by θ (Greek letter theta) by using the tangent function , one can instead make a good approximation by using the definition of a radian and the simplified formula: Since a radian is mathematically defined as the angle formed when the length of a circular arc equals the radius of the circle, a milliradian, is the angle formed when the length of a circular arc equals of the radius of the circle. Just like the radian, the milliradian is dimensionless, but unlike the radian where the same unit must be used for radius and arc length, the milliradian needs to have a ratio between the units where the subtension is a thousandth of the radius when using the simplified formula. Approximation error The approximation error by using the simplified linear formula will increase as the angle increases. For example, a % (or parts per billion) error for an angle of 0.1 mrad, for instance by assuming 0.1 mrad equals 1 cm at 100 m 0.03% error for 30 mrad, i.e. assuming 30 mrad equals 30 m at 1 km 2.9% error for 300 mrad, i.e. assuming 300 mrad equals 300 m at 1 km The approximation using mrad is more precise than using another common system where 1′ (minute of arc) is approximated as 1 inch at 100 yards, where comparably there is a: 4.72% error by assuming that an angle of 1′ equals 1 inch at 100 yd 4.75% error for 100′, i.e. assuming 100′ equals 100 in at 100 yd 7.36% error for 1000′, i.e. assuming 1000′ equals 1000 inches at 100 yd Sight adjustment Milliradian adjustment is commonly used as a unit for clicks in the mechanical adjustment knobs (turrets) of iron and scope sights both in the military and civilian shooting sports. New shooters are often explained the principle of subtensions in order to understand that a milliradian is an angular measurement. Subtension is the physical amount of space covered by an angle and varies with distance. Thus, the subtension corresponding to a mrad (either in an mrad reticle or in mrad adjustments) varies with range. Knowing subtensions at different ranges can be useful for sighting in a firearm if there is no optic with an mrad reticle available, but involves mathematical calculations, and is therefore not used very much in practical applications. Subtensions always change with distance, but an mrad (as observed through an optic)