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238 LearnersLast updated on December 3, 2025
Radian to Degree Conversion
We can measure angles using units like degrees or radians. Different units are used for different purposes in mathematics and science. A radian is a unit of angular measure in the International System of Units (SI) that is used in many areas of mathematics. A degree is another unit of angular measure that is more commonly used in everyday situations, such as measuring angles in geometry and navigation. Sometimes we need to convert radians to degrees to make it easier to understand angles. In this topic, we will learn how to convert radian to degree.
What is a Radian?
A radian is a unit of angular measure used in the metric system. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. There are 2π radians in a full circle.
The radian is widely used in trigonometry and calculus due to its natural properties.
What is a Degree?
A degree is a unit of angular measurement used to measure angles. One degree is 1/360th of a full circle.
Degrees are commonly used in various fields such as navigation, surveying, and geometry. The symbol used to denote degrees is °.
What Is Radian to Degree Conversion?
Radian to degree conversion is the process of changing an angle measured in radians to an angle measured in degrees. Students often use this conversion in geometry, trigonometry, physics, and real-world applications involving rotation or circular motion.
Radians and degrees are both units for measuring angles, but they use different systems. The conversion is based on a well-known relationship between the two:
1 radian = 57.2958 degrees
or
Degrees = Radians × (180 / π)
To convert radians to degrees, students multiply the radian value by 180/π, which changes the angle into a more familiar form used in everyday math and classroom activities.
This conversion helps students understand angles more clearly, especially when switching between formulas or graphs that use different units.
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Radian to Degree Formula
To convert radians to degrees, we use the following formula.
Formula:
Degrees = Radians × (180 ÷ π)
So, to convert radian to degree, you multiply the number of radians by 180 and then divide by π.
How to Convert Radians to Degrees?
Converting radians to degrees is simple using a standard conversion factor. Since 1 radian equals 180/π degrees, you can convert radians to degrees by multiplying the number of radians by 180 and dividing by π.
Step-by-Step Process to Convert Radians to Degrees
Step 1: Write down the angle in radians.
Step 2: Multiply the value by 180 and divide by π to get the angle in degrees.
Radian to Degree Conversion Chart
When we measure angles, sometimes we use radians and sometimes we use degrees. We use simple conversions to understand how much an angle in radians is in degrees.
Below is a radian to degree conversion table that shows us the radian-to-degree conversions.
Common Mistakes and How to Avoid Them in Radian to Degree Conversion
When converting radians to degrees, people often make mistakes. Here are some common mistakes to get a better understanding of the concepts of conversions.
Mistake 1
Using the wrong conversion factor
People get confused and use incorrect values for conversion, such as using 180 instead of 180/π.
Mistake 2
Rounding too soon
Individuals might round numbers too early while calculating, which can lead to incorrect results. For example, instead of writing (3.14 × 180/π) = 180, they might round it to 179, which is not accurate.
Mistake 3
Misplacing decimal points
People get confused and place the decimal point incorrectly, which leads to improper values. For example, instead of writing the value for π/4 radians as 45 degrees, they write it as 4.5 degrees.
Mistake 4
Incorrect use of formula
Individuals get confused and use the incorrect formula. For example, instead of multiplying by 180/π, they multiply by π/180. To convert any value from radians to degrees, multiply by 180/π.
Mistake 5
Misunderstanding the relationship between radians and degrees
People often get confused about radians and degrees. They might think 1 radian equals 1 degree, but 1 radian is approximately 57.2958 degrees.
Radians to Degrees Conversion Examples
Problem 1
Convert π radians to Degrees
π radians = 180 degrees
Explanation
We know the conversion factor: 1 radian = 180/π degrees Now, multiply π by the conversion factor: π × (180/π) = 180 degrees.
Problem 2
Convert 2 radians to degrees.
Solution: Converting 2 radians to degrees gives us approximately 114.59 degrees.
Explanation
Use the conversion factor: 1 radian = 180/π degrees 2 × (180/π) ≈ 114.59 degrees
Problem 3
A middle school in Seattle is working on a robotics project for a STEM night sponsored by the Seattle Mariners (MLB). Students purchased a sensor kit from Target for $29.99 before Washington sales tax. During testing, the robot’s arm rotates 1.2 radians, and students must convert that rotation into degrees, since US science rubrics require degree measurements. Convert 1.2 radians to degrees.
68.75°
Explanation
Use the conversion formula:
Degrees = Radians × (180 / π)
So:1.2 × (180 / π) = 1.2 × 57.2958
≈ 68.75°
Students record 68.75° as the robotic arm’s rotation for their Mariners STEM submission.
Problem 4
Converting 5 radians to Degrees,A Walgreens in Chicago receives a new automated pill-counting device used for preparing prescriptions. The machine rotates its internal sorting wheel by 0.9 radians each cycle. The technician—who watched the Chicago Bears (NFL) game last night—must convert this to degrees because the maintenance log uses US degree units. Meanwhile, the pharmacy notes gas prices nearby at $4.19 per gallon, and the medication refill total comes to $42.87 including Illinois tax.
5 radians = 286.48 degrees
,51.57°
Explanation
Step 1: Use the conversion factor. 1 radian = 180/π degrees Step 2: Multiply 5 by the conversion factor. 5 × (180/π) ≈ 286.48 degrees
,Use the standard conversion: Degrees = Radians × (180 / π) So: 0.9 × (180 / π) ≈ 0.9 × 57.2958 = 51.57° The Walgreens technician logs the machine’s rotation as 51.57° in the Chicago store’s maintenance records.
FAQs on Radians to Degrees
1.How many degrees is 1 radian?
2.What is π/3 radians in degrees?
3.Is 2π radians a full circle?
4.How do I convert π/2 radians to degrees?
5.Why do mathematicians use radians instead of degrees?
6.Should my calculator be on rad or deg?
Important Glossaries for Radians to Degrees
Conversion: The process of changing one unit of measurement into another, such as converting radians to degrees. Angle: The figure formed by two rays, called the sides of the angle, sharing a common endpoint. Radian: A unit of angle measure based on the radius of a circle. Degree: A unit of angular measure equal to 1/360th of a full circle. Pi (π): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
