The Coats and Redfern method for the determination of the activation energy has been extensively used in the kinetic analysis of thermal decomposition of coal and biomass. The relative errors involved in the apparent activation energy obtained from the Coats and Redfern method have been calculated by some researchers. However, in their calculations, the low-temperature end of the temperature integral was neglected. In this study, the precision of the Coats and Redfern method for the determination of the activation energy without neglecting the low-temperature end of the temperature integral has been obtained by means of some theoretical derivation and numerical calculations. The obtained results indicate that there is a significant influence of two dimensionless quantities gamma = E/RT0 (a dimensionless activation energy, where E is the activation energy, R is the gas constant, and To is the starting temperature of the reaction) and = T/T-0 (the normalized temperature, where T is the temperature) on the calculated activation energy values. Our results have been verified for simulated data as well as for the non-isothermal data of lignin pyrolysis.