What is the Difference Between Degrees and Radians?

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Difference Between Degrees and Radians

Two commonly used units of measurement for angles are degrees and radians. In mathematics and science, many units of measurement are used to implement ratios, etc. 

There are many similarities between these two terms and some differences as well. Keep scrolling to know these differences, along with their application in daily life. 

What is Degree?

“Degree” means a unit of measurement to calculate angles. This term is used in Geometry and Trigonometry to know angles and rotation. The full circle is divided into 360 degrees.

For example, a right angle, which is commonly found in geometric shapes like squares and rectangles, measures 90 degrees. 

What is Radian?

A radian is defined as the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.

Radians range from 0 to 2π, where 2π radians depict a complete rotation or circle. 

Also Read: Difference Between Parallel and Perpendicular

What is the Difference between Degrees and Radians?

Here’s the difference between Degrees and Radian in terms of different angles:

Measure of an Angle in DegreesMeasure of an Angle in Radians
30°30° × (π/180°) = π/6 = 0.524 Rad
45°45° × (π/180°) = π/4 = 0.785 Rad
60°60° × (π/180°) = π/3 = 1.047 Rad
90°90° × (π/180°) = π/2 = 1.571 Rad
120°120° × (π/180°) = 2π/3 = 2.094 Rad
150°150° × (π/180°) = 5π/6 = 2.618 Rad
180°180° × (π/180°) = π = 3.14 Rad
210°210° × (π/180°) = 7π/6 = 3.665 Rad
240°240° × (π/180°) = 4π/3 = 4.188 Rad
270°270° × (π/180°) = 3π/2 = 4.713 Rad
300°300° × (π/180°) = 5π/3 = 5.235 Rad
330°330° × (π/180°) = 11π/6 = 5.764 Rad
360°360° × (π/180°) = 2π = 6.283 Rad

Degrees and Radians Formulas 

Here’s the tabular representation of different formulas for Degrees and Radians:

Degrees and Radians Chart

Radians  × (180/π) Degrees × (π/180)

Application of Degrees and Radians in Real Life

Here are some of the applications for Degrees and Radians in different aspects of life:

  1. Degrees are commonly used in navigation systems, such as GPS devices and compasses, to specify directions and bearings.
  2. Engineers and architects use degrees and radians to design structures, determine angles for slopes, and calculate the rotation of mechanical parts.
  3. Astronomers use radians to measure the distances between stars and galaxies.
  4. Radians are particularly relevant in sports involving circular motion, such as cycling and skateboarding.

Also Read: Chain Rule Questions and Answers


Why do we use Radians instead of Degrees?

A lot of people prefer using the Radians unit instead of Degrees in Mathematics, and Science. 

How to convert radians to degrees?

To convert radians to degrees, multiply the number of radians by 180/π.

What is the value of 10 degrees 30 in radians?

The value of 10 degrees 30 in radians is 51π / 900. 

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