For n functions f_i in n variables x_i, the Jacobian is the determinant of the Jacobian matrix. The absolute value of the Jacobian determinant is a measure of how much area or volume is being stretched or contracted locally. So, for small changes we have

For example, with the usual spherical polar coordinates r,θ‎,ϕ‎, the Jacobian determinant equals r²sinθ‎, showing that the same change in θ‎ contributes to a larger element of volume near this equator (θ‎ = π‎/2) compared to the north pole (θ‎ = 0), but the longitude φ‎ has no effect on the element of volume. See jacobian matrix.