A mitre box (US spelling, "miter box") is a wood working tool used to guide a hand saw to make precise mitre cuts in a board.

The most common form of a mitre box is a 3-sided box which is open at the top and the ends. The box is made wide enough to accommodate the width of the boards to be cut. Slots are cut in the walls of the box at the precise angle at which the cut is to be made. These slots provide the guide for the saw to follow. Most commonly, the slots in the mitre box are cut at 45 degrees and 90 degrees.

The mitre saw combines the features of a mitre box with a backsaw.

In the past, mitre boxes were constructed mostly of wood. Some have had metal guides fitted to help prevent wear on the slots. Today, mitre boxes are also available in other materials such as moulded plastic and cast aluminium.

When carpenters used to make their own mitre boxes, it was common to use a mitre box until its guide slots became worn and then make a new one out of scrap timber. There is still a case to be made for making one today; for example, if an odd size (say, 175mm) cornice is to be fixed, then a custom mitre box with a bottom board that is 175mm wide would ensure that the cornice sits true while the cuts are being made to it. The three pieces of timber that form the mitre box are nailed together, and the top steadying pieces are fixed with smaller panel pins. The angles are marked (at any angle, not necessarily 45 degrees) and the guide slots are cut with the same saw that will be used for the rest of the cutting.

The mitre ( /ˈmaɪtər/; Greek: μίτρα, "headband" or "turban"), also spelled miter, is a type of headgear now known as the traditional, ceremonial head-dress of bishops and certain abbots in the Roman Catholic Church, as well as in the Anglican Communion, some Lutheran churches, and also bishops and certain other clergy in the Eastern Orthodox churches, Eastern Catholic Churches and the Oriental Orthodox Churches.

The word μίτρα, mítra, (or, in its Ionic form, μίτρη, mítrē) first appears in Greek and signifies either of several garments: a kind of waist girdle worn under a cuirass, as mentioned in Homer's Iliad; a headband used by women for their hair; a sort of formal Babylonian head dress, as mentioned by Herodotus (Histories 1.195 and 7.90). The former two meanings have been etymologically connected with the word μίτος, mítos, "thread", but the connection is tenuous at best; the latter word is probably a loan from Old Persian.

In ancient Israel, the Kohen Gadol (High Priest) wore a headdress called the Mitznefet (Hebrew: מצנפת, often translated into English as "mitre"), which was wound around the head so as to form a broad, flat-topped turban. Attached to it was the Tzitz (Hebrew: ציץ), a plate of solid gold bearing the inscription "Holiness to YHWH" (Exodus 39:14, 39:30). Lesser priests wore a smaller, conical turban.

Box (plural boxes) describes a variety of containers and receptacles for permanent use as storage, or for temporary use often for transporting contents. The word derives from the Greek πύξος (puxos), "box, boxwood".

Boxes may be made of durable materials such as wood or metal, or of corrugated fiberboard, paperboard, or other non-durable materials. The size may vary from very small (e.g., a matchbox) to the size of a large appliance. A corrugated box is a very common shipping container. When no specific shape is described, a box of rectangular cross-section with all sides flat may be expected, but a box may have a horizontal cross section that is square, elongated, round or oval; sloped or domed top surfaces, or non-vertical sides.

A decorative or storage box may be opened by raising, pulling, sliding or removing the lid, which may be hinged and/or fastened by a catch, clasp, or lock.

Several types of boxes are used in packaging and storage.

Depending on locale and specific usage, the terms carton and box are sometimes used interchangeably.