Reference Angle Calculator

Measurement of angle is not difficult unless you are asked to find it with a reference point. It will be difficult to find the reference angle because you may be confused about the reference axis. The reason is you may not be able to understand whether to pick the previous axes or the upcoming axes as the reference.

If you are making mistakes in this calculation, you should use this reference angle calculator. This online maths calculator has been programmed well to find this angle only. Whenever you will insert the angle measurement, it will set a reference automatically and show you the reference angle. Learn in detail here about this angle and the use of the calculator.

What is Reference Angle?

It is the smallest angle formed between the x-axis and the terminal line. Normally, we find the measure of an angle from the positive x-axis to the terminal arm/line. But the reference angle is a part of this angle that is considered the shortest one between the x-axis and the terminal arm.

In general mathematics, this type of angle is not important. But it has great significance when it comes to solving problems related to Trigonometry. The reference angle helps in finding the values of Sine and Cosine with the identification of their quadrant.

How to find the reference angle?

Finding the reference angle is not a difficult task if you follow these simple steps.

  • Choose the closest x-axis line to the terminal angle arm.
  • Set its values as a reference point.
  • If the terminal arm is beyond the reference axis, subtract its angle from the terminal angle.
  • If the terminal arm is behind the reference axis, subtract the terminal angle from the axis angle.

To let you understand these steps, we have also solved an example here. Just have a look at this example to memorize the solution.

Example 1:

Find the terminal angle of 145 degrees.


When 145 degrees is drawn on the x-y coordinate system, the closest angle on the x-axis is 180 degrees. To find the reference angle, we have to subtract the given angle from 180 degrees.


Reference angle = 180 - 145	
= 35 degrees	 

How to use Reference Angle Calculator?

You can use this online tool of Calculator’s Bag in a single step. Here is the step you have to follow:

  • Insert the given angle in the text insertion box
  • This calculator will automatically work and show you the value for the reference angle.

What is Reference Angle for...?

For quick answers, we have enlisted some angles here with their reference angles too:

Angle Measurement Reference Angle
1 1
2 2
5 5
30 30
60 60
120 60
150 30
220 40
250 70

FAQ | Reference Angle Calculator

What is the reference angle of 45 degrees?

The reference angle of 45 degrees is 45 because the closest angle on the x-axis is 0 degrees.

What is the reference angle of 120?

The reference angle of 120 degrees is 60 because the closest x-axis angle is 180 degrees.

What is the reference angle of 30?

The reference angle of 30 is also 30 degrees.

What is the reference angle of 2pi?

The reference angle of 2pi is 0 because it is on the positive x-axis terminal.