Radians

The radian - a unit of angle measure - angular velocity

The radian is the SI derived unit of angle and can be expressed as

α = d / r        (1)

where

α = radian

d = circular distance measured along the arc to the radius r

r = radius in circle

There are 2 π (pi) radians (about 6.283185) in a complete circle.

  • 1 rad = 360o / 2 π =~ 57.29578o         (2)

The radian is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.

degrees 0o 15o 30o 45o 60o 75o 90o 180o 270o 360o
radians 0 π/12 π/6 π/4 π/3 5π/12 π/2 π 3π/2
0 0.26 0.52 0.79 1.05 1.31 1.57 3.14 4.71 6.28

Radians to Degrees Converter

Radians

Converting angular velocity to other units

  • 1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps)         (3)

RPM to Radians and Degrees per Second Converter

RPM

RPM Angular Velocity
(rad/s) (deg/s)
0 0.0 0
10 1.0 60
20 2.1 120
30 3.1 180
40 4.2 240
50 5.2 300
60 6.3 360
70 7.3 420
80 8.4 480
90 9.4 540
100 10.5 600

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