Crown moulding spring angle and the compound miter it needs

What this diagram shows

A cross-section shows crown moulding nested in the corner between a wall and ceiling. The crown does not lie flat against the wall; it springs off the wall at a fixed angle — a 52/38 crown makes 38 degrees with the wall and 52 degrees with the ceiling. Because it sits on that slope, a corner cannot be cut with a single 45-degree pass: cut flat on the saw table, a 38-degree-spring crown at a 90-degree corner needs a compound cut of 31.62 degrees miter and 33.86 degrees bevel. Inside corners are coped rather than mitered; the compound miter is for outside corners.