What is a Degree Measure?

One degree is one 360th part of a full circle. To get a more clear idea we define degree measure as follows:

A central angle that is subtended by an arc equal in length to 1/360 of the circle's circumference, is said to have a measure of one degree, denoted  1°.

That is; for a circle with circumference C units, central angle of θ degrees subtended by an arc of s units, this relationship can be expressed by the following proportion:



The degree is further divided in to 60 minutes.

For even finer measurements the minute is divided again into 60 seconds; however this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude.

What is a Radian Measure

The radian is the standard unit of angular measure. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.

One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. The radian is a fixed size no matter what the size of the circle is.

Important Remarks:

• A full angle is 2Π radians, so there are 360° per 2Π radians, equal to 180° / Π.
• A right angle is Π / 2 radians and a straight angle is Π radians.

Relation between Degree and Radian

A circle subtends at the centre an angle whose radian measure is 2Π and its degree measure is 360°,

Radian to Degree We have, 2Π radian = 360° or Π radian = 180° Also, 1 radian = 180° / Π Or, Radian Measure =   x Degree Measure Degree to Radian We have, 1° = Π / 180 radian Degree Measure = x Radian Measure

On the basis of above discussion, we now solve the following questions:

1. Convert 40° 20’ into radian measure.

We know, 180° = Π radian

40° 20’ = 40    degree =   x   radian =   radian.


2. Convert 6 radians into degree measure.

We know, Π radian = 180°

6 radians =   x 6 degree =   degree

343   degree = 343° +   minute [As 1° = 60’]

343° + 38’ +   minute [As 1’ = 60’’]

343° + 38’ + 10.9’’’

343°38’11’’ approximately

Now try it yourself!  Should you still need any help, click here to schedule live online session with e Tutor!

About eAge Tutoring:

eAgeTutor.com is the premium online tutoring provider.  Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.

Contact us today to learn more about our tutoring programs and discuss how we can help make the dreams of the student in your life come true!

Reference Links:

•     http://en.wikipedia.org/wiki/Degree_(angle)
•     http://en.wikipedia.org/wiki/Circumference#Circumference_of_a_circle
•     http://en.wikipedia.org/wiki/Radian
•     http://en.wikipedia.org/wiki/Radius
•     http://wiki.answers.com/Q/'What_is_the_relationship_between_radian_and_degrees