A mitre joint (miter in American English, sometimes shortened to mitre) 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. For woodworking, a disadvantage of a mitre joint is its weakness, but it can be strengthened with a spline[i]. There are two common variations of a splined mitre joint, one where the spline is long and runs the length of the mating surfaces and another where the spline is perpendicular to the joined edges.
For mitre 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 either to rotate the piece in 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 typically is desirable to have the longitudinal edges of the joined pieces match up properly at the joint. It always is possible to close a 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 around. In general, a twist occurs, causing the edges at the last joint to be misaligned.
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