Abstract: A laser compass projects a laser beam along an axis. A mirror is rotated within a rotation plane perpendicular to the axis. The mirror is pivotally adjusted relative to the axis of the laser beam to reflect the laser beam at an angle ".alpha.". As the mirror rotates, the reflected laser beam is swept through an inverted cone having an apex at the point of intersection of the laser beam with the mirror, and having a base on whatever projection surface happens to be located above the laser compass (typically, a ceiling). The base of the cone defines a perfect circle on the projection surface. The radius "r" of the circle is governed by the distance "d" between the projection surface and the intersection of the laser beam with the mirror; and, by the angle .alpha.. The mirror pivot angle .alpha. required to yield a circle of desired radius "r" is given by the formula:tan .alpha.