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Radians vs. Degrees

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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.

degrees0 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
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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