Degrees to Radians Converter

To convert a measurement in degrees to radians, multiply the value by 0.01745329252. The conversion factor comes from the relationship between both units and the radian.

For example, to convert 5 ° to radians: 5 × 0.01745329252 = 0.0872664626 rad.

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.

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).

Anyone doing trigonometry, calculus, or physics needs this conversion constantly. Most people think in degrees, but math libraries, physics formulas, and programming functions like Math.sin() expect radians. Converting 90° to π/2 radians (about 1.5708) is one of the most common steps in engineering and graphics work.

Here are some common values converted:

1 ° = 0.01745329252 rad 5 ° = 0.0872664626 rad 10 ° = 0.174532925199 rad 50 ° = 0.872664625997 rad 100 ° = 1.745329 rad