In studies of vision and audition, stimuli can be chosen to span the visible or audible spectrum; in olfaction, the axes and boundaries defining the analogous odorous space are unknown. As a result, the population of olfactory space is likewise unknown, and anecdotal estimates of 10,000 odorants have endured. The journey a molecule must take to reach olfactory receptors (ORs) and produce an odor percept suggests some chemical criteria for odorants: a molecule must 1) be volatile enough to enter the air phase, 2) be nonvolatile and hydrophilic enough to sorb into the mucous layer coating the olfactory epithelium, 3) be hydrophobic enough to enter an OR binding pocket, and 4) activate at least one OR. Here, we develop a simple and interpretable quantitative model that reliably predicts whether a molecule is odorous or odorless based solely on the first three criteria. Applying our model to a database of all possible small organic molecules, we estimate that at least 40 billion possible compounds are odorous, six orders of magnitude larger than current estimates of 10,000. With this model in hand, we can define the boundaries of olfactory space in terms of molecular volatility and hydrophobicity, enabling representative sampling of olfactory stimulus space.