A one‐dimensional fluid theory of Langmuir probe operation in strong magnetic fields is presented. Cross‐field diffusion of ions both into and out of the the collection region is consistently accounted for, in effect taking momentum and particle diffusivity to be equal. The results differ by significant factors from previous analyses, which did not account for outward diffusion but in effect set momentum diffusivity to zero. The differences are especially large when parallel flow of the external plasma is present. It is thus clear that the value assumed for the momentum diffusivity strongly affects the interpretation of recent probe measurements. It is argued that the present results offer a more reliable basis for this interpretation.