Why is a 90° corner cut at 45°, but a 135° corner not cut at 67.5°?

Because the saw's scale does not measure the corner, it measures how far the blade swings away from a square cut. A square corner turns the trim through 90°, each piece takes half the turn, and 45° happens to be both half the turn and half the corner — the one case where the two shortcuts agree. A bay's 135° corner turns the trim through only 45°, so each piece is cut 22.5° off square. The rule that always works is 90° less half the corner measured through the room, or half the excess over 180° for an external corner.

Do inside and outside corners need different settings?

The same angle of corner takes the same setting either way; what changes is which hand each piece is cut in and which side of the blade is kept. A square internal corner and a square chimney breast both take 45°. The mistakes happen in the handing, so mark each piece where it goes, cut a pair from offcuts first, and follow the saw maker's chart for which way to swing the table for the left and the right piece.

Why does crown need a bevel when it lies flat, but none when it is nested?

Nested, the moulding leans between the fence and the table exactly as it leans between the wall and the ceiling, so the joint is a plain vertical cut, square to the table, and only the mitre moves. Laid flat, the moulding has been rotated off its working angle, and the same joint is now tilted relative to the table, so the blade has to tilt as well. That is why the flat settings change with the spring angle and the nested one does not. Nesting is simpler and easier to adjust; laying flat is the method for a moulding too deep to stand up under the fence.

How do I know my crown's spring angle?

By measuring an offcut rather than trusting the label. The two patterns a mitre saw's crown stops are made for are 38/52 and 45/45, but cornices from smaller mills, imported profiles and run plaster vary, and settings worked for one spring leave a tapering gap on a moulding of another. Two measurements settle it: how far the moulding reaches out along the ceiling, and how far it hangs down the wall. The spring from the wall is the angle whose tangent is the first divided by the second — a crown reaching 82 mm (3.23 in) out and hanging 105 mm (4.13 in) down springs at about 38 degrees.

How do I cut segments for a round or many-sided frame?

Treat it as a polygon with as many sides as segments. Twelve segments in a circle turn 30° at each joint, so each segment's ends are cut 15° off square; twenty-four turn 15° and take 7.5°. Cut every segment from a stop block so they are identical, dry-assemble the ring, and if a gap remains, split it across all the joints by adjusting the setting a little rather than recutting one piece.

Does this page work out how much crown molding to buy?

No: the Crown Molding Calculator works out the run round the room and the sticks to buy, and this page the saw settings. Those settings cover crown flat or nested at any spring angle and corner, flat trim at any corner, and frames of any number of sides.

Renovation & Construction

Miter Angle Calculator — Mitre Saw Corners, Frames and Crown

Mitre (miter) saw settings for any corner, every joint of a regular frame or polygon, and the mitre and bevel for crown moulding cut flat or nested.

Answers as you typeNo submit button
Every formula citedNamed published standards
Calculated in your browserNo account, nothing uploaded

SettingsSettings for this calculationUS

Market

Imperial · sales tax

What Is Being Cut

A corner of flat trim, a closed frame of equal sides, or a sprung crown moulding.

Flat trim — skirting, baseboard, casing, a window board, a picture-frame moulding — needs only the plain mitre for the corner. A frame or polygon with equal sides needs the same mitre at every joint, worked out from the number of sides. Crown and cornice mouldings sit at an angle between wall and ceiling, so cut flat on the table they need a bevel as well as a mitre; the page gives both, and the nested setting beside them.

Corner Angle Through the Room (degrees)

The corner measured across the room's side: under 180 for an internal corner, over 180 for an external one.

Hold an angle finder or a sliding bevel against the two walls, or the two faces the trim will sit on, and read the angle on the side the room is. A square internal corner reads 90, a square chimney breast or boxing reads 270, and the obtuse corners of a bay read about 135 inside. Measure each corner rather than assuming it: a plastered corner a degree or two off square is normal, and a degree at the wall is a visible gap in the joint.

Tools needed: Digital angle finder, Sliding bevel and protractor

Mitre setting on the saw

45 °

High confidence

An internal corner, read through the room at under 180°. The scale reads the swing from a square cut, so the setting is 90° less half the corner, and both pieces are cut at it in opposite hands. In skirting or baseboard an internal corner is often coped instead, the second board scribed over the first, because a coped joint stays closed when the wall is off square; a mitre is the usual joint wherever the ends of both pieces would otherwise show, as round a window or on a frame.

