A novel, fast, and approximate forward modelling routine for time-domain electromagnetic responses is presented. It is based on the separation of the forward problem into a configuration-independent part, mapping conductivity as a function of depth onto apparent conductivity as a function of time, and a configuration-dependent part, i.e., the half-space step response. The response of a layered model is then found as the half-space response for a half-space conductivity equal to the apparent conductivity. The mapping is ten times faster than traditional accurate forward modelling routines, and through stochastic modelling, it is found that the standard deviation of the modelling error is 0.7 %. The forward mapping lends itself to integration in a modern state-of-the-art inversion formulation in exactly the same way as traditionally computed responses, and a field example is included where inversion results using the approximate forward response are compared with those of an accurate forward response for helicopterborne transient electromagnetic data. In addition to being used in its own right in inversion of transient data, the speed and accuracy of the approximate inversion mean that it is well suited for quality control and fast turnaround data delivery of survey results to a client. It can also be used in hybrid inversion formulations by supplying initial iterations and high-quality derivatives in an inversion based on accurate forward modelling.