A new vapor-pressure equation which has only three adjustable parameters and has a simple form is established consistent with the renormalization-group theory of critical phenomena. The equation presented here is valid over the entire range from the triple point to the critical temperature for a chemically diverse set of compounds and does an excellent job representing data. The new equation also has a great advantage over all of the previous vapor-pressure equations in that it can be used to extrapolate extraordinarily from the usual range in which data are available both to the critical point and to the triple point. Furthermore, it reflects physical properties of the substance based upon the known physical behavior. Satisfactory results are presented for 44 simple, quantum, hydrobonding, nonpolar and polar substances, refrigerants, associating compounds, and others.