Radians to Degrees

Radians to degrees is a type of transformation used in geometry to convert angle measurements. There are two alternative methods for measuring an angle. Radians and degrees are the two units used to measure angles. Radian is the most commonly used unit in trigonometry. Various types of angles are measured in radians and then converted to degrees using a formula. This formula is discussed below.

Radians to Degrees Conversion

Two separate ways are used to measure angles. A right angle is split into 90 equal portions, which are referred to as degrees, in the Sexagesimal System. Each degree is split into 60 equal parts called minutes, which are divided further into 60 equal parts called seconds. Degree to Radian conversion can also be learned here.

• 60” = 1 minute (1’)
• 90° = 1 right angle

Radians

Angle subtended to center of a circle by radius after a complete rotation is called 2π radians. The angle in radians made by radius at the center of the circle is the ratio of length of an arc to length of a radius. If the length of the arc is equal to the length of the radius, the angle subtended at the center is called 1 radian. The unit of a radian is rad. Radian is the SI unit for measuring angles.

Degrees

Angles can also be measured in degrees. One revolution divides the circle into 360 equal parts and each part is equal to a degree. Thus, angle subtended at the center of a circle after one complete rotation is 360°. Symbol used to denote degrees is ‘°’. Degrees is not an SI unit for measuring an angle, but it is the most commonly used unit to measure an angle.

By comparing the measures of an angle for a complete rotation

• 360 Degrees = 2π Radians
• 180 Degrees = π Radians

How to Convert Degrees to Radians?

Value of 180° is equal to π radians. For converting the given angle from degrees to radians, we multiply the value of the angle in degrees by a factor of π/180.

Where the value of π = 22/7 or 3.14

Steps shown below are used for the conversion of angle in degrees to radians.

Step 1: Mark the value of the given angle in degrees

Step 2: Multiply the value obtained from the above step by π/180

Step 3: Solve the expression and rationalize the answer

Step 4: The result obtained is the measure of the angle in radian

Example: Convert 60 degrees to radians.

Solution:

Given angle is 60 degrees

Angle in radian = Angle in degree x (π/180)

                           = 60 x (π/180)

                           = π/3

Hence, 60 degrees is equal to π/3 in radian.

Radians to Degrees Formula

Radians to Degrees formula converts the value of angle in radians to degrees. To convert the angle in radians to degrees we multiply the value in radians by 180°/π. Angles are used in two units: degrees and radians, 1 degree is expressed as 1° whereas 1 radian is expressed 1^c or 1 i.e. no unit is also used to express angle in radian. The formula for changing the angle in radians to degrees is:

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

2π radians = 360°

π radians = 180°

1 radian = 180/π degrees = 57.296 degrees

Radians to Degrees Conversion Table

The table is given below shows the values angle in radian and their respective value in degree.

Angle in radian	Angle in degree
0	0°
π/6	30°
π/4	45°
π/3	60°
π/2	90°
π	180º
(3π)/2	270º
2π	360º

Solved Examples on Radians to Degrees

Example 1: Convert 9π/5 radians to degrees.

Solution:

Since, π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (9π/5)^c = (9π/5 × 180/π)° = 324°

Thus, (9π/5)^c = 324^o

Example 2: Convert −5π/6 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (−5π/6)^c = (−5π/6 × 180/π)° = −150°

Thus, (9π/5)^c = −150°

Example 3: Convert 18π/5 into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (18π/5)^c = (18π/5 × 180/π)° = 648°

Thus, (18π/5)^c = 648°

Example 4: Convert −3 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (−3)^c = (−3 × 180/π)° = (180 × 7 × −3/22)° = (−1719/11) = −171°(9 × 60/11)’ = −171°49’5”

Thus, (−3)^c = −171^o49’5”

Example 5: Convert 11 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1^c = (180/π)°

Hence, (11)^c = (11 × 180/π)° = (11 × 180 × 7/22) = 630°

Thus, (11)^c = 630°

Example 6: Convert 1 radian to degrees.

Solution:

We know that π radians = 180° or 1 radian = 1^c = (180/π)°

Hence, (1)^c = (1 × 180/π)° = (180 × 7/22) = 57°(3 × 60/11) = 57°16′(4 × 60/11)” = 57°16’21”

Thus, (1)^c = 57^o16’21”

FAQs on Radians to Degrees

Question 1: What is the Difference between Radians and Degrees?

Answer:

Radians and Degrees both are units used to measure angles. Radian is the SI unit for measurement of angle, whereas degree is the general unit used to measure angles. The relationship between them is π rad = 180°

Question 2: What is the Radian of 1 Degree?

Answer:

A complete revolution of a circle is equal to 2π radians that is equivalent to 360°, i.e. 2π rad = 360°
1° = 2π/360 rad
Thus, 1 degree is equal to π/180 radians.

Question 3: What is the value of 1 radian in degrees?

Answer:

We know that π radians are equal to 180 degrees. So, 1 radian = 57^o16’21”

Question 4: Is π radians equal to 180 degrees?

Answer:

Yes, we know that 2π radians are equal to 360 degrees. Thus, π radians equal 180 degrees.

Question 5: Why are 360 degrees equal to 2π?

Answer:

The Right angle is equal to π/2 radians. One complete revolution is considered as the length of an entire circumference of a circle divided by its radius, or 2πr / r. Thus 2π radians equals to 360 degrees,