The stadimeter is based on the same principle as the sextant. But rather than directly measuring an angle the stadimeter is set-up in such a way that it translates the measured angle into a distance using the height or width of an object.
Depening on the model the angle is measured using a fixed (horizon) mirror with a movable index mirror or using a prism. In both cases the front / bottom of the object is brought in line with the end / top of the same item. The length between the bottom and top (or front and end) of the object is set on the instrument and the length read of from the corresponding scale.