Radians To Degrees Formula

Radians To Degrees Formula

The Radians To Degrees Formula is a type of conversion used in geometry to convert angle measurements. There are two alternative ways of measuring angles. Angles are measured using radians and degrees. The unit radians is most commonly used in trigonometry. The Radians To Degrees Formula can be used to convert angles from radians to degrees. To comprehend this formula and the conversion of radians to degrees, students must first comprehend the definition of each unit of angle. The Extramark page, “Radians To Degrees Formula,” will also provide a conversion chart for radians to degrees.

Radians to Degrees Conversion 

Angles are measured using two separate units: radians and degrees. As a result, students must be comfortable converting angle units such as radians to degrees and degrees to radians. When students revolve the radii of a circle, they begin to generate an angle that can be measured in radians or degrees. The Radians To Degrees Formula is commonly used in various fields of Mathematics.


One revolution is completed when students rotate the radius entirely around the circle. After one complete rotation, the angle subtended by the radius at the centre of the circle is 2 radians. The angle in radians subtended by the radius at the centre of the circle is the ratio of the arc length to the radius length. The angle subtended at the centre becomes one radian when the length of the arc equals the length of the radius. The unit radian is abbreviated as rad. Radians are the SI unit of measurement for angles.


Angles are expressed in degrees. One revolution is split into 360 equal pieces, each of which is referred to as a degree. After one complete revolution of the radius, the angle subtended in the centre of the circle is 360°. ‘°’ represents the degree sign. Although degrees are not a SI unit for measuring angles, they are a commonly used measurement unit. As a result, while addressing problems, it is preferable to change the angle unit from radians to degrees to better comprehend it. An instrument used to measure angles in degrees is a protractor.

When students compare the angle measurements for a complete revolution, they find that

360 Degrees = 2π Radians

180 Degrees = π Radians 

Radians to Degrees Formula

To convert radians to degrees, use the Radians To Degrees Formula. To convert radians to degrees, multiply the number of radians by 180°/radians. When measuring angles, students use two units: degrees and radians. One degree is expressed as 1°. And 1 radian is expressed as 1 (or) 1c, which signifies that if there is no unit following the angle measurement, it is in radians. A circle’s rotation is split into 360 equal pieces, each of which is referred to as a degree. In radians, one full counterclockwise revolution is 2; in degrees, it is 360°. Thus, the degree and radian measures are connected. The  Radians To Degrees Formula for converting a radian angle to a degree angle is:

Angle in Degrees =Angle in Radians × 180°/π  

A complete circle rotation yields 2 radians, which is equivalent to 360°. As a result, students have 2 radians = 360°. They will now reduce this equation to find the  Radians To Degrees Formula  

Derivation of Radians to Degrees Formula

 To understand the derivation of the Radians To Degrees Formula, students must use the Extramarks Radians To Degrees Formula. All the derivation methods are provided by the instructor.

How to Convert Radians to Degrees? 

The unit of measurement for 180° is radians. Any given angle must be multiplied by π/180 to be converted from degrees to radians. The Radians To Degrees Formula for converting degrees to radians is to multiply the number of degrees by π/180.

 Angle in Radian = Angle in degree × π / 180°

Radians to Degrees Conversion Table

The conversion of specific angles from the Radians To Degrees Formula, which is more commonly employed in problem-solving The table displays the radian values for the related angle measurements in degrees.

Radians to Degrees Chart

Students can also use the radians-to-degrees chart to determine the measure of any angle in degrees from its measure in radians. They know that the circumference of a unit circle is equal to 2π,

Radians to Degrees Examples

The  Radians To Degrees Formula is critical for problem-solving. Students must practise problems that use the Radians to Degrees Formula. Each of them can be effectively practised with the assistance of Extramarks.

Radians to Degrees

The geometrical units used to indicate angle measurement are degrees and radians. In geometry, one full anticlockwise revolution is defined as 360° (in degrees) or 2π (in radians). Converting degrees to radians is useful for measuring different angles in Geometry. Angles are measured in degrees, which are represented by the sign (°).

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FAQs (Frequently Asked Questions)

1. What is the difference between Radians and Degrees?

Angles are measured using both radians and degrees. The radian is a SI unit, although the degree is not, yet it is a commonly used unit for measuring angles. Degrees measure angles by tilting, whereas radians measure angles by distance travelled.

2. What is a Radian?

The radian is the standard unit of angular measurement in mathematics. The length of a concurrent arc of a unit circle is numerically identical to the length of an angle measured in radians. The radian of a circle is described by the link or relationship between the arc length and radius of a circle. The degree formula and the radian formula are used to convert between degrees and radians.