Quadrant (Lat. quadrans, a quarter), the fourth part of the circle or an arc of 90°, and hence an instrument employed for measuring angles in any plane. The use of quadrants has been for surveying and for making astronomical observations, and especially in navigation for determining the meridian altitude of the sun, and through this the latitude of the observer. They have been constructed of a great variety of forms and dimensions adapted for their several uses; but at present the interest attached to them is historical only, as they have been entirely superseded either by the sextant or the full circle. The former, of more portable form than the quadrant, by the use of two reflecting mirrors doubles the angle included between the direct and reflected line of light, and thus with an arc of 60° or one sixth of the circle includes a range of 120°; while the circle, on account of the symmetry of its form and the completeness of its graduated arc-all around, secures greater exactness in its readings, and is less liable to the introduction of any unsuspected source of error. Ptolemy made use of a quadrant for determining the obliquity of the ecliptic.

Tycho Brahe had a large mural quadrant (so called from its being suspended upon an axis secured in a solid wall of masonry) with which he observed altitudes, and also another on a vertical axis for measuring horizontal angles. The mural quadrants of that period were of 6 or 8 ft. radius, and for some time continued to be employed in the principal observatories. Sir Isaac Newton is said to have constructed a reflecting quadrant as early as 1672; but the first instrument of this character brought before the public was that afterward known as Hadley's, the invention of which was claimed by Godfrey, a mechanician of Philadelphia. This instrument, which has been in general use in navigation, is a graduated octant of 90 half degrees, reading as 90°. With the radial bars at each extremity of the arc it forms a triangular frame, which is made of convenient dimensions for holding in the hands. A movable radial bar or index revolves in the plane of the sector upon a pin passing through the centre. At the centre it carries a mirror, the face of which is perpendicular to this plane, and which in making an observation is turned toward the object, as the sun or a star, and at the other end it carries a vernier for subdividing the angles on the graduated limb.

On the outer edge of the radial bar, back of the movable mirror, is the sight vane, which is directed across to a second mirror fixed upon the opposite bar, its plane perpendicular to that of the bar, and its face so adjusted that a ray reflected from the first mirror to the second is transmitted from this to the eye at the sight vane. Only half of the glass of the second mirror, called the fore horizon glass, is silvered, and consequently rays passing through it from any object, as the horizon at sea, meet the eye in a direct line; and if at the same instant, while the instrument is held to this position, the index is moved so as to bring the reflected image of the sun upon the silvered part of the glass and from this to the eye, the reading of the vernier is the elevation of the sun above the horizon. Various other appendages are introduced in the quadrant, as a telescope for the sight vane, colored glasses for diminishing the intensity of the light, and a third mirror called the back horizon glass, with its sight vane, for taking a back observation. (For Gunter's quadrant, see Gun-tee.) - In gunnery, the quadrant or gunner's square is a rectangular frame with a graduated arc between the two limbs.

One of the limbs is extended beyond the arc, so as to be set into the mouth of the piece, the elevation of which it is to measure. A plummet suspended from the point of meeting of the two arms marks by the intersection of its line on the graduated arc the degree of elevation.