Human breath causes indoor air quality (IAQ) to get worse in overcrowded places such as schools, hospitals, and offices where people spend most of their time, and it is rarely felt. For a healthy and comfortable living environment, pollutant gases must also be monitored in addition to temperature and humidity control. In this respect, carbon dioxide (CO$_{2})$ is considered as one of the main indoor air pollutants to determine ventilation requirements. In this study, a mathematical model and simulator software have been developed to predict CO$_{2}$ concentrations under different indoor conditions and to visualize the predicted results that come from the model. During the study some experiments are conducted to validate the model at a faculty building of Sakarya University. In these experiments, first CO$_{2}$ concentrations are predicted using the model and then they are measured to validate the model for target classrooms under different indoor conditions depending on the number of students, their physical characteristics, and activities. The study shows that increasing the number of students has considerable impacts on the amount of CO$_{2}$ produced and it can be used as the minimum value of the outdoor ventilation rate. The modeling and simulator software can be used for analyzing alternative building designs such as different ventilation types, occupant profiles, and numbers and dimensions of windows, doors and rooms in terms of IAQ.