The leading-edge vortex (LEV) is a universal and robust lift enhancement mechanism in biological flapping and autorotating flight. It is characterized by comparatively low Reynolds number and large angle of attack leading to separated three-dimensional flow, which has long precluded analytical approach to this problem. Here we propose a reduced-order analytical model, which is capable of delivering a fast closed-form estimate of the LEV strength and position for a revolving wing at arbitrary angle of attack. It is postulated that equilibrium state of the vortex is primarily maintained by the competing effects of vorticity production at the leading edge and its three-dimensional transport in the presence of spanwise flow and downwash. The results of the model are found consistent with the LEV strength and centroid coordinates measured previously in experiments, as well as determined from numerical solution of the Navier-Stokes equations, in a wide range of the Reynolds number. The agreement is good not only for rectangular wings, but also for bio-inspired shapes of fruit fly, bumblebee, and hawkmoth. Hence, the model offers a simple, versatile, and reliable tool for practical estimation of the LEV parameters.