Quick guide
How to calculate a compound miter cut
- Choose a tapered box, a flat polygon, crown molding, or a two-board joint.
- Enter the number of sides or the measured inside corner angle. Define slopes from vertical or horizontal; do not mix the two.
- Read miter and bevel on standard zero-at-square saw scales. Follow the setup notes for your stock orientation.
- Test on scrap, dry-fit the joint, then copy or print your setup card.
Miter vs. bevel: which scale?
Miter turns the cut away from a square crosscut, as seen on the saw table. Bevel tilts the blade away from vertical. The miter complement is a geometric layout angle—not a second saw setting. A scale that labels a square cut 90° may use the complement.
For an upright four-sided box cut with the broad face flat, the side-edge joint is miter 0°, bevel 45°. For a flat square picture frame, the end joint is miter 45°, bevel 0°. Orientation changes the answer.
Tapered planter and hopper joints
Box mode assumes equal outward side slopes and equal plan corner angles. A four-sided rectangle can use different side lengths while retaining these angles. When neighboring sides have different slopes, use two-board mode; it calculates a separate face miter for each board with a shared equal-split bevel.
The cut schedule covers side-to-side joints only. It does not calculate stock lengths, bottom panels, bottom-edge bevels, thickness offsets, or kerf allowances.
Crown molding cut flat
Measure the spring angle from the wall to the broad back of the installed molding. Enter the smaller angle between the walls for either corner type. The setup table assumes the broad back is down and the blade bevels left; changing face or edge orientation changes the directions.
The wall edge is the molding edge nearest the wall when installed; the ceiling edge is nearest the ceiling. Left and right pieces are named as viewed facing the corner from the room.
Unequal-slope two-board joints
Both bottom reference edges lie in one horizontal plane. Each face rises and leans outward from the inside of the joint. The model assumes equal stock thickness and bisects the joint between the broad faces. Each board may need a different miter, even though the blade bevel is the same.
The signed face-layout angle helps identify seams that lean in opposite directions. It is not a universal left/right saw instruction; mark inside faces and top edges, then verify each orientation on scrap.
Compound miter formulas
For equal slopes, let C be the inside plan corner and β the outward slope from vertical. For an n-sided polygon, C = 180° − 360°/n. A slope measured from horizontal converts with β = 90° − slope.
Miter = atan(sin β / tan(C / 2))Bevel = asin(cos β × cos(C / 2))For unequal slopes, the calculation constructs unit inward face normals nA and nB. The bisecting cut-plane normal is q = (nA − nB) / |nA − nB|. For each board, its signed seam angle is atan(−(q·w)/(q·e)), where e follows the bottom reference edge and w goes across the broad face. Bevel is asin(|q·nA|). All displayed trigonometric angles are in degrees.
Worked reference cases
| Project | Inputs | Miter | Bevel |
|---|---|---|---|
| Upright four-sided box, cut flat | C = 90°, β = 0° | 0.00° | 45.00° |
| Four-sided planter | C = 90°, β = 10° | 9.85° | 44.14° |
| Standard 38° crown | C = 90°, spring = 38° | 31.62° | 33.86° |
| 45° crown | C = 90°, spring = 45° | 35.26° | 30.00° |
| Flat hexagonal frame | 6 sides; C = 120° | 30.00° | 0.00° |
| Only board A leans | C = 90°, βA = 15°, βB = 0° | A: 0.00°; B: 15.00° | 45.00° |
Frequently asked questions
Why does an upright box show zero miter?
These settings assume the board is laid with its broad face flat, with the bottom reference edge along the fence. Its side-edge joint is a blade bevel. Do not substitute settings for stock held on edge or crown held nested against a fence.
Can I use a non-square corner or different slopes?
Yes. Two-board mode accepts an inside corner between 0° and 180° and independent outward slopes below 90° from vertical. Crown mode also accepts non-square wall corners. Inward slopes, compound lengthwise slopes, unequal-thickness joints, and butt joints are outside this model.
What if the angle exceeds my saw's capacity?
Do not force the setup. The calculator flags settings above a common 45° bevel or 60° miter, but actual limits depend on the saw and stock. Check your manual; some valid geometric cuts cannot safely be made with your equipment.
Does the calculator save or upload my project?
No. Inputs and calculations stay in this browser page. Copy a setup card if you want to keep the values; refreshing restores defaults.
References and validation
The equal-slope equations can be derived from a face triangle and plane normals, as shown in Bjorn Jansson's compound-angle derivation. Our vector implementation extends that geometry to unequal slopes.
The DEWALT DW713 manual, English pages 45–46 provides the 38° crown reference and cut orientations. Its bevel mark is 33.85°; direct trigonometry for exactly 38° gives 33.8629°. Use scrap to fine-tune the actual fit.