How to convert degrees to radians

To convert a degree measurement to a radian measurement, multiply the angle by the conversion ratio.

Since one 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 above.
5° = (5 × 0.017453) = 0.087266 rad 

Since pi radians is equal to 180°, this conversion formula is preferred because it is more precise and convenient in advanced mathematics.

radians = degrees × π180

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

To use this formula, start by adding the degrees to the formula. Then, move the degrees to the top of the fraction. Then, simplify the fraction.

For example, let's convert 5 degrees to radians using the preferred formula.
radians = 5° × π180
radians = 5° × π180
radians = 1 × π36
radians = 136π

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

Degrees

A degree is a measure of angle equal to 1/360th of a revolution, or circle. 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.

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 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.

Degree to Radian Conversion Table

Degree values converted to the equivalent radian value as a mathematical expression and decimal form.
DegreesRadians (expression)Radians (decimal)
0 rad0 rad
15°π/12 rad0.261799 rad
30°π/6 rad0.523599 rad
45°π/4 rad0.785398 rad
60°π/3 rad1.047198 rad
90°π/2 rad1.570796 rad
120°2π/3 rad2.094395 rad
150°5π/6 rad2.617994 rad
180°π rad3.141593 rad
270°3π/2 rad4.712389 rad
360°2π rad6.283185 rad

Degrees to radians in terms of pi

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = (α(degrees) / 180°) × π

Example

Convert 30 degrees angle to radians in terms of pi:

α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π

 = (1/6) × π = π/6 rad = 0.166667π rad

How to convert radians to degrees »


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