Miter Angle Calculator

How to use this tool

Pick what you are cutting. "Corner miter" is for baseboard, casing, chair rail and picture frames: enter the corner angle, 90 if it is square, choose inside or outside, and read the saw setting. "Polygon" takes 3 to 24 sides for a frame, box or planter. "Crown molding" takes the wall angle and the spring angle and gives the settings for the crown lying flat on the saw and for the crown nested against the fence.

Enter the angle of the corner, not the cut: 90 for a square corner, not 45. If you measured around the outside of a corner and read 270, enter 90. Left and right mean the wall on your left and right as you face the corner. For crown, the spring angle is the smaller number on 52/38 crown, so 38, and 45 on 45/45 crown. The table under the result says which way to swing the saw for each piece.

What the calculation is doing

Two pieces meeting at a corner share it, so each is cut at half the corner. Half of 90° is 45°, and half of a 135° octagon corner is 67.5°. A saw scale reads from a square cut, which is 0, so the setting is 90° minus that half, or (180° minus the corner) ÷ 2. That gives 45° for a square corner and 22.5° for an octagon. For a regular polygon with n sides the interior angle is (n − 2) × 180° ÷ n and the saw setting simplifies to 180° ÷ n.

Crown molding leans out from the wall, so the joint between two pieces is a vertical plane through the corner while the crown itself is tilted. Laid on its back, the cut becomes compound: miter = arctan(sin s ÷ tan(θ ÷ 2)) and bevel = arcsin(cos(θ ÷ 2) × cos s), where θ is the wall angle and s is the spring angle. US patent 7,574,813 prints the same formulas. Nested, held as it sits on the wall but upside down, the cut is a plain miter of (180° − θ) ÷ 2 for any spring angle.

Why crown molding needs two angles at once

The spring angle is the angle between the back of the crown and the wall once it is installed. A 38° crown makes 52° with the ceiling, so it is sold as 52/38. A 45° crown makes 45° with both and is sold as 45/45. Check yours in the corner of a framing square: the wall and ceiling readings are equal for 45/45, and for 38° crown the ceiling reading is about 0.78 of the wall reading, since tan 38° = 0.78.

Because the crown is tilted, cutting it flat means swinging the table and tilting the blade together: a 31.6° miter with a 33.9° bevel for 38° crown, and 35.3° with 30.0° for 45° crown, at a 90° corner. Some saws have detents at 31.6° and 33.9°, and the Bosch 4310 manual notes that they cannot be used with 45° crown. Detents suit square corners only, so on a real wall override them and set the scale.

Nesting avoids the compound cut. Stand the crown upside down against the fence and table at its spring angle, wall edge on the fence and ceiling edge on the table, and every cut is a plain miter with the bevel at zero. An out of square wall then changes one angle, not two. The price is holding the crown at exactly the right angle, so use a stop, and tall crown may not fit under the fence. Both methods give the same joint.

Check your saw before you trust a setting. Many saws stop at 45° to 50° on the miter scale and 45° to 48° on the bevel scale: one 12 inch dual bevel saw lists 52° left, 60° right and a 47° bevel, and another lists a 48° bevel each way. The tool flags any setting past 45° so you can compare it with your own scale.

Saw settings for common corners

Flat miter for trim and frames. The saw setting is the same inside and outside; only the direction changes.

Crown molding compound settings, laid flat, for the two common spring angles, with the nested miter for comparison. The nested bevel is always 0°.

A worked example you can check on paper

Baseboard on a 90° inside corner, the tool's default. Half the corner = 90° ÷ 2 = 45°. Saw setting = 90° − 45° = 45°. Each piece is cut at 45° to its edge, and the two 45° cuts add up to the 90° corner. For an 87° corner, half is 43.5° and the saw setting is 90° − 43.5° = 46.5°.

Crown with a 38° spring on a 90° wall, laid flat. Half the wall angle is 45°, tan 45° = 1 and sin 38° = 0.6157, so the miter is arctan(0.6157 ÷ 1) = 31.62°. Then cos 45° = 0.7071 and cos 38° = 0.7880, so sin(bevel) = 0.7071 × 0.7880 = 0.5572 and the bevel is 33.86°. On an 87° wall, half is 43.5°, tan 43.5° = 0.9490, so the miter is arctan(0.6157 ÷ 0.9490) = 32.97° and sin(bevel) = 0.7254 × 0.7880 = 0.5716 gives 34.86°. Nested at 87° the miter is 90° − 43.5° = 46.5°, with no bevel.

Mistakes that catch people out

Entering the cut instead of the corner. A square corner is 90, not 45. The calculator halves whatever you enter, so a 45 gives a 67.5° saw setting.

Assuming the wall is square. Most are a degree or two out. A 1° error opens a seam of about 0.02 inch across 3/4 inch baseboard, and more on crown. Measure with a protractor or a sliding bevel, enter that angle, and cut a scrap corner before cutting good stock.

