By definition one radian is equal to a corner which is formed by two pieces which are carried out from the center of a circle to extreme points of an arch of one radius of this circle. Though the radian is also recommended for use in the SI system, it is not the only unit of measure of flat corners. It sometimes results in need of transformation of other angular units to radians.
1. If it is necessary to transfer the corner size measured in degrees to radians, you recognize what one whole revolution contains 360 ° and this size is equivalent 2*π a radian (it follows from length of a circle of single radius). Divide the known number of angular degrees into a ratio 360/(2*π)=180/π to learn number a radian to which there corresponds this corner. If rather approximate value, then instead of a ratio 180/π use number 57.3.
2. Sometimes a fractional part of size of the corner measured in degrees is expressed in angular minutes and seconds (for example, 27 ° 15' 42""). Such designation is used, in particular, at designation of geographical and astronomical coordinates. In this case at recalculation keep in mind that each radian is approximately equal 57 ° 17' 45"" or 206265"".
3. One more of the existing units of measure of corners is called "turn". From the name it is clear that one turn corresponds to a corner in 360 °, that is 2*π a radian. For recalculation of turns in radians multiply them on 2*π or approximately by 6.28.
4. Except these units for measurement of corners the hail - the one 100-th share direct (90 °) a corner can be used. For transfer to radians of sizes of corners in grads multiply a reference value by the one two-hundredth part from Pi's number. This number of approximately equally decimal fraction 0.016.
5. In navigation the measurement of corners in points still has application. Here the cycle with the zero point corresponding to the direction on the North is broken into 32 sectors (point). From this follows that to each point there corresponds the corner in 2*π/32=π/16≈0.196 a radian - multiply points by this coefficient at recalculation them in radians. At the same time keep in mind that each of 32 points has own name - for example, "northeast" (northeast) corresponds to a point the corner approximately equal to 0.79 radians.
6. In artillery the designation of corners in terms of division of the angle meter is applied. There are big and small divisions. To small division there corresponds the corner in one six-thousandth share of a whole revolution (2*π) therefore for transfer to radians multiply a reference value by coefficient 0.001047. Big division of the angle meter contains hundred small therefore for recalculation use coefficient 0.1047.