Degrees to Radians Conversion

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

Results in Radians:

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360° = vi.283185 rad
360° = 2π

How to Catechumen Degrees to Radians

To convert a caste measurement to a radian measurement, multiply the angle past the conversion ratio.

Since 1 degree is equal to 0.017453 radians, you can use this simple formula to convert:

radians = degrees × 0.017453

The angle in radians is equal to the degrees multiplied by 0.017453.

For example, here's how to convert 5 degrees to radians using the formula higher up.

5° = (5 × 0.017453) = 0.087266 rad

conversion scale showing degrees and equivalent radians angle values

Since pi radians is equal to 180°, this conversion formula is preferred because information technology is more precise and user-friendly in avant-garde mathematics.

radians = degrees × π 180

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

To utilise this formula, start by adding the degrees to the formula. And so, move the degrees to the top of the fraction. And so, simplify the fraction.

For example, permit'south convert v degrees to radians using the preferred formula.

radians = 5° × π 180
radians = 5° × π 180
radians = 1 × π 36
radians = 1 36 π

Degrees and radians are both units used to measure out angle. Keep reading to learn more about each unit of measure.

Degrees

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

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

Degrees tin can as well be expressed using minutes and seconds every bit 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 i/60th of a degree, and 1 2d is equal to ane/60th of a infinitesimal.

Protractors are normally used to measure angles in degrees. They are semi-circle or total-circumvolve devices with caste markings assuasive a user to measure an angle in degrees. Larn more than about how to employ a protractor or download a printable protractor.

Radians

A radian is the measurement of angle equal to the beginning to the terminate of an arc divided by the radius of the circle or arc.[two] 1 radian is equal to 180/π, or about 57.29578°. There are well-nigh half-dozen.28318 radians in a circle.

The radian is the SI derived unit for bending in the metric system. Radians can be abbreviated as rad, and are too sometimes abbreviated as c , r, or R . For example, 1 radian can be written as one rad, i c, i r, or i 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 southward divided by the radius r. Thus, radians may as well be expressed as the formula of arc length over the radius.

Degree to Radian Conversion Table

Degree values converted to the equivalent radian value as a mathematical expression and decimal form.
Degrees Radians (expression) Radians (decimal)
0° 0 rad 0 rad
15° π/12 rad 0.261799 rad
30° π/6 rad 0.523599 rad
45° π/4 rad 0.785398 rad
60° π/3 rad one.047198 rad
ninety° π/two rad ane.570796 rad
120° 2π/3 rad two.094395 rad
150° 5π/half dozen rad two.617994 rad
180° π rad iii.141593 rad
270° 3π/2 rad 4.712389 rad
360° 2π rad 6.283185 rad

References

  1. Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/caste
  2. International Agency of Weights and Measures, The International Arrangement of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-ix-EN.pdf

More Degree & Radian Conversions

  • degrees to milliradians
  • degrees to minutes of arc
  • degrees to seconds of arc
  • degrees to gradians
  • degrees to revolutions
  • degrees to circles
  • degrees to mils (NATO)
  • milliradians to radians
  • minutes of arc to radians
  • seconds of arc to radians
  • gradians to radians
  • revolutions to radians
  • circles to radians
  • mils (NATO) to radians