In many cases, it is convenient to have approximate relations to evaluate thermoacoustic gain and efficiency. G. W. Swift [J. Acoust. Soc. Am.84, 1145–1180 (1988)] has provided such relations for short stacks in a standing wave. This paper describes an approximation method based on a finite difference form of the thermoacoustic equations and provides results for thermoacoustic engines or refrigerators for both standing and traveling waves. The short stack assumption is retained. The method is limited at present to linear temperature gradients across the stack. The calculations are compared to measurements and in the appropriate limits to Rott’s boundary conditions for a temperature discontinuity [N. Rott, Adv. Appl. Mech.20, 135–175 (1980)]. The approximation is applied to both thermoacoustic prime movers and thermoacoustic refrigerators.