Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

## The radian - unit of angle - and angular velocity The radian is the SI derived unit of an angle where

θ = d / r                              (1)

where

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 = 360o / (2 π) = ~ 57.29578o                            (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

1o = 2 π / 360o = ~ 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.

degrees0o15o30o45o60o75o90o180o270o360o
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

Degrees

### 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

Revolutions
(rpm)
Angular Velocity
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 - The SI-system, unit converters, physical constants, drawing scales and more
• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

## Tag Search

• en: radian angle unit 360
• de: Bogenmaß Einheit 360

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

## Citation

• Engineering ToolBox, (2005). Radian. [online] Available at: https://www.engineeringtoolbox.com/radian-d_942.html [Accessed Day Mo. Year].

Modify access date.

. .

#### Scientific Online Calculator 7 3