We present a fast computational technique for the electrochemical impedance of solid oxide fuel cells (SOFCs) based on detailed electrochemistry and transport models. The technique is based on the transient numerical simulation of a fast, submicrosecond potential step followed by current relaxation. The impedance is reconstructed by applying a Fourier transform to the resulting current and potential traces. The successful application of this technique is based on the combination of (i) numerical time integration of the governing equations using a time-adaptive solution algorithm, and (ii) a Fourier transform algorithm for arbitrarily spaced time points. Results are presented for a two-dimensional model of a symmetrical SOFC including gas-phase transport, pore phase transport, surface chemistry, and elementary kinetic charge transfer. Calculation speed is increased by a factor of 10-200 in comparison to a conventional simulation technique based on frequency-resolved sinusoidal excitation, depending on the frequency resolution of the conventional technique and the imposed precision of the numerical solver. The technique is an important tool for a model-based interpretation of experimental impedance data without using equivalent circuits.