A novel set of SAC/FEMA-style closed-form expressions is presented to accurately assess structural safety under seismic action. Such solutions allow the practical evaluation of the risk integral convolving seismic hazard and structural response by using a number of idealizations to achieve a simple analytical form. The most heavily criticized approximation of the SAC/FEMA formats is the first-order power-law fit of the hazard curve. It results to unacceptable errors whenever the curvature of the hazard function becomes significant. Adopting a second-order fit, instead, allows capturing the hazard curvature at the cost of necessitating new analytic forms. The new set of equations is a complete replacement of the original, enabling (a) accurate estimation of the mean annual frequency of limit-state exceedance and (b) safety checking for specified performance objectives in a code-compatible format. More importantly, the flexibility of higher-order fitting guarantees a wider-range validity of the local hazard approximation. Thus, it enables the inversion of the formulas for practically estimating the allowable demand or the required capacity to fulfill any design objective. Copyright © 2012 John Wiley & Sons, Ltd.