution of the structures of MgSiO3, YAlO3, (La1–x
Nd
x
)GaO3 (0 ≤ x ≤ 1) and YAl0.25Cr0.75O3 is modelled with the appropriate structural parameters, thereby also addressing the characteristics of the Pbmn → R
3
c transition. Simulation of MgSiO3 up to 125 GPa and of YAlO3 up to 52 GPa in space group Pbnm is carried out by using the Birch–Murnaghan equation of state. In both cases, full sets of oxygen coordinates assuming regular octahedra are generated. Octahedral distortion is also modelled in the latter system and predicted to have a key influence on structural evolution and the sequence of phase transitions. The core modelling procedures are made available as a Microsoft Excel file.