Scattering losses in various electron and proton synchrotrons by residual gas molecules are obtained for a variety of conditions. Evaluation is made of the effects of (1) injection energy of the particles, (2) the spread of the injected beam, (3) the pressure of the residual gas, (4) the rate at which energy is supplied to the beam particles, and (5) the aperture of the accelerator. It is shown that multiple scattering is the really important factor and that losses due to single scattering are of relative importance only when the total effect of single and multiple scattering is rather small.Scattering losses are tabulated and estimates made of the residual gas pressures in synchrotrons which will not produce prohibitively large losses.