Convert radians to degrees
Please provide values below to convert radian [rad] to degree [°], or vice versa.
Definition: A radian (symbol: rad) is the standard unit of angular measure. It is a derived unit (meaning that it is a unit that is derived from one of the seven SI base units) in the International System of Units. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. One radian is equal to 180/π (~57.296) degrees.
History/origin: Measuring angles in terms of arc length has been used by mathematicians since as early as the year 1400. The concept of the radian specifically however, is credited to Roger Cotes who described the measure in 1714. Although he described the unit, Cotes did not name the radian, and it was not until 1873 that the term "radian" first appeared in print.
Current use: The radian is widely used throughout mathematics as well as in many branches of physics that involve angular measurements. Although the symbol "rad" is the accepted SI symbol, in practice, radians are often written without the symbol since a radian is a ratio of two lengths and is therefore, a dimensionless quantity. As such, when angle measures are written, the lack of a symbol implies that the measurement is in radians, while a ° symbol would be added if the measurement were in degrees.
Definition: A degree (symbol: °) is a unit of angular measurement defined by a full rotation of 360 degrees. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians. Although a degree is not an SI (International System of Units) unit, it is an accepted unit within the SI brochure.
History/origin: The origin of the degree as a unit of rotation and angles is not clear. One of the theories suggests that 360 is readily divisible, has 24 divisors, and is divisible by every number from one to ten, except for seven, making the number 360 a versatile option for use as an angle measure.
Current use: The degree is widely used when referencing angular measures. While the degree might be more prevalent in common usage, and many people have a more practical understanding of angles in terms of degrees, the radian is the preferred measurement of angle for most math applications. This is because the radian is based on the number π which is heavily used throughout mathematics, while the degree is largely based on the arbitrary choice of 360 degrees dividing a circle.
Radian to Degree Conversion Table
|Radian [rad]||Degree [°]|
|0.01 rad||0.5729577951 °|
|0.1 rad||5.7295779513 °|
|1 rad||57.2957795131 °|
|2 rad||114.5915590262 °|
|3 rad||171.8873385392 °|
|5 rad||286.4788975654 °|
|10 rad||572.9577951308 °|
|20 rad||1145.9155902617 °|
|50 rad||2864.7889756541 °|
|100 rad||5729.5779513082 °|
|1000 rad||57295.779513082 °|
How to Convert Radian to Degree
1 rad = 57.2957795131 °
1 ° = 0.0174532925 rad
Example: convert 15 rad to °:
15 rad = 15 × 57.2957795131 ° = 859.4366926962 °