Convert radians to degrees

Radian

Definition: A radian (symbol: rad) is the standard unit of angular measure in the International System of Units (SI). It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. One complete revolution (360 degrees) is equal to 2π radians (approximately 6.28318 radians).

History/origin: The concept of radian measure was first introduced by Roger Cotes in 1714 in his book "Harmonia Mensurarum." However, the term "radian" wasn't used until 1873 when James Thomson (brother of Lord Kelvin) coined it. Radians became increasingly important in mathematics and physics during the 19th century as calculus developed, since they provide a more natural way to express angular measurement in many mathematical contexts. The radian was officially adopted as an SI supplementary unit in 1960.

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.

Degree

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

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 °