A physically based analytic model (λ model) is presented to describe the wind profile of tropical cyclones in terms of the pressure deficit and a single shape parameter (λ). To test the λ model, an idealized full-physics numerical model is employed to provide wind-profile samples and also to show the influence of environmental temperature and the properties of initial vortices on tropical cyclone size. It is found that the λ model provides an accurate fit of the azimuthal wind profile at the top of the boundary layer. In the simulations, tropical cyclone size is sensitive to sea-surface temperature, upper tropospheric temperature and initial vortex structure. The numerical model confirms the assumed Gaussian distribution with width λ of the moist entropy in the boundary layer. A linear relationship between model cyclone size and inline image is found, in agreement with the λ model. The λ model predicts a weak relationship between tropical cyclone size and intensity, as is observed. In addition, the λ model suggests that change in tropical cyclone size should be closely related to angular momentum transport near the boundary layer, as has been found in observations. The good agreement of the λ model with the numerical model shows that the λ model could be a reasonable alternative for characterizing the wind structure of tropical cyclones with only one scaling parameter.