Degrees to Radians: Formula, Conversion, Chart & Examples

Degrees to Radians is a conversion method used to convert the unit of measurement of angles in Geometry and Trigonometry. Degrees and Radians are two important units of measurement of angles in Geometry.

• Degree is a unit of measurement of horizontal angles denoted by (°). 
• Radian is the angle formed at the center of a circle by an arc whose length is equal to the radius of the circle. 
• A complete counterclockwise rotation is expressed as 2π in Radians and 360° in Degrees.

Degrees to Radians Conversion is essential to convert the given measurement of an angle in Degrees to Radians. The values of angles in Degrees are converted to Radians using the given equation:

Read More: NCERT Solutions for Class 11 Mathematics Trigonometric Functions  

Key Terms: Degrees, Radians, Degrees to Radians, Degrees to Radians Formula, Geometry, Rotation, Angles, Degrees to Radians Chart

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What is Degree?

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Degree is a unit used for measuring horizontal angles in Geometry. 

• It is denoted by the symbol (°).
• Degree in Maths is also known as Degree of Arc or Arc Degree.
• One complete rotation of an angle in Geometry is denoted by a 360° angle.
• Angles in Degrees are measured using a Protractor in Geometry.

 Radians and Degrees

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What is Radian?

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Radian is a commonly used unit of measuring angles, especially in Trigonometric Functions and Geometry.

• One radian is defined as the angle subtended at the center by an arc of length 1 unit in a unit circle.
• It is denoted by ‘π (Pi)’ which has an approximate value of 3.14 or 22/7.
• One complete rotation of an angle (360^o) is 2π in radians. 
• Thus, a straight angle, i.e. a 180^o angle, is denoted as π radians. 
• A right angle, i.e. a 90^o angle is denoted as π/2 radians.

Trigonometric Functions Detailed Video Explanation

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Degrees to Radians Formula

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Degrees and Radians are two commonly used units of angle measurement in Geometry. Degrees to Radians Formula is a generalized formula that is used to convert the given value in Degrees to value in Radians. 

Degrees to Radians Formula is given as: 

Derivation of Degrees to Radians Formula

One complete counterclockwise revolution is 360°in Degrees while it is 2π in Radians.

• 1 Complete Counterclockwise Revolution in Degrees = 360°
• 1 Complete Counterclockwise Revolution in Radians = 2π

Degrees to Radians Equation: The relation between degrees and radians can be expressed as follows: 

On dividing the equation by 2, the simpler form of the relationship between degrees and radians is 

Thus, 

Read More: 

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How to Convert Degrees to Radians?

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Degrees to Radians Conversion is used for measuring the different angles in Geometry in different units. The value of angle 180° is equal to π radians. In order to convert any specified angle from the measure of degrees to radians, the value must be multiplied by π/180. The formula for Degrees to Radians Conversion is: 

Where, π = 22/7 or 3.14.

The following steps need to be followed to convert angles in Degrees to Radians.

• Write the numerical value of the measure of the given angle in degrees.
• Multiply the number by π / 180.
• Simplify the formula by canceling the common factors. 
• After the simplification, the obtained value will be the measure of the angle in radians.

Negative Degree to Radians

The conversion method for negative degrees to radians is the same as for positive degrees. In order to convert negative degrees into radians, multiply the specified value of the angle in degrees by π / 180.

Example: 180 Degrees can be converted into Radians as follows: 

Radian = (π/180) x (Degrees)

Radian = (π/180) x (-180°)

Angle in Radian = -π

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Radians to Degrees Conversion

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The measurement of an angle in Radians can also be converted into Degrees in a similar manner as Degrees to Radians Conversion.

• 360^o = 2π Radians
• 180^o = π Radians
• 90^o = π/2 Radians

Radians to Degrees Conversion is done through the given formula: 

Radian to Degree Equation

One complete revolution, i.e. a counterclockwise in the XY plane is equal to 2π in Radians or 360° in Degrees. Thus, the Radian to Degree Equation is given as: 

It can also be written as: 

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Degrees to Radians Solved Examples

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Here are some solved examples on Degrees to Radians Conversion for a better understanding of the formula: 

Example 1: Convert 15 Degrees to Radians.

Solution: The given angle is 15 Degrees (15°).

Degrees to Radian Formula is given as: 

Angle in Radian = Angle in Degree x (π/180)

Substituting the values, we get

= 15 x (π/180)

= π/12

Therefore, 15 Degrees is equal to π/12 in Radians. 

Example 2: Convert 330 Degrees to Radians.

Solution: The given angle is 330 Degrees (330°).

Using the Degrees to Radian Formula, 

Angle in Radian = Angle in Degree x (π/180)

Putting the values in the formula, 

= 330 x (π/180)

= 11π/6

Thus, 330 Degrees is equal to 11π/6 in Radians. 

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Degrees to Radians Conversion Table

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Degrees to Radians Conversion Table shows the radian values for the corresponding angle measures in degrees. It helps in the easier and faster calculation for some commonly used angles: 

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Degrees to Radians Chart

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Degrees to Radians Chart is used to make the calculations easier and faster during Degrees to Radians Conversion. It shows the degree measures and their corresponding radian measures. 

Degrees to Radians Chart is as follows: 

Degrees to Radians Chart

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Degrees to Radians Conversion of Some Common Angles

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Here is the conversion of some common angles in comparison to the number of turns: 

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Things to Remember

• Degrees and Radians are two commonly used units for the measurement of angles. 
• Degree is a unit used for measuring angles in Geometry with the help of a protractor.
• Radians is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.
• Radian is the SI unit of measurement of an angle in the International System of Units.
• One complete rotation is 360° in Degrees and 2π in Radians. 
• 360^o is equal to 2π Radians, 180^o is equal to π Radians, and 90^o is equal to π/2 Radians.
• Degrees to Radians Conversion is done through the formula: Angle in Radian = Angle in Degree x π/180.
• Radians to Degrees Conversion is done through the formula: Angle in Degrees = Angle in Radians x (180/π).

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