degree [deg] to radian [rad] Converter

deg

rad

How to Convert degree to radianradian

1 deg = 0.017453292519943295 rad
1 rad = 57.29577951308232 deg

Example: convert 49 deg to rad:
49 deg = 49 x 0.017453292519943295 = 0.8552113334772214 rad

degree

Definition: A degree (symbol: °) is a unit of angular measure, representing 1/360 of a full rotation. It is a common unit for measuring angles, particularly in geometry and navigation.

History/origin: The division of a circle into 360 degrees is attributed to the ancient Babylonians, who used a base-60 (sexagesimal) numeral system. They may have chosen 360 because it is close to the number of days in a year.

Current use: Degrees are widely used in everyday contexts for measuring angles, such as in maps, compasses, and architectural drawings. They are also commonly used in mathematics and science, although radians are preferred in many theoretical contexts.

radian

Definition: A radian is the standard unit of angular measure, used in many areas of mathematics. One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

History/origin: The concept of radian measure was developed in the mid-18th century. Roger Cotes was one of the first to recognize the naturalness of using the radius as the unit of angle measurement. The term 'radian' first appeared in print on 1873, in examination questions set by James Thomson at Queen's College, Belfast.

Current use: Radians are widely used in mathematics, physics, and engineering, particularly in calculus, trigonometry, and signal processing. They simplify many formulas and are the standard unit for angular measurement in scientific and mathematical contexts.

degree to radian Conversion Table

degree [deg]radian [rad]
0.01 deg0.00017453292519943296 rad
0.1 deg0.0017453292519943296 rad
1 deg0.017453292519943295 rad
10 deg0.17453292519943295 rad
50 deg0.8726646259971648 rad
100 deg1.7453292519943295 rad
1000 deg17.453292519943297 rad
10000 deg174.53292519943295 rad