The Bowen ratio, Bo, is the ratio of the sensible heat flux (Hs) at the surface to the latent heat flux (HL). One use for the Bowen ratio is in the Bowen ratio and energy budget method, which presumes a balance in the surface energy budget, Rn + C = Hs + HL, where Rn is the net radiation and C is the conductive flux up to the surface from below. If the Bowen ratio and Rn + C are known, the turbulent fluxes Hs and HL, which are difficult to measure, can be obtained from Rn + C = Hs(1 + Bo1) and Rn + C = HL(Bo + 1), respectively. Over surfaces like sea ice, where the water vapor at the surface is in saturation, the Bowen ratio is tightly constrained. Using eddy-covariance measurements from Ice Station Weddell (ISW) and from the main 20-m tower at SHEBA (the experiment to study the Surface Heat Budget of the Arctic Ocean), we investigate these constraints on Bo. Measurements of the surface-air temperature and humidity differences from ISW, from the SHEBA tower, and from several remote SHEBA sites supply further insights into constraints on the Bowen ratio. Three regimes represent approximately 95% of our data over sea ice: Hs > 0, HL > 0; Hs < 0, HL < 0; and Hs < 0, HL > 0. (In our convention, positive fluxes are upwardfrom ice to air.) In this work, we deduce simple mathematical relationships to predict Bo in each of these regimes from measurements of only surface temperature and barometric pressure. These relationships allow using the Bowen ratio and energy budget method, suggest quality controls for measurements and model values of Hs and HL and other terms in the surface energy budget, and potentially provide a missing relationship to use in deriving the surface energy budget over sea ice from satellite data.