Radians to Degrees Converter

To convert a measurement in radians to degrees, multiply the value by 57.29578. The conversion factor comes from the relationship between both units and the radian.

For example, to convert 5 rad to degrees: 5 × 57.29578 = 286.478898 °.

A radian is the SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. A full turn equals 2π radians. The concept dates to the 18th century, but the term 'radian' was coined by James Thomson in 1873. It is the natural unit of angle in mathematics and physics because it makes calculus formulas for trigonometric functions clean and dimensionless.

Common uses of radians include: Calculus, physics, and engineering calculations; Angular velocity and rotational motion (rad/s); Computer graphics and game math libraries; Signal processing and wave phase (2π per cycle).

A degree is a unit of plane angle equal to 1/360 of a full turn, so a full circle contains exactly 360 degrees. The 360-degree circle traces back to ancient Babylonian astronomers, whose base-60 (sexagesimal) number system made 360 a convenient, highly divisible count for tracking the roughly 365-day solar year. It remains the most widely used angle unit in everyday life.

Common uses of degrees include: Geometry, trigonometry, and school mathematics; Compass bearings and navigation headings; Latitude and longitude coordinates; Camera field of view and lens specifications.

Programmers and engineers often get a result in radians from a calculation or an API and need it in degrees to display or reason about it. A rotation of 1 radian is roughly 57.3°, and knowing this conversion turns an abstract radian value into an angle you can picture.

Here are some common values converted:

1 rad = 57.29578 ° 5 rad = 286.478898 ° 10 rad = 572.957795 ° 50 rad = 2,864.789 ° 100 rad = 5,729.578 °