Measurements in a van der Pauw configuration often require the use of complicated mathematical expressions or implicit relations, which may be computer-time-consuming or tedious to implement in a given software. Thus, a closed-form expression is often desirable. We propose to approximate these relations by closed-form analytical functions using only basic operators that can be easily implemented. We present explicitly the functions and the numerical values of their parameters for the cases of standard van der Pauw measurement, anisotropic resistivities, and the probe position correction factor. The discrepancy with the exact values is smaller than 10-5, which is sufficient for practical purposes.