Most trim problems are really angle problems. Walls are rarely exactly 90°, frames are rarely perfectly square, and every degree of error shows up as a gap that caulk can only partly hide. Knowing the few formulas behind miter cuts, and when to cope instead, makes finish carpentry faster and cleaner.
Miters for any corner
When two pieces meet at a corner, each piece is cut at half the amount the corner turns: mitre = (180° − corner) ÷ 2. A 90° corner gives 45°. A 135° bay window corner gives 22.5°. A 120° corner gives 30°.
The corner angle is the angle between the two walls, measured on the room side. Measure it with a digital angle finder or an adjustable bevel, then halve it with the formula. Don't assume 90°. Plastered corners are often 88–92°, and a 1° error at each piece leaves a 2° gap.
Polygons and frames
For a frame, planter or box with n equal sides: mitre = 180° ÷ n. A square is 45°, a hexagon 30°, an octagon 22.5°. Every joint repeats the same small error, so on an octagon a ¼° mistake becomes a 4° gap at the last joint. Cut test pieces and dry-fit before cutting the good stock.
To find each side's length from the overall size, use side = point-to-point diameter × sin(180° ÷ n). The mitre angle calculator does this for you.
Crown molding
Crown sits at an angle between wall and ceiling, called the spring angle. Cut flat on a compound miter saw, it needs both a mitre and a bevel:
| Crown | Corner | Mitre | Bevel |
|---|---|---|---|
| 38° spring (52/38) | 90° | 31.6° | 33.9° |
| 45° spring (45/45) | 90° | 35.3° | 30.0° |
For other corners: mitre = atan(sin(spring) ÷ tan(corner ÷ 2)) and bevel = asin(cos(spring) × cos(corner ÷ 2)). The crown angle calculator works them out for any corner.
The alternative is cutting it "nested": upside down and backwards on the saw, with the flats sitting against the fence and table exactly as the crown sits on the wall and ceiling. Then you only need a simple miter of (180° − corner) ÷ 2 with no bevel. Many carpenters find this easier to visualize. A stop block on the saw table keeps the spring angle consistent.
Cope inside corners
On inside corners, many carpenters cut one piece square into the corner and cope the other. Cut a 45° miter to reveal the profile, then back-cut along that line with a coping saw, file or grinder, leaving just the face edge. The coped piece slides over the face of the first like a jigsaw piece.
Coped joints stay tight as houses move and wood shrinks, where mitres open up. They also forgive walls that aren't quite square, because the coped face can move along the profile.
Outside corners
Outside corners are always mitred. Glue the joint and pin through both faces, then sand it flush. For long runs, cut the corner pieces first and fit the straight runs between them, so any length error ends up in a straight run where it's easier to fix.
Measuring and ordering trim
Measure each wall, round up to the next foot, and add about 15% for waste: mitres eat length, short pieces get wasted, and the odd board is split or bowed. Buy the longest lengths you can handle, so long walls have no joins. Where a join is unavoidable, use a scarf joint (two 45° cuts overlapping) over a stud, never a square butt joint.
The baseboard and trim calculator totals the run for whole rooms, with doorways deducted, and turns it into stock lengths, nails and caulk.
Tools that help
- A digital angle finder to read true corners
- A sharp, fine-tooth blade for clean ends
- A coping saw or coping attachment
- A stop block and a crown jig for consistent spring angles
- Wood glue and pins for mitred outside corners
Common questions
Why don't my 45° mitres close on a square corner?
Either the corner isn't really 90°, the saw isn't set exactly to 45°, or the trim is slightly bowed. Check the saw with a square, measure the corner, and test with two offcuts before cutting the real pieces. A small back-bevel on the cut (a degree or so) helps the face close tightly.
Should I mitre or cope baseboard?
Cope inside corners and mitre outside corners. It's the standard approach because it gives the tightest joints over time.
This guide is general information for estimating. It is not engineering, legal or tax advice. Check local codes and your inspector for your project.