# how to calculate miter and bevel angles

trove of timber framing math was a huge help. A quick search of the web for

or 20° from vertical and the capping piece has an angle of 45°. out there, I wasn't able to find to for calculate a butted joint at a compound angle. Unlike a mitered joint where the two pieces to be The mitre cut is necessary when joining two boards at an angle-- most often when joining the trim around a door or window, the corners of baseboard and moulding or in building a picture frame. 0° is a square ended piece, 45° is a piece cut with a 1:1 angle. End angle is the angle you'd set your crosscut fence to. Sides: Piece Thick Sides Flat Miter ? Miter angle (of deviation or bend) of flat piece - eg: 90° corner = 45° Flat Miter 60° corner = 30° Flat Miter.

so in the calculator, they are simply referred to as A and B. (fig 1), The two pieces are joined at an angle of 135° of research, I discovered the possible reason why  calculating a butted joint is much more When setting bevel and miter angles for all compound miters, remember that: The angles presented for crown moldings are very precise and difficult to set exactly. Slope angle is measured from the horizontal plane. Both pieces are beveled at a 45.373° angle. Bevel angle: asin( cos(slopeA) * cos(slopeB) - sin(slopeA) * cos(slopeB) * cos(corner_angle)). Since they can shift slightly and very few rooms have exactly square corners, all settings should be tested on scrap moldings.

complicated than calculating a mitered joint. How to Calculate Angles for a Miter. 0° a square edge (no bevel), 45° is a piece cut with a 1:1 bevel.

Capping piece  the end is cut at a -18.939° angle End angle: atan( cos( slope_angle ) * tan( corner_angle / 2 ) ) Calculation of Miter and Bevel Angles Photo courtesy of Tim Uhler Diagrams and Calculations from other Reference Planes Calculating with respect to a level plane through the Ridges The Cricket Valley Roof Plane is assumed to be 22.5°, half of the 45° on the 12 ÷ 12 Slope. Two inputs define the angles of the box: 1. φ is the angle the sides make with the XY-plane 2. nis the number of sides in the box From n we can calculate the angle θ which separates the ncutting planes in the XY-plane. θ = 360° / n Notice that the long point of the angle on the butting piece is toward the top, and the long point of the capping piece The main Navigation tabs at top of each page are Metric - inputs in millimeters (mm), Miter angle (of deviation or bend) of flat piece - eg: 90° corner = 45° Flat Miter 60° corner = 30° Flat Miter. Butted compound angles are more complex than a simple mitered joint. Bevel is the angle you'd set your blade to. The ridge of the 22.5° slope meets the 7 ÷ 12 ridge (30.25644° Pitch Angle) at 90° as measured on a Level Plane. steeper angled piece. Input: Compound Miter Template Generator - Calculator Print Template - Fold over piece to align saw, mark or cut through template. Select output Fraction Precision, Decimal Inch or Metric mm. Bevel angle: asin( sin( slope_angle ) * sin( corner_angle / 2 ) ), For the butted joint: Results:

Bevel is the angle you'd set your blade to. Bevel is given in degrees from vertical, when the piece is laying flat on a horizontal plane (like on the top of a saw table). Included angle refers to the angle the two pieces meet in plan view. c = |s| |c| cos β Written on: July 14, 2020. corner mitre 3 image by nebari from Fotolia.com. Bevel is given in degrees from vertical, when the piece is laying flat on a horizontal plane (like on the top of a saw table). In this example, the butting piece is tipped at an angle of 70°, This happens when a shallower angled piece intersects a Written by: Ron Sardisco. This can be tricky to visualize when cutting -- mark your material carefully!

The results for this calculation is as follows: Butting piece  the end is cut at a 44.622° angle If it doesn't do what you want, go ahead and make your own, If either of these values exceed 90°, I subtract from 180 to provide a negative angle that indicates the angle goes the other way. End angle A: 90 - atan( ( tan(slopeB) * sin( corner_angle) ) / ( sin(slopeA) + tan(slopeB) * cos(slopeA) * cos(corner_angle) ) ) All calculators on this site are geometric only.

and also to Joe Bartok whose archived treasure If you find a mistake, I'd love to hear about it. Sides Angle like this excellent page: Bjorn Jansson's Compound Miter Saw Calculator (his does butted joint too! End angles are given in relation to a square end. joined are tipped at the same angle, in a butted joint, the two pieces to be joined can have different angles. ), Bjorn Jansson's Compound Miter Saw Calculator. ...where |s|=1 and |c|=1, Reference: The Calculus with Analytic Geometry, 6th Edition, Louis Leithold, ISBN 0-06-043930-0, φ is the angle the sides make with the XY-plane. If you're interested in playing or checking my work (please! End angle B: 90 - atan( ( tan(slopeA) * sin( corner_angle) ) / ( sin(slopeB) + tan(slopeA) * cos(slopeB) * cos(corner_angle) ) ).