Box miter calculator
A four-sided box with sides sloped 45° cuts at a 35.3° miter and a 30.0° blade tilt. Enter the number of sides and how far they lean, and this gives the compound miter saw settings for a mitered joint and a butt joint, checked against your saw's limits. For planters, hoppers, trays, and segmented bowl rings.
Cutting crown molding? Crown molding angle calculator
Updated
Sides from 3 to 16. Tilt from vertical is 0 for straight-sided boxes and 90 for a flat frame; a planter whose sides lean out 15 degrees is 15. Results are saw settings, read off the miter and bevel scales.
- Miter (saw table)
- 22.2°
- Blade tilt, mitered joint
- 20.7°
- Blade tilt, butt joint
- 48.6° (over your saw)
- Corner angle (plan view)
- 120.0°
- Angle between sides
- 138.6°
The butt-joint blade tilt exceeds your saw. Use the mitered joint setting instead.
How the math works
Seen from above, a box with N sides has corners of (N - 2) × 180° ÷ N: 90° for a square, 120° for a hexagon, 135° for an octagon. When the sides lean, each corner becomes a compound cut, and the saw needs two settings: a miter on the table and a tilt on the blade.
With the side tilt T measured from vertical and half the corner angle H, the miter is atan(sin T × cos H ÷ sin H) and the blade tilt for a mitered joint is asin(cos T × cos H). This is the same compound-miter formula the crown molding calculator uses, with the side tilt in place of the spring angle, and the CutOnce app runs both through one shared function.
A butt joint puts one piece's edge against the other's face instead of splitting the corner. Its blade tilt is 90° less twice the mitered tilt. Straight sides (tilt 0) give a 0° miter and a 45° blade tilt on a square box; a flat frame (tilt 90) gives a plain miter of 180° ÷ N with the blade square, and a butt joint does not apply.
A worked example: a hexagon hopper with 45° sides
Six sides leaning 45° from vertical, cut on a saw that bevels to 45° and miters to 50°. This is one of the app's own test cases.
| Corner angle (plan) | 120.0° | (6 - 2) × 180° ÷ 6 |
| Miter | 22.2° | atan(sin 45° × cos 60° ÷ sin 60°) |
| Blade tilt, mitered joint | 20.7° | asin(cos 45° × cos 60°) |
| Blade tilt, butt joint | 48.6° (over a 45° saw) | 90° - 2 × mitered tilt |
| Angle between sides | 138.6° | 180° - 2 × mitered tilt |
The butt-joint tilt is past what most miter saws bevel, so cut the mitered joint. The app flags this against the limits saved in your settings; the widget above does the same.
A second example: a square planter with a 15° flare
Four sides leaning out 15° from vertical cut at a 14.5° miter and a 43.1° blade tilt for mitered corners. For butted corners, both pieces keep the 14.5° miter and take a 3.8° blade tilt, with the cuts on opposite faces.
Compound miter chart
Miter / blade tilt for a mitered joint, by number of sides and side tilt from vertical. Read the miter on the saw table and the tilt on the bevel scale.
| Tilt | 4 sides | 6 sides | 8 sides |
|---|---|---|---|
| 0° | 0.0° / 45.0° | 0.0° / 30.0° | 0.0° / 22.5° |
| 5° | 5.0° / 44.8° | 2.9° / 29.9° | 2.1° / 22.4° |
| 10° | 9.9° / 44.1° | 5.7° / 29.5° | 4.1° / 22.1° |
| 15° | 14.5° / 43.1° | 8.5° / 28.9° | 6.1° / 21.7° |
| 20° | 18.9° / 41.6° | 11.2° / 28.0° | 8.1° / 21.1° |
| 30° | 26.6° / 37.8° | 16.1° / 25.7° | 11.7° / 19.4° |
| 45° | 35.3° / 30.0° | 22.2° / 20.7° | 16.3° / 15.7° |
| 60° | 40.9° / 20.7° | 26.6° / 14.5° | 19.7° / 11.0° |
Segmented bowl rings and flat frames
A segmented ring or a picture frame lies flat, so the blade stays square and only the miter changes: 180° ÷ the number of segments.
| Segments | Miter |
|---|---|
| 6 | 30° |
| 8 | 22.5° |
| 10 | 18° |
| 12 | 15° |
| 16 | 11.25° |
What the app adds
The app keeps your saw's bevel and miter limits in settings and flags each setting that goes past them, draws the joint, enters the tilt from vertical or horizontal on the same keypad as every other calculator, and prints the cut settings as a PDF.
Common questions
- What angles do I cut for a four-sided planter with sloped sides?
- It depends on the slope. Sides leaning 15° cut at a 14.5° miter with a 43.1° blade tilt; sides leaning 45° cut at 35.3° and 30.0°. Enter your slope above for the exact settings.
- Should the tilt be measured from vertical or from horizontal?
- Either works; pick the one you measured. Tilt from vertical is how far the side leans out from straight up, so straight sides are 0°. Tilt from horizontal is the angle the side makes with the base, so straight sides are 90°. The calculator converts one to the other.
- What is the difference between a mitered joint and a butt joint?
- A mitered joint splits the corner so both pieces get the same compound cut and no end grain shows. A butt joint runs one piece past the other: both pieces take the same miter and the butt-joint blade tilt, with the cuts on opposite faces. With straight sides (tilt 0) that tilt is 0 and both ends are square crosscuts. The butt joint is easier to clamp; the mitered joint looks cleaner.
- What does "opposite face" mean on the butt-joint setting?
- On boxes with few sides and steep walls, such as a triangle with straight sides, the butt-joint tilt comes out negative. It means tilting the blade the other way, or flipping the board so the cut is on the opposite face.
- What miter do I cut for a segmented bowl ring?
- 180° divided by the number of segments, with the blade square: 22.5° for 8 segments, 15° for 12, and 11.25° for 16. A ring is a flat frame, so pick Flat frame in the calculator.
Two settings, cut once
CutOnce solves box miters like this page, then checks them against your saw, draws the joint, and prints the settings as a PDF, with no signal needed.
Free to download, with a 7-day trial of everything. This page gives the saw settings; the app keeps them with the job.
See also