The inductance of a planar air-core inductor with complex geometry is generally difficult to be ascertained. In this paper, we propose a versatile and accurate vector-based method to ascertain the inductance of planar air-core inductors with virtually any geometry, including novel complex geometry inductors. We benchmark our proposed method against the conventional electromagnetic field solver simulations to estimate the inductances of several planar inductors embodying different and complex geometries, and show that our method is highly accurate with a worst-case error of ~5% compared to that obtained using conventional electromagnetic field solver.