Distributions of flame front curvature obtained by laser sheet tomography agree with those derived from numerical simulations of passive flame propagation within three-dimensional Navier-Stokes turbulence. The experimental configuration is that of grid turbulence impinging upon a plate which stabilizes a premixed methane/air flame, planar images of the flame allow construction of flame curvature as a function of flame location within the spatial zone that contains products and reactants. In the simulations the flame burning velocity is twice the turbulence intensity and the Reynolds number based on the computed Taylor length scale is approximately 55. The computed flame geometry and flame strain rate are obtained as a function of location based on the mean progress variable (defined by the passive surface displacement or by the scalar fluctuations defined over transverse planes). The shape of the mean progress variable profile compares well with experiment and with two reaction-diffusion models of propagation (KPP and an independent Gaussian model). From the simulations planar slices are created in order to provide curvature information which is directly comparable to the experimental data. Distributions of curvature, based on planar information, exhibit a change with location in the turbulent flame zone: an overall positive curvature (convex to the reactants) at the front to a negative value at the rear; however, this behavior is composed of positive curvature (which by itself has an average value with no spatial variation) and negative curvature (which increases in magnitude with distance from the front). A single length scale allows a good match between experimental and computed curvature throughout the flame zone. The passive flame simulations show the most probable flame shape to be cylindrical, and this feature, allows the planar information to be scaled in order to match the curvature distributions based on three dimensional information. The scaling factor is obtained by observing a cylinder with planar slices at all possible angles.