Internal back-and-forth propagation of photons within a light emitting diode (LED) will naturally tend towards a Lambertian intensity profile when surface texturing is sufficiently rough. Novel designs in light extraction efficiency (LEE) can therefore benefit by optimizing under this expectation. This paper develops a framework for calculating LEE from a planar LED structure with textured surface features under the assumption of Lambertian intensity within the substrate. The method can estimate the total LEE value when given a substrate width w , an attenuation constant α , and the transmittance function T ( θ,Φ ) through the top interface. We demonstrate our theory on a pyramidal surface texture over a GaSb substrate at 4.5 μ m wavelength by computing the expected LEE as a function of w .