Name the angle before setting the saw
Miter angle can mean several quantities. This miter angle calculator defines corner or included angle C as the interior angle between board centerlines in the finished flat joint. A cut-line angle is measured from a board's long edge. A saw miter setting is measured from the saw's 0° square-cut position. Showing all three prevents a 60° cut line from being copied as a 60° saw setting when the required rotation is 30°.
The miter angle calculator uses equal widths for a symmetric joint and unequal widths for the offset-boundary construction. Enter C strictly between 0° and 180°, use positive widths in the same unit, and select whether the diagram presents the inside or outside finished face. The results keep Board A and Board B separate even when their values match.
From included corner to two cut references
- Obtain the included angle between the finished board centerlines. Do not enter an exterior reflex angle or an existing saw scale reading as C.
- Choose Equal widths only when both faces have the same width. Then each cut line is C ÷ 2 and each saw setting is (180° − C) ÷ 2.
- For unequal widths, enter A and B separately in the same unit. The miter angle calculator solves the boundary intersections instead of continuing to halve C.
- Read each cut-line angle from its named long edge, then read the corresponding saw rotation from square. Keep the A and B labels with the reference.
- Confirm the direction and zero convention in the actual saw manual and verify fit with an appropriate scrap test cut before finished material.
Two-dimensional unequal-width methodology
- Board A is a strip centered on the positive x-axis. Board B is a strip whose centerline is rotated counterclockwise by C; each receives parallel boundaries offset by half its width.
- The inner seam endpoint is the intersection of the boundaries facing the included corner. The outer endpoint is the intersection of the opposite boundaries. Their connecting line is the common seam.
- Board A's cut angle is atan2(wA sin C, wB + wA cos C). Board B's angle is C minus A. This follows from the documented coordinates rather than an unexplained rule.
- When wA = wB, symmetry makes both cut-line angles C/2 and both saw settings 90° − C/2 = (180° − C)/2.
- A negative signed saw result means the seam falls on the opposite side of square for that board orientation. The UI reports magnitude plus opposite side instead of hiding direction.
Worked miter joint examples
- 90° equal-width corner: each cut line is 45° from its board edge and each saw setting is 45° from square.
- 120° equal-width corner: each cut line is 60° from the edge, while each saw setting is 30° from square. The labels use complementary references.
- Unequal 90° corner with Board A 60 mm and Board B 90 mm: A's cut line is about 33.690° and B's is about 56.310°. Their saw settings are about 56.310° for A and 33.690° for B.
- Inside and outside views of the same 90° equal-width joint retain 45° magnitudes, but the drawing mirrors the finished face and cut-facing interpretation.
Why unequal widths are not simply halved
An angle bisector crosses two equal-width strips at compatible offsets. If one board is wider, the same bisector reaches the corresponding edges at different places. Moving the seam to connect the common inner and outer intersections produces two different angles whose sum still checks against C.
The width unit does not change the angular answer because the width ratio controls the construction. It still belongs on the reference so stock is not confused with another piece.
Inside, outside, and compound work
Inside and outside name the finished face being reviewed, not a universal alternate formula. Mirroring the face reverses the diagram and cut-facing interpretation while the flat seam magnitudes remain. Profiles, crown spring angles, bevels, and compound miters require dimensions this two-dimensional calculator does not model.
Calculation is not a tool-operation instruction
The diagram is a flat geometric reference, not a fabrication approval or machine procedure. Saw zero calibration, blade kerf, fence alignment, stock profile, cupping, spring-back, wall error, and material compression affect fit. Some rotations exceed a saw's scale or require another stock orientation. Follow the equipment manual and safe shop practice; this page gives no blade, guard, hand-position, or cutting instructions and does not replace woodworking experience or a test fit.
Dimensions and selections are calculated locally. The share URL contains only the corner angle, width mode, numeric widths, unit, and inside/outside choice.