**mitre**or

**miter joint**is a joint made by bevelling each of two parts to be joined, usually at a 45° angle, to form a corner, usually a 90° angle. It is often used in making picture frames.

For miter joints occurring at angles other than 90°, for materials of the same width and height the proper cut angle must be determined so that the two pieces to be joined meet flush. 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 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 .

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.

A mathematical treatment of 3D mitering can be found in.

### Woodworking and carpentry

In woodwork, it is one way of joining two pieces of moulding that meet at an angle. In carpentry it is a joint to create a pleasing look to skirting boards and architrave around door frames and windows or any feature requiring a moulding or a border. It is a popular method of joining as it is easy and attractive. By itself, it is one of the weakest joints to choose, but it can be strengthened with a spline .### Piping and ducting

It is also done in pipe work, to take ducts around a corner, or in pipe organs, to fit a large bass pipe into a small space.miter joint: Published with permission from Wikipedia, the free encyclopedia