Abstract <p>An approach to determining and describing the distribution of the longitudinal and transverse components of the magnetic field in an axisymmetric laboratory electromagnet is proposed based on a polynomial expansion of the field induction taking into account the restrictions imposed by Maxwell’s equations. It is shown that the proposed approach allows obtaining high accuracy in describing the magnetic field distribution with a small number of measurements. It may also be of interest for refining the parameters of laboratory equipment and be used as a training task in laboratory practice when studying the properties of the electromagnetic field.</p>