In ballistics or aerodynamics, an ogive is a pointed, curved surface used to form the approximately streamlined nose of a bullet, shell, missile or aircraft.

The traditional or secant ogive is a surface of revolution of the same curve that forms a Gothic arch; that is, a circular arc, of greater radius than the cylindrical section ("shank"), is drawn from the edge of the shank until it intercepts the axis.

If this arc is drawn so that it meets the shank at zero angle (that is, the distance of the centre of the arc from the axis, plus the radius of the shank, equals the radius of the arc), then it is called a tangential or spitzer ogive. This is a very common ogive for high velocity (supersonic) rifle bullets.

A secant ogive of sharpness E = 120 / 100 = 1.2

The sharpness of this ogive is expressed by the ratio of its radius to the diameter of the cylinder; a value of one half being a hemispherical dome, and larger values being progressively more pointed. Values of 4 to 10 are commonly used in rifles, with 6 being the most common.

Another common ogive for bullets is the elliptical ogive. This is a curve very similar to the spitzer ogive, except that the circular arc is replaced by an ellipse defined in such a way that it meets the axis at exactly 90°. This gives a somewhat rounded nose regardless of the sharpness ratio. An elliptical ogive is normally described in terms of the ratio of the length of the ogive to the diameter of the shank. A ratio of one half would be, once again, a hemisphere. Values close to 1 are common in practice. Elliptical ogives are mainly used in pistol bullets.

Missiles and aircraft generally have much more complex ogives, such as the von Kármán ogive.

In rocketry "ogive" has become a synonym of nose cone.

In Gothic architecture, ogives are the intersecting transverse ribs of arches that establish the surface of a Gothic vault. An ogive or ogival arch is a pointed, "Gothic" arch, drawn with compasses as outlined above, or with arcs of an ellipse as described. A very narrow, steeply pointed ogive arch is sometimes called a "lancet arch.". Villard de Honnecourt, a 13th century itinerant master-builder of Picardy in the north of France, was the first writer to use the word ogive. The French term's origin is considered obscure by O.E.D.; it might come from the Late Latin obvita, the feminine past participle of obvire, to resist, i.e. the arches resisting the downward thrust of the structure's mass.

In later Gothic styles, an ogival arch is a decorative arch delineatng a void with a pointed head, formed of two ogee, or S-shaped curves.

In woodworking, an ogive is a type of curve a piece of wood can be shaped in. See also: ogee

In statistics, an ogive is the curve of a cumulative distribution function (which, for the normal distribution, resembles one side of an Arabesque or ogival arch).

In glaciology, ogives are bands of light and dark ice on the surface of a glacier.

Ogives is a set of pieces for piano by the composer Erik Satie.