How to Convert From Radians to Degrees on Calculator
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
Converting radians to degrees is a fundamental skill in trigonometry and physics. This guide explains the conversion process, provides a built-in calculator, and includes practical examples to help you understand and apply this conversion in real-world scenarios.
Conversion Formula
The relationship between radians and degrees is defined by the formula:
Degrees = Radians × (180/π)
Where π (pi) is approximately 3.141592653589793. This formula allows you to convert any angle measurement from radians to degrees by multiplying the radian value by 180/π.
Note: The conversion factor 180/π comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, 180/π radians equals 180 degrees.
Step-by-Step Conversion
- Identify the angle in radians that you want to convert.
- Multiply the radian value by 180.
- Divide the result by π (approximately 3.141592653589793).
- The result is the equivalent angle in degrees.
For example, to convert 2 radians to degrees:
Degrees = 2 × (180/π) ≈ 2 × 57.2958 ≈ 114.5916 degrees
Examples
Example 1: Converting π/2 Radians
π/2 radians is a common angle in trigonometry. Let's convert it to degrees:
Degrees = (π/2) × (180/π) = (180/2) = 90 degrees
This makes sense because π/2 radians is equivalent to a right angle (90 degrees).
Example 2: Converting 3 Radians
Let's convert 3 radians to degrees:
Degrees = 3 × (180/π) ≈ 3 × 57.2958 ≈ 171.8873 degrees
This shows that 3 radians is approximately 171.8873 degrees.
Common Uses
Converting radians to degrees is useful in various fields:
- Trigonometry: Many trigonometric functions (sine, cosine, tangent) are often expressed in degrees, especially in educational contexts.
- Physics: Some physical quantities, like angular velocity, are measured in radians per second, but degrees per second is more intuitive for many applications.
- Engineering: Engineers often work with degrees in design and construction, but radians are used in calculations involving rotation and circular motion.
- Computer Graphics: Many graphics libraries use radians for rotations and transformations, but degrees are more familiar to designers.