Radians

The radian - a unit of angle measure - angular velocity

radians

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

θ = d / r        (1)

where

θ = radian

d = circular distance measured along the arc 

r = radius in circle

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 as 

θ = 2 π r / r

2 π

=~ 6.283185 

One radian can be calculated to degrees as

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

One radian can be calculated to revolutions as

1 rev = 1 / (2 π) = ~ 0.16         (2a)

One degree can be calculated to radians as

1o = 2 π / 360o = ~ 0.01745 radian      (2c)

Note! - radians are used by default 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 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

Degrees to Radians Converter

Degrees

Angular Velocity 

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

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

Related Topics

  • Basics - Basic Information as SI-system, Unit converters, Physical constants
  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Mathematics - Mathematical rules and laws - areas, volumes, exponents, trigonometric functions and more

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