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Converting angles from radians to degrees is a fundamental concept in mathematics and physics. Radians and degrees are two commonly used units to measure angles, with radians being the preferred choice in most mathematical calculations. To perform various mathematical operations or communicate angles in a more comfortable format, it is essential to know how to convert measurements from radians to degrees. This process involves using a simple conversion formula that allows us to express angles in terms of degrees, providing a more widely understood measurement. By understanding and mastering the conversion of radians to degrees, we can seamlessly navigate between these units and effectively analyze and communicate angles in various contexts.
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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.
- /12 x 180/π =
- 180π/12π 12π/12π =
- 15°
- π/12 radians = 15°
- 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°
- 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
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 relatively simple process that involves multiplying the given radian measure by 180 and dividing the result by π. This conversion allows us to express angular measurements in degrees, which is a more familiar unit for many people. Understanding how to convert between radians and degrees is essential in various mathematical and scientific disciplines, such as geometry, trigonometry, and physics. By applying the conversion formula, individuals can easily interconvert between radians and degrees to communicate angular measurements effectively and accurately. Whether in practical applications or theoretical calculations, the ability to convert radians to degrees is a valuable skill that enhances our understanding and utilization of angular measures.
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