The alpha-proton hyperfine coupling is a major source of information useful for identifying the chemical and physical structure of free radicals. Use of the isotropic component for estimating spin distributions has been particularly widespread. However, the proportionality between the measured isotropic component and the unpaired spin is known to depend on radical geometry. Using DFT-based computational methods, this work explores the geometry dependence with the model structure (CalphaHalpha)-C-.(R1)(R2), where R1 and R2 are all combinations of H, Me, COOH, NH2, and OH. Results indicate that symmetrical bending of all bonds to C-alpha from planar to tetrahedral geometries (1) leads to a change in the isotropic component, dependent on the identity of R1 and R2, which can exceed 200%, (2) leads to very small change in the most-positive dipolar component (less than 6%), and (3) preserves the property that the vector associated with the most-positive dipolar component indicates the direction of the CalphaHalpha bond (within 6degrees or less). Other geometrical features, associated with possible constraints from surrounding molecules, also affect the isotropic coupling and emphasize the need to account for the surroundings when computing optimized structures.