Optical coatings are widespread in everyday life, from camera lenses to glasses, to complex optics experiments. A simple, reliable device that can quickly and inexpensively analyze optical coatings is a valuable laboratory tool. Such a device can identify unknown or mislabelled optics, and characterize the transmission spectra of optical elements used in an experiment. We present the design and characterization of a LED-based spectrophotometer, and demonstrate its ability to identify different optical coatings. Our approach uses ten LEDs that cover a spectrum from 365 nm to 1000 nm. A small servomotor and microcontroller rotates a LED board to sequentially position each LED over an optical sample, and the transmitted light corresponding to each LED is measured with a silicon photodetector. The device is automated, portable, inexpensive, user-friendly and simple to build.