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Eddy current (EC) sensors placed in the vicinity of a rail track and sensitive to passing train components are safety-critical components commonly used in the railway sector. From the engineering point of view they form a system with numerous variables including their geometry, the lift-off, magnetic properties of the applied materials, the operating frequency and electrical characteristics of the built-in circuits. Although some simple configurations of the EC devices have been studied experimentally, numerically and analytically, there have so far been no universal algorithm allowing for predicting, understanding and optimizing output signals for arbitrarily device/track/wheel characteristics. A significant step towards such an universal algorithm is presented in this work, combining a linear 3D finite element modelling and a set of analytical formulas derived directly from the constants of the resonance circuit. Functions correlating the magnetic induction space/time characteristics with the circuit outputs are proposed and validated against experiment in three stages: (a) by determination of the signal from a flat thin FeSi plate (i.e. in fully controlled laboratory conditions), (b) by laboratory measurements of a highly degraded rail with uncertain material properties, (c) by tests of a commercial EC wheel detector, with reference to averaged service data. The proposed methodology can be extended to any NDT field where EC devices are applied.