By enclosing a completely circular waveguide, of mean radius of curvatureRcwithin a surface of referenceSon which the electric field is assumed to be known, and using accurate Green's functions which take account of the planar air/dielectric (or similar) strong dielectric discontinuity, a new scalar curvature loss formula of Huygens-type is produced. The formula bridges the gap between the familiarRc−1/2-and-exponential variation of the attenuation coefficient for space waves and the less familiarRc−3/2-and-exponential variation. The methodology also separates the surface and space wave losses and reduces to existing formulas under appropriate circumstance. Numerical results are presented for a rib waveguide. These indicate that (a) surface wave loss can greatly increase the curvature loss (b) the presence of a strong planar dielectric discontinuity helps to reduce the space wave loss. The results are in good agreement with experiment.