Quadrants To Radians Conversion


1 quadrant = 1.5707963268 rad

Want to convert from radians to quadrants instead?

Disclaimer: We've spent hundreds of hours building and testing our calculators and conversion tools. However, we cannot be held liable for any damages or losses (monetary or otherwise) arising out of or in connection with their use. Full disclaimer.

How to convert quadrants to radians (quadrant to rad)

The formula for converting quadrants to radians is: rad = quadrant × 1.5707963268. To calculate the quadrant value in radians first substitute the quadrant value into the preceding formula, and then perform the calculation. If we wanted to calculate 1 quadrant in radians we follow these steps:

rad = quadrant × 1.5707963268

rad = 1 × 1.5707963268

rad = 1.5707963268

In other words, 1 quadrant is equal to 1.5707963268 radians.

Example Conversion

Let's take a look at an example. The step-by-step process to convert 8 quadrants to radians is:

  1. Understand the conversion formula: rad = quadrant × 1.5707963268
  2. Substitute the required value. In this case we substitute 8 for quadrant so the formula becomes: rad = 8 × 1.5707963268
  3. Calculate the result using the provided values. In our example the result is: 8 × 1.5707963268 = 12.5663706144 rad

In summary, 8 quadrants is equal to 12.5663706144 radians.

Converting radians to quadrants

In order to convert the other way around i.e. radians to quadrants, you would use the following formula: quadrant = rad × 0.636619772365513. To convert radians to quadrants first substitute the radian value into the above formula, and then execute the calculation. If we wanted to calculate 1 radian in quadrants we follow these steps:

quadrant = rad × 0.636619772365513

quadrant = 1 × 0.636619772365513

quadrant = 0.636619772365513

Or in other words, 1 radian is equal to 0.636619772365513 quadrants.

Conversion Unit Definitions

What is a Quadrant?

A quadrant is an angular measure that is equal to one quarter of a circle or 90 degrees. The term "quadrant" comes from the Latin word "quadrans" which means "a quarter."
To better understand this definition, it's important to note that a circle is divided into 360 degrees. Each quadrant is a portion of the circle that spans 90 degrees or one quarter of the circle. When measuring angles using quadrants, angles are usually denoted using the quadrant symbol (Q), which is placed after the numerical value of the angle. For example, an angle of 2 quadrants would be written as 2Q or 180°.
The quadrant is not as commonly used as other angular measures such as degrees, radians, or mils, but it is still used in some fields such as astronomy, where it is used to measure celestial coordinates. In addition, the term "quadrant" is also used to refer to a device used in navigation and astronomy to measure the altitude of celestial objects.

What is a Radian?

A radian is a unit of angular measure that is used to quantify the size of an angle, particularly in trigonometry and calculus. One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
To better understand this definition, it's important to note that a circle has a circumference of 2π times the radius, where π is the mathematical constant pi (approximately 3.14159). Therefore, an angle of one radian is subtended by an arc that is equal in length to the radius of the circle, which is one unit in length.
When measuring angles using radians, angles are usually denoted using the radian symbol (rad), which is often omitted for simplicity. For example, an angle of 2 radians would be written as 2 rad.

Quadrants To Radians Conversion Table

Below is a lookup table showing common quadrants to radians conversion values.

QuadrantRadian (rad)
1 quadrant1.5707963268 rad
2 quadrant3.1415926536 rad
3 quadrant4.7123889804 rad
4 quadrant6.2831853072 rad
5 quadrant7.853981634 rad
6 quadrant9.4247779608 rad
7 quadrant10.9955742876 rad
8 quadrant12.5663706144 rad
9 quadrant14.1371669412 rad
10 quadrant15.707963268 rad
11 quadrant17.2787595948 rad
12 quadrant18.8495559216 rad
13 quadrant20.4203522484 rad

Quadrants To Radians Conversion Chart