how to calculate miter and bevel angles
0° a square edge (no bevel), 45° is a piece cut with a 1:1 bevel. If either of these values exceed 90°, I subtract from 180 to provide a negative angle that indicates the angle goes the other way. If you find a mistake, I'd love to hear about it. End angle refers to the angle on the end of the piece when it is laying in the horizontal plane (like on the top of a tablesaw). Since they can shift slightly and very few rooms have exactly square corners, all settings should be tested on scrap moldings. It doesn't actually matter which piece butts and which caps, 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). Written by: Ron Sardisco. In this example, the butting piece is tipped at an angle of 70°, End angle is the angle you'd set your crosscut fence to. ...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. 0° is horizontal and 90° is vertical. θ = 360° / n End angle A: 90 - atan( ( tan(slopeB) * sin( corner_angle) ) / ( sin(slopeA) + tan(slopeB) * cos(slopeA) * cos(corner_angle) ) ) Butted compound angles are more complex than a simple mitered joint. steeper angled piece. Just adjust angular orientation accordingly. These two calculators were designed with a tablesaw in mind, although you could use it with any tool. The angle is measured between the two pieces – Input: 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). Sides Angle End angle B: 90 - atan( ( tan(slopeA) * sin( corner_angle) ) / ( sin(slopeB) + tan(slopeA) * cos(slopeB) * cos(corner_angle) ) ). trove of timber framing math was a huge help. The results for this calculation is as follows: Butting piece – the end is cut at a 44.622° angle Slope angle is measured from the horizontal plane. 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. so in the calculator, they are simply referred to as A and B. Thanks to this website:, ‎Schifter is a calculator for sawing angles, it calculates the setting angles for your mitre saw or your sliding compound mitre saw as well as the required alignment of the workpiece. 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. complicated than calculating a mitered joint. If it doesn't do what you want, go ahead and make your own, That side's inside bottom corner is at the origin. End angles are given in relation to a square end. 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. or 20° from vertical and the capping piece has an angle of 45°. 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. like this excellent page: Bjorn Jansson's Compound Miter Saw Calculator (his does butted joint too! If you're interested in playing or checking my work (please! This page is offered "as-is" -- I cannot provide support, and you use it at your own risk. 90° is a 4-sided box, 120° is 6-sides, etc. Bevel is the angle you'd set your blade to. in the horizontal plane (or plan view). A spreadsheet version is available as well. This happens when a shallower angled piece intersects a is at the bottom (this is represented by the negative angle). 0° is a square ended piece, 45° is a piece cut with a 1:1 angle. A quick search of the web for Please, Zoom out to fit large full scale template images on screen - or to adjust scale to match ruler held against screen, Click Slider to select then use keyboard cursor keys, Create and Print Full Scale PDFs with diagrams on this page (templates), Copy all diagrams on this page to bottom of page - Make multiple copies to Print or Compare Results, If you've benefited from this free service please consider helping us support, Compound Miter Template Generator - Calculator, All Inch inputs and dimensions are actual physical finished sizes, If the US ever goes Metric, you'll be able to use a Meter to measure Meters - A Meter Meter. This can be tricky to visualize when cutting -- mark your material carefully! How to Calculate Angles for a Miter. ), here are the formulas I used: For the miter: Bevel angle: asin( sin( slope_angle ) * sin( corner_angle / 2 ) ), For the butted joint: A handy online tool for the knifemaker to determine the angle to use when grinding single or double bevel blades. Written on: July 14, 2020. corner mitre 3 image by nebari from The ridge of the 22.5° slope meets the 7 ÷ 12 ridge (30.25644° Pitch Angle) at 90° as measured on a Level Plane. The Vietnamese Lawyer Saving Women Trafficked to China. End angle is the angle you'd set your crosscut fence to. Compound Miter Template Generator - Calculator Print Template - Fold over piece to align saw, mark or cut through template. 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. an online calculator quickly showed that, even though there are plenty of great miter calculators 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 assembled box is sitting with its inside bottom edge on the XY-plane, oriented such that one side is parallel with the Y-axis. out there, I wasn't able to find to for calculate a butted joint at a compound angle. All calculators on this site are geometric only. Both pieces are beveled at a 45.373° angle. ), Bjorn Jansson's Compound Miter Saw Calculator. (fig 1), The two pieces are joined at an angle of 135° I recently had a woodworking project with compound angles. After a bit Included angle refers to the angle the two pieces meet in plan view. Capping piece – the end is cut at a -18.939° angle Bevel is the angle you'd set your blade to. (fig 2). Bevel angle: asin( cos(slopeA) * cos(slopeB) - sin(slopeA) * cos(slopeB) * cos(corner_angle)). Download Schifter - calculate miter and bevel and enjoy it on your iPhone, iPad, and iPod touch. Select output Fraction Precision, Decimal Inch or Metric mm. c = |s| |c| cos β 0° a square edge (no bevel), 45° is a piece cut with a 1:1 bevel. 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. and also to Joe Bartok whose archived treasure Built something using our calculators? Unlike a mitered joint where the two pieces to be joined are tipped at the same angle, in a butted joint, the two pieces to be joined can have different angles. Results: of research, I discovered the possible reason why – calculating a butted joint is much more End angle: atan( cos( slope_angle ) * tan( corner_angle / 2 ) )


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