Radians to Degrees Conversion

Enter the angle in radians below to get the value converted to degrees.

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Results in Degrees:
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2 rad = 114.591559°
2 rad = 114° 35′ 29.61″
2 rad = 360 π
Do you want to convert degrees to radians?

How to Convert Radians to Degrees

conversion scale showing radians and equivalent degrees angle values

To convert a radian measurement to a degree measurement, multiply the angle by the conversion ratio. One radian is equal to 57.29578 degrees, so use this simple formula to convert:

degrees = radians × 57.29578

The angle in degrees is equal to the radians multiplied by 57.29578.

For example, here's how to convert 5 radians to degrees using the formula above.
5 rad = (5 × 57.29578) = 286.478898°

Since pi radians is equal to 180° this conversion formula is preferred in mathematics for it's accuracy and convenience.

degrees = radians × 180π

In other words, the angle in degrees is equal to the radians times 180 divided by pi.

The first step to using this formula is to add the radians to the formula. Then, move them to the top of the fraction. And finally, simplify the fraction.

For example, let's convert 5 radians to degrees using the preferred formula.
degrees = 5 rad × 180π
degrees = 5 × 180π
degrees = 900π

Radians and degrees are both units used to measure angle. Keep reading to learn more about each unit of measure.

Radians

A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.

Radians are often expressed using their definition. The formula to find radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.

Degrees

A degree is a measure of angle equal to 1/360th of a revolution, or circle.[2] The number 360 has 24 divisors, making it a fairly easy number to work with. There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day.

The degree is an SI accepted unit for angle for use with the metric system. A degree is sometimes also referred to as a degree of arc, arc degree, or arcdegree. Degrees can be abbreviated as °, and are also sometimes abbreviated as deg. For example, 1 degree can be written as 1° or 1 deg.

Degrees can also be expressed using minutes and seconds as an alternative to using the decimal form. Minutes and seconds are expressed using the prime (′) and double-prime (″) characters, although a single-quote and double-quote are often used for convenience.

One minute is equal to 1/60th of a degree and one second is equal to 1/60th of a minute.

Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor.

Radian to Degree Conversion Table

Radian values as a mathematical expression converted to a decimal value and degree value.
Radians (expression)Radians (decimal)Degrees
0 rad0 rad
π/12 rad0.261799 rad15°
π/6 rad0.523599 rad30°
π/4 rad0.785398 rad45°
π/3 rad1.047198 rad60°
π/2 rad1.570796 rad90°
2π/3 rad2.094395 rad120°
5π/6 rad2.617994 rad150°
π rad3.141593 rad180°
3π/2 rad4.712389 rad 270°
2π rad6.283185 rad360°

References

  1. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
  2. Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree