The Angle Cut Calculator determines the correct miter and bevel angles for angled joints, compound cuts, and polygon frames in woodworking, carpentry, and construction. Enter the desired joint angle or polygon sides to find the exact saw blade settings for accurate, gap-free angle cuts.
36.8699
°
53.1301
°
25
ft
25
ft
36.8699
°
53.1301
°
25
ft
25
ft
The calculator for angle cuts determines the correct miter and bevel angles for cutting boards at precise angles in woodworking, carpentry, metalworking, and construction. Whether you are building a polygon picture frame, cutting a roof rafter, making an angled joint, or fitting a handrail, this calculator provides the exact saw settings needed for accurate, gap-free cuts.
Two independent angle adjustments are available on a miter saw:
For flat frame joints (picture frames, door casings): only the miter angle is needed. For crown molding and compound cuts: both miter and bevel angles must be set simultaneously. For a simple 90° corner (two pieces joining at a right angle): each piece is cut at 45° miter. Use this online calculator for any joint angle or polygon. The miter angle calculator specializes in complex multi-sided polygon frame calculations.
For a regular polygon frame with N equal sides, each corner miter cut angle is:
Miter angle = 90° − (180° / N)
Common polygon frames:
Note that most miter saws have a maximum miter angle of 45–52°; polygons requiring cuts steeper than the saw's range require alternative methods such as rotating the workpiece.
Roof framing requires three angle cuts on each rafter: the plumb cut (vertical cut at the ridge), the bird's mouth (seat cut where rafter sits on the wall plate), and the tail cut (overhang end). All three are derived from the roof pitch angle: Pitch angle = arctan(rise/run). For a 6:12 pitch: angle = arctan(0.5) = 26.57°. Plumb cut angle = 26.57° from vertical; seat cut angle = 90° − 26.57° = 63.43°. The slope calculator and angle and slope calculators provide complementary roof geometry tools.
Staircase handrails require cuts at the stair pitch angle where the rail meets newel posts and walls. The handrail angle = arctan(total rise / total run) — the same as the stringer angle. Where a handrail changes direction at a landing or wraps around a corner, compound angle cuts are required. The ramp calculator provides the incline angle calculation for ramps, which follow the same geometric principles as stair pitch calculations.
Enter the required input values in the fields provided. The calculator uses established formulas and mathematical relationships to compute the results in real-time. All calculations are performed client-side for instant feedback.
The Angle Cut Calculator applies standard angle & slope formulas to deliver accurate results. Adjust any input value to see how it affects the output.
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For a regular hexagonal frame with 6 equal sides, each corner interior angle is 120°. Each piece must be cut at a miter angle of 30° (half of the exterior angle of 60°) on each end. Set the miter saw to 30° and cut both ends of each of the six pieces. When assembled, the six 30° cuts at each corner produce a precise 120° interior angle with no gaps.
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For a standard square or rectangular frame with 90° corners, each piece is cut at exactly 45° on each end. Set the miter saw to 45° and cut both ends of each of the four pieces. This is the most common angle cut in woodworking — picture frames, door casings, window trim, and baseboards all use 45° miter cuts at corners.
The Angle Cut Calculator uses precise mathematical formulas and provides results with up to 6 decimal places of precision. The accuracy depends on the precision of your input values.
The calculator uses standard units commonly used in angle & slope calculations. Each input and output field displays its unit for clarity.
Yes, the Angle Cut Calculator is fully responsive and works on all devices including smartphones, tablets, and desktop computers.
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