Finding the Quadrant of the Angle Tools

Created By : Veerendra
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Apr 18,2023

Free online calculator that determines the quadrant of an angle in degrees or radians and that tool is nothing but finding the quadrant of the angle calculator. To use this tool there are text fields and in that, we need to give the values and then just tap the calculate button for getting the answers instantly.

Enter Angle in Degrees

How to determine the Quadrants of an angle calculator: Struggling to find the quadrants in which the angle lies? Have no fear as we have the easy-to-operate tool for finding the quadrant of an angle lies in a very simple way. Learn more about the step to find the quadrants easily, examples, and many others. We will help you with the concept and how to find it manually in an easy process.

How do Find a Quadrant where an Angle lies and Given in Degrees or Radians?

A quadrant is defined as a rectangular coordinate system which is having an x-axis and y-axis that divides the plane into four quadrants. An angle is said to be in a particular position where the initial side of an origin is on the positive x-axis.

Angles between 0° and 90° then we call it the first quadrant. If the angle is between 90° and 180° then it is the second quadrant. Angle is between 180° and 270° then it is the third quadrant. Finally, the fourth quadrant is between 270° and 360°.

Angle is said to be in the first quadrant if the terminal side of the angle is in the first quadrant. And all these angles of the quadrants are called quadrantal angles.

Quadrants of Positive and Negative Angles

Let us have a look at the below guidelines on finding a quadrant in which an angle lies. Go through the steps carefully.

  • First, write down the value that was given in the problem.
  • Then, if the value is positive and the given value is greater than 360 then subtract the value by 360, if the value is still greater than 360 then continue till you get the value below 360.
  • If the value is negative then add the number 360.
  • Next, we need to divide the result by 90.
  • When we divide a number we will get some result value of whole number or decimal. If it is a decimal truncate the value.
  • Then, if the value is 0 the angle is in the first quadrant, the value is 1 then the second quadrant, if it is 2 then it is in the third quadrant, and finally, if you get 3 then the angle is in the fourth quadrant.


Question 1: Find the quadrant of an angle of 252°?


Given angle is 252°

As the given angle is less than 360, we directly divide the number by 90.

252 / 90 = 2.8

Truncate the value to the whole number. After reducing the value to 2.8 we get 2.

As we got 2 then the angle of 252° is in the third quadrant.

Question 2: Find the quadrant of an angle of 723°?


Given angle is 723°

Now, the number is greater than 360, so subtract the number with 360

723 - 360 = 363

Still, it is greater than 360, so again subtract the result by 360.

363 - 360 = 3

Then, divide the result with 90

3/90 = 0.03

After truncating the value we get 0

As we got 0 then the angle of 723° is in the first quadrant.

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FAQs on Finding the Quadrants of an Angle Tools

1. How to use this finding quadrants of an angle lies calculator?

Simply, give the value in the given text field and click on the calculate button, and you will get the answer immediately.

2. What is quadrant angle mean?

A quadrant angle is an angle whose terminal sides lie on the x-axis and y-axis. Some of the quadrant angles are 0°, 90°, 180°, 270°, and 360°.

3. In which quadrant does a 270° lie?

270° does not lie on any quadrant, it lies on the y-axis separating the third and fourth quadrants.

4. What are four quadrants?

  • Quadrant I: (+x, +y)
  • Quadrant II: (-x, +y)
  • Quadrant III: (-x, -y)
  • Quadrant IV: (+x, -y)

5. Where is the second quadrant?

The second quadrant lies in between the top right corner of the plane. In this (-x, +y) is available.