Small angles, 30′ or less, cannot be measured with sufficient accuracy by a goniometer. The newly developed small‐angle measurement apparatus (SAM) described here is capable of measuring angles as small as 6′ with a precision of 2%. Theoretical calculations are compared with experimental results derived from both SAM and the goniometer. While this technique was developed for application to polished silicon wafers, it can be used to measure small angles on any reflecting surface.