The Seebeck coefficient, thermoelectric power factor, electrical conductivity, and electronic thermal conductivity of the orthorhombic Pbnm phase of SrRuO3 are studied comprehensively by combining first-principles density functional calculations and Boltzmann transport theory. The influence of exchange-correlation functional on the Seebeck coefficient is carefully investigated. We show that the best agreement with experimental data is achieved when SrRuO3 is described as being at the limit of a half-metal. Furthermore, we analyze the role of individual symmetry-adapted atomic distortions on the Seebeck coefficient, highlighting a particularly strong sensitivity to R-4(+) oxygen rotational motions, which may shed light on how to manipulate the Seebeck coefficient. We confirm that the power factor of SrRuO3 can only be slightly improved by carrier doping. Our results provide a complete understanding of the thermoelectric properties of SrRuO3 and an interesting insight on the relationship between exchange-correlation functionals, atomic motions, and thermoelectric quantities.