Radians vs. Degrees - Definition and Conversions

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                                    (2b)

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.

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

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Degrees to Radians Converter

Degrees

• Degrees - decimal to minutes and seconds 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)

• Formulas of motion

RPM to Radians and Degrees per Second Converter

RPM

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 .