Computing the gradients of capacitances in an integrated circuit chip layout with respect to design and process parameters is described. Included is a shape processing engine in the form of a variational mapping engine and a capacitance calculation engine that includes a gradient calculation engine. The variational mapping engine translates physical parameter variations into variations on the edges of the elementary patterns to which the layout of the integrated circuit is decomposed. The gradient calculation engine computes capacitance gradients by combining information from two sources. The first source consists of pre-existing gradients in a capacitance lookup table. The second source consists of analytical expressions of capacitance correction factors.