For example, here's how to convert 5 revolutions to radians using the formula above. Table showing various radian measurements converted to revolutions. Since one revolution is equal to 6.283185 radians, you can use this simple formula to convert: radians revolutions × 6.283185 The angle in radians is equal to the angle in revolutions multiplied by 6.283185. For example, 1 revolution can be written as 1 r, 1 rev, or 1 cyc. Revolutions can be abbreviated as r, and are also sometimes abbreviated as rev or cyc. Revolutions are commonly used to measure the speed of rotation,įor example when measuring the revolutions per minute (RPM) of a vehicle's engine.Ī revolution is sometimes also referred to as a turn, cycle, or complete rotation. If θ were in degrees, however, then s would have units of degree-meters.Ī revolution, or turn, is equal to 1 rotation around a circle, or 360°.
If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.įor example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. Radians are also considered to be a "unitless" unit. Thus, radians may also be expressed as the formula of arc length over the radius. The formula to find an angle in radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Radians are often expressed using their definition. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.
Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. The radian is the SI derived unit for angle in the metric system. There are about 6.28318 radians in a circle. 1 radian is equal to 180/π degrees, or about 57.29578°. A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.
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