The radian - unit of angle - and angular velocity
The radian is the SI derived unit of an angle where
θ = d / r (1)
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
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.
Radians to Degrees Converter
Degrees to Radians Converter
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
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.