Angle between each cut and the edge of its piece: 45 °
Angle the two pieces include: 90 °
Turn of the trim at the corner: 90 °

Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

Euclid, Elements, Book I, Proposition 32 with Proclus's corollaries (D. E. Joyce's edition, Clark University): the exterior angles of any convex rectilinear figure together make four right angles — so each corner of a regular frame of n sides turns it through 360° ÷ n, and each of the two mitres at that corner takes half
L.S. Starrett Company, CP505A-12 aluminum combination protractor user guide (crown molding user guide, Form 969): the inner 'Miter Cut' scale gives the mitre saw reading for a measured corner, and the Compound Cut Conversion Table gives the mitre and bevel for 38° and 45° crown laid flat, for Miter Cut readings of 1 to 60
DeWALT DWS779 double bevel sliding compound miter saw, instruction manual N445793: most crown has 52° at the ceiling and 38° at the wall; mitre latch points at 31.62° and bevel stop pawls at 33.9° for 52/38 crown laid flat, the pawl reversible to 30° for 45/45 crown; the alternative method with the crown angled between fence and table needs no bevel and is cut at 45°; the saw mitres 60° right and 50° left and bevels 49° each way
Joseph Fusco, crown moulding mitre and bevel angle chart for 38/52 and 45/45 stock at wall angles of 1° to 179°, reprinted by WOODWEB's knowledge base: at walls of 90° the 38/52 settings are 31.61 and 33.86, and at 45° they are 56.06 and 46.72 — the formulas above to two decimals, mostly cut off rather than rounded
Compound mitre for a sprung moulding laid flat, derived from the geometry of the cut: with M the plain mitre for the corner and S the spring angle from the wall, mitre = arctan(sin S · tan M) and bevel = arcsin(cos S · sin M); nested against the fence, the same joint is the plain mitre M with no bevel

Inputs used

What Is Being Cut: Flat trim meeting at a corner (skirting, baseboard, casing)
Corner Angle Through the Room (degrees): 90
Number of Sides: 8
Spring Angle from the Wall (degrees): 38
Wall Corner Through the Room (degrees): 90

Intermediate steps

Angle between each cut and the edge of its piece: 45 °
Angle the two pieces include: 90 °
Turn of the trim at the corner: 90 °

Final result45 °

Confidence note: An internal corner, read through the room at under 180°. The scale reads the swing from a square cut, so the setting is 90° less half the corner, and both pieces are cut at it in opposite hands. In skirting or baseboard an internal corner is often coped instead, the second board scribed over the first, because a coped joint stays closed when the wall is off square; a mitre is the usual joint wherever the ends of both pieces would otherwise show, as round a window or on a frame.

What this calculation does not cover

The settings are magnitudes. Which way the table swings, which way the blade tilts, which edge of a crown goes against the fence and which side of the cut is kept depend on whether the piece is the left or the right one and whether the corner is internal or external, and they differ between saws; follow the maker's chart for the saw in use and cut a trial pair from offcuts first.
The corner has to be measured, not assumed. A plastered corner a degree or two off square is ordinary, and the error goes straight into the joint, so read each corner with an angle finder or a sliding bevel at the height the trim will run.
Both pieces are taken as the same width and section. Two trims of different widths meeting at a corner need a different cut angle on each, and a frame of unequal sides needs each joint worked separately.
A setting near or past the end of a saw's scale needs a jig or a hand cut. The DeWALT DWS779 cited here mitres to 60° one way and 50° the other and bevels to 49°, so very sharp corners and small polygons can run off the scale; check the saw before buying stock for an unusual shape.
The crown settings depend on the spring angle entered. A moulding whose real spring differs from the figure used will gap at the ceiling or the wall however carefully the settings are dialled in, and the nested method only works while the moulding's drop fits under the fence.
Only angles are given: the length of each piece, the stock to buy and the offcuts lost to mitres are left to the trim and crown take-off pages.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-10-05 · v1.0.0

Regulatory standards & verification citations5

Euclid, Elements, Book I, Proposition 32 with Proclus's corollaries (D. E. Joyce's edition, Clark University): the exterior angles of any convex rectilinear figure together make four right angles — so each corner of a regular frame of n sides turns it through 360° ÷ n, and each of the two mitres at that corner takes half
L.S. Starrett Company, CP505A-12 aluminum combination protractor user guide (crown molding user guide, Form 969): the inner 'Miter Cut' scale gives the mitre saw reading for a measured corner, and the Compound Cut Conversion Table gives the mitre and bevel for 38° and 45° crown laid flat, for Miter Cut readings of 1 to 60
DeWALT DWS779 double bevel sliding compound miter saw, instruction manual N445793: most crown has 52° at the ceiling and 38° at the wall; mitre latch points at 31.62° and bevel stop pawls at 33.9° for 52/38 crown laid flat, the pawl reversible to 30° for 45/45 crown; the alternative method with the crown angled between fence and table needs no bevel and is cut at 45°; the saw mitres 60° right and 50° left and bevels 49° each way
Joseph Fusco, crown moulding mitre and bevel angle chart for 38/52 and 45/45 stock at wall angles of 1° to 179°, reprinted by WOODWEB's knowledge base: at walls of 90° the 38/52 settings are 31.61 and 33.86, and at 45° they are 56.06 and 46.72 — the formulas above to two decimals, mostly cut off rather than rounded
Compound mitre for a sprung moulding laid flat, derived from the geometry of the cut: with M the plain mitre for the corner and S the spring angle from the wall, mitre = arctan(sin S · tan M) and bevel = arcsin(cos S · sin M); nested against the fence, the same joint is the plain mitre M with no bevel

Cite this page

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These guides cover the work this quantity is for — the first ones run this calculator inside the section that raises the question.

Trimming Out a Room: Crown, Stock Lengths and Board Feetuses this calculator
Crown runs the whole ceiling line, so corners and stock lengths set the order — and the hardwood shed prices the same room by the board foot instead.

How to calculate miter angle — mitre saw corners, frames and crown in 6 steps

What Is Being CutA corner of flat trim, a closed frame of equal sides, or a sprung crown moulding.
Corner Angle Through the Room (degrees)The corner measured across the room's side: under 180 for an internal corner, over 180 for an external one.
Number of SidesHow many equal sides the frame or shape has: 4 for a square frame, 6 for a hexagon, 8 for an octagon.
Spring Angle from the Wall (degrees)The angle between the back of the moulding and the wall: 38 for 38/52 stock, 45 for 45/45.
Wall Corner Through the Room (degrees)The wall corner measured across the room's side, near the ceiling: 90 for a square internal corner, 270 for a square external one.
Mitre setting on the sawThe tool computes the mitre setting on the saw from those figures and shows the formula, its sources, and a confidence rating alongside it.

Mitre setting on the saw by corner angle through the room (degrees)

Page defaults, not your figures above.

Corner Angle Through the Room (degrees)	Mitre setting on the saw (°)
10	85
20	80
50	65
100	40
200	10

Frequently asked questions

Why is a 90° corner cut at 45°, but a 135° corner not cut at 67.5°?: Because the saw's scale does not measure the corner, it measures how far the blade swings away from a square cut. A square corner turns the trim through 90°, each piece takes half the turn, and 45° happens to be both half the turn and half the corner — the one case where the two shortcuts agree. A bay's 135° corner turns the trim through only 45°, so each piece is cut 22.5° off square. The rule that always works is 90° less half the corner measured through the room, or half the excess over 180° for an external corner.
Do inside and outside corners need different settings?: The same angle of corner takes the same setting either way; what changes is which hand each piece is cut in and which side of the blade is kept. A square internal corner and a square chimney breast both take 45°. The mistakes happen in the handing, so mark each piece where it goes, cut a pair from offcuts first, and follow the saw maker's chart for which way to swing the table for the left and the right piece.
Why does crown need a bevel when it lies flat, but none when it is nested?: Nested, the moulding leans between the fence and the table exactly as it leans between the wall and the ceiling, so the joint is a plain vertical cut, square to the table, and only the mitre moves. Laid flat, the moulding has been rotated off its working angle, and the same joint is now tilted relative to the table, so the blade has to tilt as well. That is why the flat settings change with the spring angle and the nested one does not. Nesting is simpler and easier to adjust; laying flat is the method for a moulding too deep to stand up under the fence.
How do I know my crown's spring angle?: By measuring an offcut rather than trusting the label. The two patterns a mitre saw's crown stops are made for are 38/52 and 45/45, but cornices from smaller mills, imported profiles and run plaster vary, and settings worked for one spring leave a tapering gap on a moulding of another. Two measurements settle it: how far the moulding reaches out along the ceiling, and how far it hangs down the wall. The spring from the wall is the angle whose tangent is the first divided by the second — a crown reaching 82 mm (3.23 in) out and hanging 105 mm (4.13 in) down springs at about 38 degrees.
How do I cut segments for a round or many-sided frame?: Treat it as a polygon with as many sides as segments. Twelve segments in a circle turn 30° at each joint, so each segment's ends are cut 15° off square; twenty-four turn 15° and take 7.5°. Cut every segment from a stop block so they are identical, dry-assemble the ring, and if a gap remains, split it across all the joints by adjusting the setting a little rather than recutting one piece.
Does this page work out how much crown molding to buy?: No: the Crown Molding Calculator works out the run round the room and the sticks to buy, and this page the saw settings. Those settings cover crown flat or nested at any spring angle and corner, flat trim at any corner, and frames of any number of sides.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.