What does radian mean?
A radian is a unit used to measure plane angles. It is defined by the geometry of a circle: an angle of one radian is subtended by an arc whose length equals the circle’s radius. This definition gives radian a useful mathematical role, because it relates angle directly to arc length and makes formulas involving angular speed, circular motion, and trigonometric functions especially simple. A full rotation equals 2π radians, while one radian is approximately 57.3 degrees. Although degrees remain common in everyday geometry and education, radians are preferred in advanced mathematics, physics, and engineering, particularly in calculus. When writing the unit, “rad” is used after a numerical value, as in “2.5 rad,” although the plural form “radians” is also widely used.
nounA unit of plane angle equal to the angle subtended at the centre of a circle by an arc whose length equals the radius. One radian is approximately 57.3 degrees, and a full turn is 2π radians.
- A unit of plane angle defined by an arc whose length is equal to the radius of the circle on which it is measured.
"The rotation was measured in radians rather than degrees."
"The angle between the two vectors is 1.2 radians."
"In trigonometry, angles are often expressed in radians when using calculus."
Use the plural when the unit occurs with a value other than one, as in “three radians.” The symbol form is typically “rad” and does not take a plural s.
"The wheel completed four radians of rotation in one second."
A radian is the angle a radius sweeps when it travels once around its own length along a circle.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of radian
The word radian derives from the Latin radius, meaning “spoke” or “ray of a circle,” through the formation of the English mathematical term in the 19th century. Its name reflects the defining relationship between the angle and the radius of a circle. The word belongs to a family of English terms from the same Latin root, including radial, radiate, radiant, and radius.
How radian is actually used
Radians are especially common in mathematics, physics, and engineering. The symbol for radian is rad, while the abbreviated form “rads” is informal and less common in formal writing.
Easily confused with radian
A degree is one of 360 equal divisions of a full turn, whereas a radian is defined by the relationship between arc length and circle radius.