Reference Angle Calculator
The reference angle is defined as the smallest possible angle made by the terminal side of the given angle with the xaxis.
What is Reference Angle Calculator?
'Reference Angle Calculator' is an online tool that helps to calculate the reference angle. Online Reference Angle Calculator helps you to calculate the reference angle in a few seconds.
Reference Angle Calculator
NOTE: Enter angle in degrees only and enter angle from 0 to 360 degrees only.
How to Use Reference Angle Calculator?
Please follow the below steps to find the reference angle:
 Step 1: Enter the angle theta in the given input boxes.
 Step 2: Click on the "Calculate" button to find the reference angle.
 Step 3: Click on the "Reset" button to clear the fields and enter the different values.
How to Find Reference Angle Calculator?
When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. Since all the angles in the first quadrant are less than 90°.
When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle.
When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°.
When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle.
Note: 1. The reference angle of an angle is always nonnegative
2. The reference angle of any angle always lies between 0 and π / 2.
Solved Examples on Reference Angle Calculator

Example1:
Find reference angle for a given angle 33°?
Solution:
Given angle theta(θ) = 47°
47° lies in the first quadrant (angles from 0° to 90°)
Reference angle = θ = 47° 
Example2:
Find the reference angle for a given angle 130°?
Solution:
Given angle theta(θ) = 130°
130° lies in the second quadrant (angles from 90° to 180°)
Reference angle = 180°  θ
= 180°  130°
= 50° 
Example3:
Find the reference angle for a given angle 240°?
Solution:
Given angle theta(θ) = 240°
240° lies in the third quadrant (angles from 180° to 270°)
Reference angle = θ  180°
= 240°  180°
= 60° 
Example4:
Find the reference angle for a given angle 300°?
Solution:
Given angle theta(θ) = 300°
300° lies in the fourth quadrant (angles from 270° to 360°)
Reference angle = 360°  θ
= 360°  300°
= 60°
Similarly, you can use the calculator to find the reference angle for the following:
 Angle(θ) = 58°
 Angle(θ) = 294°
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