Radians vs. Degrees
Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.
The radian is the SI derived unit of an angle where
θ = d / r (1)
where
θ = radian
d = circular distance measured along the arc (m, in)
r = radius in circle (m, in)
Since the length of a circle is 2 π r, and the radius of the circle is r  the radians in a complete circle can be calculated to
θ = 2 π r / r
= 2 π
=~ 6.283185
One radian can be expressed in degrees as
1 rad = 360^{o} / (2 π) = ~ 57.29578^{o } (2a)
One radian can be expressed in revolutions as
1 rev = 1 / (2 π) = ~ 0.16 (2a)
One degree can be expressed in radians as
1^{o} = 2 π / 360^{o} = ~ 0.01745 radian (2c)
Note!  radians are used by default in angular expressions in most computer languages.
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  0^{o}  15^{o}  30^{o}  45^{o}  60^{o}  75^{o}  90^{o}  180^{o}  270^{o}  360^{o} 

radians  0  π/12  π/6  π/4  π/3  5π/12  π/2  π  3π/2  2π 
0  0.26  0.52  0.79  1.05  1.31  1.57  3.14  4.71  6.28 
Radians to Degrees Converter
Degrees to Radians Converter
Angular Velocity
Converting angular velocity (ω) to other units
 ω = 1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps) (3)
RPM to Radians and Degrees per Second Converter
Revolutions (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 
Download and print Angular Velocity chart
Example  Angular velocity 100 rad/s
An angular velocity of 100 rad/s can as indicated in the chart above be estimated to aprox. 950 rpm and 5700 deg/s.
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