Stadiametric rangefinding

Stadiametric rangefinding, or the stadia method is a technique of measuring distances with a telescopic instrument. The term stadia comes from a Greek unit of length. Stadiametric rangefinding is used for surveying and in the telescopic sights of firearms, artillery pieces, or tank guns, as well as some binoculars and other optics. It is still widely used in long-range military sniping, but in many professional applications it is being replaced with microwave, infrared, or laser rangefinding methods. Although much easier to use, electronic rangefinders can give away the shooter's position to a well-equipped adversary, and the need for accurate range estimation existed for much longer than electronic rangefinders small and rugged enough to be suitable for military use.

The stadia method is based upon the principle that in similar triangles homologous sides are proportional. This means that, for a right triangle with a given angle, the ratio of adjacent side length to opposite side length (see tangent) is constant. By using a reticle with marks of a known angular spacing, the principle of similar triangles can be used to find either the distance to objects of known size or the size of objects at a known distance. In either case, the known parameter is used, in conjunction with the angular measurement, to derive the length of the other side.

Since a radian is defined as the angle formed when the length of a circular arc equals the radius of the circle, a milliradian (sometimes called a mil, or mrad), is the angle formed when the length of a circular arc equals 1/1000 of the radius of the circle. An object 5 meters high, for example, will cover 1 mrad at 5000 meters, or 5 mrad at 1000 meters, or 25 mrad at 200 meters. Since the radian expresses a ratio, it is independent of the units used; an object 6 feet high covering 1 mrad will be 6000 feet distant.

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