How to Convert radians to degrees

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In mathematics, there is often a need to convert between different units of measurement. One such conversion that is frequently encountered is the conversion between radians and degrees. Radians and degrees are both units used to measure angles, but they are based on different scales. Radians are a unit of measurement based on the radius of a circle, while degrees are a unit of measurement based on dividing a circle into 360 equal parts. To convert radians to degrees, a specific formula or set of steps can be followed. This process is useful in many fields, including physics, engineering, and trigonometry. By understanding how to convert radians to degrees, individuals can effectively work with and compare angle measurements in different units.

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Radians and degrees are units of measure for angles. As you know, a circle has 2π radians, which is equivalent to 360°; both of these values represent “one round” of the circle. So, 1π radians stands for 180° on the circle, which makes 180/ a perfect converter from radians to degrees. To convert radians to degrees, you simply multiply the radian value by 180/π. If you want to know how to calculate and understand the concept in that calculation, read the article below.

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Table of Contents

Steps

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Understand that 1π radians equals 180 degrees. Before starting the conversion, you must know π radians = 180°, which is equivalent to a semicircle. This is important because you will be using 180/π as the converter. That’s because 1 radian equals 180/π degrees. ^{[1] X Research Source}

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Multiply radians by 180/π to get the measure in degrees. Just that simple! Let’s say you have π/12 radians. To convert to degrees, you must multiply it by 180/π and reduce as necessary. Here’s how: ^{[2] X Research Sources}

• /12 x 180/π =
• 180π/12π 12π/12π =
• 15°
• π/12 radians = 15°

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Practice with a few examples. If you want to be more proficient then practice converting from radians to degrees for more examples. Here are some exercises you can do:

• Example 1 : 1/3π radian = /3 x 180/π = 180π/3π 3π/3π = 60°
• Example 2 : 7/4π radians = 7π/4 x 180/π = 1260π/4π 4π/4π = 315°
• Example 3 : 1/2π radian = /2 x 180/π = 180π /2π 2π/2π = 90°

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Remember that “radian” is different from “π radian”. 2π radians and 2 radians are completely different. As you know, 2π radians is equal to 360 degrees but if you have 2 radians, then you want to convert it to degrees then you will have to do the calculation 2 x 180/π. You should get 360/π or 114.5°. Here’s another answer, because if you don’t work with π radians π won’t cancel out in the equation, thus resulting in a different value. ^{[3] X Research Sources}

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Advice

• When multiplying, leave pi in radians as the symbol is not a decimal, so you will easily cancel it out during the calculation.
• Many graphing calculators have functions to convert units, or you can download a program to convert. Ask your teacher if your calculator has that function.

Things you need

• Ballpoint pen or pencil?
• Paper
• Laptop

X

wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 12 people, some of whom are anonymous, have edited and improved the article over time.

This article has been viewed 116,625 times.

Radians and degrees are units of measure for angles. As you know, a circle has 2π radians, which is equivalent to 360°; both of these values represent “one round” of the circle. So, 1π radians stands for 180° on the circle, which makes 180/ a perfect converter from radians to degrees. To convert radians to degrees, you simply multiply the radian value by 180/π. If you want to know how to calculate and understand the concept in that calculation, read the article below.

In conclusion, converting radians to degrees is a simple process that requires knowledge of the conversion formula. By multiplying the radian value by 180/π, one can easily obtain the equivalent degree value. Additionally, understanding the relationship between radians and degrees allows for accurate conversion and measurements in various mathematical calculations and applications. It is essential to remember that radians and degrees are different units of measuring angles, and conversions between the two are necessary for interdisciplinary communication and problem-solving. Overall, mastering the skill of converting radians to degrees is crucial for effectively navigating the world of mathematics and its numerous real-world applications.

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