An innovative computationally efficient method for the simultaneous determination of top dead centre (TDC) offset and pressure offset is presented. It is based on characteristic deviations of the rate of heat release (ROHR) that are specific for both offsets in compression phase and expansion phase after the end of combustion. These characteristic deviations of the ROHR are derived from first principles and they were also confirmed through manual shifts of the pressure trace. The ROHR is calculated based on the first law of thermodynamics using an in-cylinder pressure trace, engine geometrical parameters and operating point specific parameters. The method can be applied in off-line analyses using an averaged pressure trace or in on-line analyses using a single pressure trace. In both application areas the method simultaneously determines the TDC position and the pressure offset within a single processing of the pressure trace, whereas a second refinement step can be performed for obtaining more accurate results as correction factors are determined more accurately using nearly converged input data. Innovative analytic basis of the method allows for significant reduction of the computational times compared to the existing methods for the simultaneous determination of TDC offset and pressure offset in fired conditions. The method was validated on a heavy-duty and a light-duty diesel engine.