Radians vs. Degrees
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 = 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.
| 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 | 2π |
| 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
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
| 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.
Related Topics
• Basics
The SI-system, unit converters, physical constants, drawing scales and more.
• Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
• Mechanics
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Related Documents
Angle Calculator - Carpenter's Square
Calculate angles with a straight board across carpenter's square.
Angular Motion - Power and Torque
Angular velocity and acceleration vs. power and torque.
British Imperial System
A principal system of units.
Circle - Equation
The equation for a circle
Circle - the Chord Lengths when Divided in to Equal Segments
Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
Complex Numbers
Complex numbers are used in alternating current theory and mechanical vector analysis.
Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.
Formulas of Motion - Linear and Circular
Linear and angular (rotation) acceleration, velocity, speed and distance.
Latitude and Longitude Converter
Convert between Degrees, Minutes and Seconds and Decimal Units (or vice versa).
Minutes to Decimal Hours
Convert minutes to descimal hours.
Minutes vs. Degrees - Converting Chart
Convert from minutes to degrees.
Polar vs. Cartesian Coordinates
Convert between Cartesian and Polar coordinates.
SI System
An introduction to the SI metric system.
Steradian
A unit of solid-angle measure in the International System of Units (SI)
Triangle
Triangle analytical geometry.
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions.