A miter joint (mitre in British English), sometimes shortened to miter, is a joint made by beveling each of two parts to be joined, usually at a 45° angle, to form a corner, usually a 90° angle. A disadvantage of a miter joint is its weakness, but it can be strengthened with a spline.
For miter joints occurring at angles other than 90°, for materials of the same cross-section the proper cut angle must be determined so that the two pieces to be joined meet flush (i.e. one piece's mitered end is not longer than the adjoining piece). To find the cut angle divide the angle at which the two pieces meet by two. Technically two different cut angles are required; one for each piece, where the second angle is 90° plus the aforementioned cut angle, but due to angular limitations in common cutting implements (hand circular saws, table saws) a single angle is required and is used to cut the first piece in one direction and the second piece in the opposite direction.
When a piece is beveled at both ends, such that the two attached pieces do not lie in the same plane, a three-dimensional structure is obtained. In that case, it is also necessary to either rotate the piece along its longitudinal axis or to tilt the saw blade before beveling the second end.
When employing the miter joint to connect two pieces that have a non-circular cross-section it is typically desirable to have the longitudinal edges of the joined pieces match up properly at the joint. It is always possible to close a planar structure constructed with pieces having non-circular cross section into a loop through properly matched miter joints (e.g. a picture frame). However, a three-dimensional loop from pieces with non-circular cross section need not close properly when attempting to miter it all the way round. In general, a twist occurs, causing the edges at the last joint to be misaligned.
- Oxford English Dictionary. Oxford University Press. 2009. "A usually right-angled joint in wood or other material in which the angle made by the joined pieces is bisected by the line or plane of junction; more fully mitre joint."
- "Splined Miter Joint". Woodworkingtips.com. Retrieved 2012-04-01.
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- Verhoeff, Tom and Koos Verhoeff, PDF "The Mathematics of Mitering and Its Artful Application", Bridges Leeuwarden: Mathematical Connections in Art, Music, and Science, Proceedings of the Eleventh Annual Bridges Conference, in The Netherlands, pp. 225–234, July 2008.