Swinging the saw the wrong way. The two pieces are mirror images, so the wrong swing gives two pieces of the same hand. Hold them together dry: the long point is at the back on an inside corner and at the front on an outside corner.

Mixing up the spring angle. On 52/38 crown the spring is 38°, and typing 52 gives the settings for a different molding.

Mitering inside corners. A mitered inside joint opens as the wood moves and shows every out of square wall. Trim carpenters usually cope the second piece and keep miters for outside corners and frames.

Popular calculations

Each opens the calculator with those figures filled in, and they can be changed once it is open.

Baseboard, casing and trim: flat miters

Polygon frames, boxes and planters

Crown molding, 38 degree spring, laid flat

Crown molding, 45 degree spring, laid flat

Crown molding nested against the fence

How this was checked

The crown formulas were tested against a separate 3D vector model in a Node script. It builds the two pieces from the crown profile and the wall geometry, places each on a simulated saw as the direction table describes, builds the cut plane from the miter and bevel settings and swing directions, and checks that the two end faces meet. Over 3,000 wall and spring angle combinations from 20° to 180° and 15° to 75°, for inside and outside corners and both flat setups and the nested setup, the end faces met to floating point precision. Flipping any one direction, or moving an angle by 0.05°, was caught in all 2,400 trials. Flat trim was checked over 3,000 corners, and polygon frames from 3 to 24 sides closed exactly.

Published figures were compared too. At 90° the calculator gives 31.6° and 33.9° for 38° spring and 35.3° and 30.0° for 45° spring, matching the Bosch 4310 and Metabo HPT C 3607DRA manuals, US patent 7,574,813 and a Woodweb thread, and 31.62° and 33.86° against DeWalt's 31.62° and 33.85°. A Starrett conversion table lists 60 wall angles from 60° to 178°: of its 240 values, 225 match at the printed 0.1° precision, 14 are 0.1° higher than the formula, and one, 31.8° for a 38° miter at 90°, disagrees with every other source, which give 31.6°. Swing and bevel directions match the Bosch and Metabo HPT manuals. Starrett's outside corner rows print a right bevel for both pieces, which contradicts the Bosch manual and the model, so the calculator follows Bosch. Polygon settings agree with the Woodworker's Journal octagon example, 22.5° per cut. Every address in the lists above was then opened and checked for a distinct title, a chart and clean CSV, image and print output, at desktop, tablet and phone widths.

Common questions

What is the miter angle for a 90 degree corner?

45 degrees on each piece. The two pieces share the corner, so each takes half of 90 degrees, and because a square cut reads 0 on the saw scale, the setting is 90 minus 45 = 45 degrees. Inside corners and outside corners swing the saw in opposite directions.

What angle do I cut for a hexagon, octagon or pentagon?

Divide 180 by the number of sides. A hexagon takes 30 degrees at each end of every piece, an octagon 22.5 degrees, a pentagon 36 degrees and a square frame 45 degrees. All the pieces must be the same width for the shape to close.

What are the miter and bevel settings for crown molding?

Laid flat on the saw at a 90 degree corner, 38 degree spring crown (sold as 52/38) takes a 31.6 degree miter and a 33.9 degree bevel, and 45 degree spring crown (45/45) takes 35.3 and 30. Nested upside down against the fence and table, the same corner takes a plain 45 degree miter with the bevel at 0.

How do I cut a miter for a corner that is not 90 degrees?

Measure the corner with a protractor or a sliding bevel, enter it, and cut what the calculator gives. For baseboard the saw setting is 90 minus half the corner, so an 87 degree corner takes 46.5 degrees. For crown laid flat both angles change: 38 degree spring at 87 degrees gives a 33 miter and a 34.9 bevel, against 31.6 and 33.9 at 90. Cut a scrap corner to confirm.

What does spring angle mean on crown molding?

It is the angle between the back of the crown and the wall when the crown is installed. Common crown is 38 degrees, sold as 52/38, or 45 degrees, sold as 45/45. With the wall angle it decides the compound cut.

Why does my miter joint still leave a gap?

Usually because the wall is not the angle you assumed. A 1 degree error in the corner is half a degree on each piece and opens about 0.02 inch across 3/4 inch baseboard, more on tall crown. A saw that is out of square and wood that moves after cutting also open joints, and coping the second piece on inside corners hides most of it.

Related Calculators and Reference

• Rafter Calculator: the plumb and seat cut angles when the same saw is cutting roof framing.
• Angle Converter: switch between degrees, gradians and other units when a gauge or app reads differently.
• Trig Calculator: check the sines, cosines and tangents behind the crown formulas.
• Deck Board and Screw Calculator: the boards and screws for a mitered picture frame border on a deck.
• Board Foot Calculator: how much lumber a frame, box or planter needs once the miters are set.
• DeWalt: how to cut crown molding: the nested and flat methods for 52/38 crown from a saw manufacturer.