Select the unit you wish to convert to

Abbreviations / Symbols:

c

Unit of:

Angle

Wordwide use:

Radians are a widely used unit of measurement in mathematics and physics, particularly in the field of trigonometry. Unlike degrees, which divide a circle into 360 equal parts, radians divide a circle into 2π (approximately 6.28) equal parts. This unit of measurement is preferred in many mathematical and scientific calculations due to its simplicity and compatibility with calculus.

The use of radians is not limited to a specific region or country; it is a universally accepted unit of measurement used by mathematicians, physicists, and engineers worldwide.

Definition:

The angle made by taking the radius of a circle and wrapping it along the circle's edge. Therefore 1 Radian is equal to (180/π) degrees

The radian is a unit of measurement used in mathematics to quantify angles. It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. In simpler terms, a radian is the angle formed when the length of the arc is equal to the radius of the circle.

The radian is a fundamental unit of angular measurement in the International System of Units (SI). Unlike degrees, which divide a circle into 360 equal parts, radians divide a circle into 2π (approximately 6.28) equal parts. This makes radians a more natural and convenient unit for many mathematical calculations involving angles.

Radian measurements are widely used in various branches of mathematics, physics, and engineering. They are particularly useful in calculus, trigonometry, and complex analysis, where they simplify calculations and provide a more intuitive understanding of circular motion and periodic phenomena. Radians are also commonly used in computer graphics, robotics, and navigation systems, where precise angular measurements are required.

Origin:

Roger Cotes, a colleague of Isaac Newton who helped proofread the Principia, is credited with defining the Radian in 1714, although other mathematicians had been using angle measurements based on the length of the arc as far back as the 15th Century

The origin of radians can be traced back to the concept of measuring angles in mathematics. The term "radian" was first introduced by the mathematician James Thomson in the late 19th century.

Common references:

Usage context:

Radians are particularly useful in calculus, where they simplify the calculation of derivatives and integrals involving trigonometric functions. They also have applications in physics, such as measuring angles of rotation, angular velocity, and angular acceleration.

In addition to their mathematical and scientific applications, radians are also used in various practical fields. For example, in navigation and astronomy, radians are used to measure the position and movement of celestial bodies. They are also used in computer graphics and animation to represent rotations and orientations of objects in three-dimensional space.