Single-molecule Förster resonance energy transfer (smFRET) experiments can detect the distance between a donor and an acceptor fluorophore on the 3-10nm scale. In ratiometric smFRET experiments, the FRET efficiency is estimated from the ratio of acceptor and total signal (donor + acceptor). An excitation scheme involving two alternating lasers (ALEX) is often employed to discriminate between singly- and doubly-labeled populations thanks to a second ratiometric parameter, the stoichiometry S. Accurate FRET and S estimations requires applying three well-known correction factors: donor emission leakage into the acceptor channel, acceptor direct excitation by the donor excitation laser and the "gamma factor" (i.e. correction for the imbalance between donor and acceptor signals due to different fluorophore's quantum yields and photon detection efficiencies). Expressions to directly correct both raw FRET and S values have been reported in (Lee et al. BJ2005) in the context of freely-diffusing smFRET. Here we extend Lee et al. work providing several expressions for the direct excitation coefficient and highlighting a clear interpretation in terms of physical parameters and experimental quantities. Moreover, we derive a more complete set of analytic expressions for correcting FRET and S. We aim to provide a clear and concise reference for different definitions of correction coefficients and correction formulas valid for any smFRET experiment both in immobilized and freely-diffusing form.