Three-dimensional (3D) single-layer microcoils have always been a key element for electromagnetic systems; but they lack an easy and accurate method to calculate the inductance value for their complex 3D micro-structures. This paper employed a curve-fitting process to obtain the associated equation for the inductance value and geometric parameters based on the simulation results. The correction factors regarding helical pitch and wire diameter were reviewed, which are used for compensation in the Nagaoka formula. The simulation process numerically simulated the performance of the 3D microcoils using a FEM electro-magnetic-coupled analysis method. Comparison of the simulated inductance value and the Nagaoka formula was undertaken, which shows that the helical pitch and wire diameter contribute a main role in the calculation error. The derived formula was expressed in a concise form to precisely calculate the inductance value of 3D microsolenoids with single-layer coils.