The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns
in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of
a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the
instability, using elementary geometry and the physics of bending and stretching. Our main result is a
set of simple scaling laws; the wavelength of the wrinkles

K1=4, where K is the stiffness due to an
‘‘elastic substrate’’ effect with a multitude of origins, and the amplitude of the wrinkle A

. These
could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.