Abstract | SPO2IDA is introduced, a software tool that is capable of recreating the seismic behaviour of oscillators with complex quadrilinear backbones. It provides a direct connection between the static pushover (SPO) curve and the results of incremental dynamic analysis (IDA), a computer‐intensive procedure that offers thorough demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. To achieve this, the seismic behaviour of numerous single‐degree‐of‐freedom (SDOF) systems is investigated through IDA. The oscillators have a wide range of periods and feature pinching hysteresis with backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative‐stiffness segment plus a final residual plateau that terminates with a drop to zero strength. An efficient method is introduced to treat the backbone shape by summarizing the analysis results into the 16, 50 and 84% fractile IDA curves, reducing them to a few shape parameters and finding simpler backbones that reproduce the IDA curves of complex ones. Thus, vast economies are realized while important intuition is gained on the role of the backbone shape to the seismic performance. The final product is SPO2IDA, an accurate, spreadsheet‐level tool for performance‐based earthquake engineering that can rapidly estimate demands and limit‐state capacities, strength reduction R‐factors and inelastic displacement ratios for any SDOF system with such a quadrilinear SPO curve. Copyright © 2006 John Wiley & Sons, Ltd.