A technique for measuring the radius of dielectric microcylinders with subdiffraction-limited precision is presented. Diffraction fringes arising from the dielectric cylinder are measured using conventional bright-field optical microscopy and compared with theory to deduce the radii. The technique has been demonstrated measuring the radii of the major-ampullate silks from Plebs eburnus spiders. Precision better than 50 nm is demonstrated, using a standard optical microscope with a numerical aperture of 0.6 for the objective. Accuracy was verified using scanning electron microscopy. This technique will facilitate rapid, precise measurement of dielectric microcylinder radii, enabling a new optical-microscopy-based measurement approach for these challenging micro-optics.