Common Angles Around a Circle


The circle below can be thought of as being divided into angles that are integer multiples of 30, 45, 60, and 90 degree angles. Click one of the points on the circle to see the angle and its measurement in both degrees and radians. See notes below.

? Degrees
? Radians
Click on an angle button.
This is a 0 degree angle.

This angle has a radian measurement of (0??).

Or: 0
This is a 30 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
We have one 30 degree angle.

This angle has a radian measurement of (?? / 6).

Or about:
(?? / 6) ??? (3.142 / 6) ??? 0.524
This is a 45 degree angle.

Since:
Every 45 degree angle is equal to (?? / 4) radians.

And since:
We have one 45 degree angle.

This angle has a radian measurement of (?? / 4).

Or about:
(?? / 4) ??? (3.142 / 4) ??? 0.785
This is a 60 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Two 30 degree angles equal a 60 degree angle.

This angle has a radian measurement of (2(?? / 6)) or (2?? / 6) or (?? / 3).

Or about:
(?? / 3) ??? (3.142 / 3) ??? 1.047
This is a 90 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Three 30 degree angles equal a 90 degree angle.

This angle has a radian measurement of (3(?? / 6)) or (3?? / 6) or (?? / 2).

Or about:
(?? / 2) ??? (3.142 / 2) ??? 1.571
This is a 120 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Four 30 degree angles equal a 120 degree angle.

This angle has a radian measurement of (4(?? / 6)) or (4?? / 6) or (2?? / 3).

Or about:
(2?? / 3) ??? (2(3.142) / 3) ??? 2.094
This is a 135 degree angle.

Since:
Every 45 degree angle is equal to (?? / 4) radians.

And since:
Three 45 degree angles equal a 135 degree angle.

This angle has a radian measurement of (3(?? / 4)) or (3?? / 4).

Or about:
(3?? / 4) ??? (3(3.142) / 4) ??? 2.356
This is a 150 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Five 30 degree angles equal a 150 degree angle.

This angle has a radian measurement of (5(?? / 6)) or (5?? / 6).

Or about:
(5?? / 6) ??? (5(3.142) / 6) ??? 2.618
This is a 180 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Six 30 degree angles equal a 180 degree angle.

This angle has a radian measurement of (6(?? / 6)) or (6?? / 6) or (??).

Or about:
(??) ??? 3.142
This is a 210 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Seven 30 degree angles equal a 210 degree angle.

This angle has a radian measurement of (7(?? / 6)) or (7?? / 6).

Or about:
(7?? / 6) ??? (7(3.142) / 6) ??? 3.665
This is a 225 degree angle.

Since:
Every 45 degree angle is equal to (?? / 4) radians.

And since:
Five 45 degree angles equal a 225 degree angle.

This angle has a radian measurement of (5(?? / 4)) or (5?? / 4).

Or about:
(5?? / 4) ??? (5(3.142) / 4) ??? 3.927
This is a 240 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Eight 30 degree angles equal a 240 degree angle.

This angle has a radian measurement of (8(?? / 6)) or (8?? / 6) or (4?? / 3).

Or about:
(4?? / 3)) ??? (4(3.142) / 3)) ??? 4.189
This is a 270 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Nine 30 degree angles equal a 270 degree angle.

This angle has a radian measurement of (9(?? / 6)) or (9?? / 6) or (3?? / 2).

Or about:
(3?? / 2) ??? (3(3.142) / 2) ??? 4.712
This is a 300 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Ten 30 degree angles equal a 300 degree angle.

This angle has a radian measurement of (10(?? / 6)) or (10?? / 6) or (5?? / 3).

Or about:
(5?? / 3) ??? (5(3.142) / 3) ??? 5.236
This is a 315 degree angle.

Since:
Every 45 degree angle is equal to (?? / 4) radians.

And since:
Seven 45 degree angles equal a 315 degree angle.

This angle has a radian measurement of (7(?? / 4)) or (7?? / 4).

Or about:
(7?? / 4) ??? (7(3.142) / 4) ??? 5.498
This is a 330 degree angle.

Since:
Every 30 degree angle is equal to (?? / 6) radians.

And since:
Eleven 30 degree angles equal a 330 degree angle.

This angle has a radian measurement of (11(?? / 6)) or (11?? / 6).

Or about:
(11?? / 6) ??? (11(3.142) / 6) ??? 5.760

The angles marked on this circle represent common angles that are often used in introductory geometry and trigonometry problems. They are all multiples of 30, 45, 60, and 90 degree angles.

Try figuring out the angle measurement before you click on the point. Then use this program to check your value. When you click on an angle, the explanation for the radian measure appears to the right of the circle diagram.

All of the angles will be shown as arcs when they are drawn. You should notice that all of these angles are in standard position.