Thermodynamics-based modelling of the fraction of martensite formed upon quenching in low-alloy steels is developed. The adopted modelling approach has two distinct features: 1) it applies the driving force of the transformation, i.e. the difference of Gibbs energy between austenite and martensite, from thermodynamic calculations; 2) it predicts the sigmoidal shape of transformation to capture also the initial 10-20% of martensite formation, which is distinct from some previous modelling using e.g. the Koistinen-Marburger equation. It is found that the general equation can describe the experimental data of martensite fraction versus quenching temperature for plain carbon steels and low-alloy steels well. Furthermore, the only model parameter that is needed is linearly proportional to the martensite start temperature of the steel, which opens the possibility for a thermodynamics-based simple but yet predictive model if it is coupled with the previously developed thermodynamics-based model for the Ms temperature.