Degrees to Radians (° → rad)

Degrees to Radians Conversion

Degrees and radians both measure angles, with 360 degrees equal to 2π radians. Conversion uses the scale factor π/180 without any offset. Radians are standard in mathematics and physics, especially for trigonometric functions and calculus.

Sources: BIPM SI Brochure, 9th edition

Degrees → Radians

Converting Degrees (°) to Radians (rad) is a common angle conversion. 1 ° equals 0.017453 rad. For example, 100 ° is equal to 1.745329 rad.

Quick Mental Math: Degrees to Radians

Multiply degrees by 0.01745 (π/180) for a quick radian estimate.

Why is converting Degrees to Radians tricky?

Radians use an irrational constant π, complicating exact mental conversions and requiring understanding of radian definition.

Quick Reference Values

1 ° = 0.017453 rad. 5 ° = 0.087266 rad. 10 ° = 0.174533 rad. 25 ° = 0.436332 rad. 50 ° = 0.872665 rad. 100 ° = 1.745329 rad.

What is Degrees?

Degrees (°) is a unit of angle. A degree is a unit of angular measurement defined as 1/360 of a full rotation or circle. One degree equals exactly π/180 radians, aligning with the International System of Units (SI) conventions for angles. It is commonly used in geometry, navigation, and geospatial coordinates to measure angles and directions [iso-80000]. The degree originated with the ancient Babylonians around 3000 BCE, who divided a circle into 360 parts likely based on their sexagesimal numeral system. This system was formalized over centuries and incorporated into modern angle measurement standards. The consistent division into 360 degrees became globally accepted due to its mathematical convenience and historical use [iso-80000]. Degrees are used worldwide in navigation, astronomy, cartography, and engineering. Countries including the United States, Canada, and members of the European Union employ degrees for geographic coordinates. Scientific organizations such as ISO and BIPM recognize degrees as a standard unit for angles [bipm-si-brochure].

What is Radians?

Radians (rad) is a unit of angle. 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. One radian equals approximately 57.2958 degrees or exactly 1 rad = radius/arc length ratio. It is a dimensionless unit used extensively in mathematics, physics, and engineering [bipm-si-brochure]. The radian concept was formalized in the 19th century, with mathematicians like Roger Cotes contributing to its development. The radian was adopted as the standard angular unit in the SI system to provide a natural measure of angles based on circle geometry [bipm-si-brochure]. Radians are the standard unit of angular measurement in science, engineering, and technology worldwide. They are used in trigonometry, rotational dynamics, and signal processing, with formal adoption by the BIPM and ISO 80000 standards [bipm-si-brochure, iso-80000].

Common Misspellings

People often search for this conversion using these alternate spellings: degres, degreess, degreees, degre, degr, radianes, radias, radans, radiens. All of these refer to the Degrees to Radians conversion.

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