Table showing various radian measurements converted to revolutions. For example, 1 revolution can be written as 1 r, 1 rev, or 1 cyc. Second, you convert the number of revolutions to radians by noting that 1 rev 2 rad. First, you convert between seconds and minutes, by either dividing or multiplying by 60. Revolutions can be abbreviated as r, and are also sometimes abbreviated as rev or cyc. You can convert RPM (revolutions per minute) to rad/s (radians per second) or rad/s to RPM using a two-stage process. 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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