Coterminal Angle Calculator

Use our coterminal angle calculator to find the positive and negative coterminal angles for any angle in degrees or radians.

Have a Question or Feedback?

Result:

Positive Coterminal Angles

435°
795°
1,155°
1,515°
1,875°

Negative Coterminal Angles

-285°
-645°
-1,005°
-1,365°
-1,725°
Learn how we calculated this below

scroll down


On this page:


How to Find Coterminal Angles

An angle is the measure of the opening between two lines that intersect at a common vertex. Coterminal angles are angles that meet at the same initial and terminal sides.

Coterminal angles will measure the opening between the same two lines revolving around the vertex multiple times. When measured in standard position, coterminal angles always end at the same position.

In standard position, an angle is formed by a rotation originating from the positive x-axis and extending counterclockwise around the origin. This allows angles to be measured consistently.

To better understand coterminal angles, see the diagram below of an angle and the first coterminal angle.

Graphic showing coterminal angles on a graph.

You can find coterminal angles by adding or subtracting multiples of 360 degrees. Since a full rotation is equal to 360 degrees, rotating an additional 360 degrees about a point will arrive at the same position.

For example, let’s find a coterminal angle of 20 degrees.

20 + 360 = 380

By adding 360 to 20 degrees, you’ll find the first coterminal angle of 380 degrees.

This can be expressed using a formula.

Coterminal Angles Formula

You can use the following formulas to find coterminal angles of an angle in degrees or radians.

Coterminal Angles in Degrees:

coterminal angle = θ ± 360n

The coterminal angle is equal to the angle θ in degrees plus or minus 360 times an integer n representing the revolutions about the point.

Coterminal Angles in Radians:

coterminal angle = θ ± 2πn

The coterminal angle is equal to the angle θ in radians plus or minus 2 times pi times an integer n representing the revolutions about the point.

You can also use our degrees to radians converter to allow you to use either formula.

You can apply this formula to find multiple coterminal angles by changing the number n to any whole number.

Graphic showing the formulas to calculate coterminal angles for an angle in degrees or radians.

How to Find Negative Coterminal Angles

Negative coterminal angles are negative angles that start at the standard position and end at the same position as the initial angle. A negative coterminal angle represents a revolution about the point in the opposite direction, as shown in the graphic below.

Graphic showing a negative coterminal angle on a graph.

To find a negative coterminal angle, subtract 360 degrees from the angle, which represents one full revolution clockwise, and will arrive at the same position as the angle.

You may also find our reference angle calculator useful for similar trigonometry problems.

Coterminal Angle Chart

The following chart shows the coterminal angle of various angles in degrees.
Angle Positive Coterminal Angle Negative Coterminal Angle
0 360 -360
10 370 -350
20 380 -340
30 390 -330
40 400 -320
50 410 -310
60 420 -300
70 430 -290
80 440 -280
90 450 -270
100 460 -260
110 470 -250
120 480 -240
130 490 -230
140 500 -220
150 510 -210
160 520 -200
170 530 -190
180 540 -180
190 550 -170
200 560 -160
210 570 -150
220 580 -140
230 590 -130
240 600 -120
250 610 -110
260 620 -100
270 630 -90
280 640 -80
290 650 -70
300 660 -60
310 670 -50
320 680 -40
330 690 -30
340 700 -20
350 710 -10
360 720 -360

Frequently Asked Questions

Which angles are Coterminal with a 125 degree angle?

The angles that are coterminal with 125° are 485° and -235°.

Why do we use coterminal angles?

Coterminal angles will measure the openings between the same two lines revolving around the vertex multiple times. This helps simplify calculations in geometry and trigonometry.

How do you find a coterminal angle for an angle in radians?

The coterminal angle is equal to the angle θ in radians plus or minus 2 times π times and integer n representing the revolutions about the point.