Formulas are developed for the calculation of the whole-body gamma-radiation dose from a cloud of radioactive gases. The complexity of the formulas is greatly reduced by the simplifying assumption that the cloud does not change in size and shape during the time that the receptor is exposed to radiation. For most cases of interest, the numerical solutions based on this assumption are nearly identical with more detailed solutions. The formulas have been programmed for computer solution so that large parametric studies are possible in an hour or two of machine time. The numerical solutions can be displayed as a contour map or an isometric drawing as a function of cloud size and shape. When lines that are functions of meteorological conditions and distance from the release point of the cloud are added to such a display, the details of the solution are graphically presented to provide a very clear visual comprehension.