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# Difference Between Radian and Degree

Degrees and radians are units of angular measurement. Both are commonly used in practice, in fields such as mathematics, physics, engineering, and many other applied sciences. Degree has a history running back to ancient Babylonian history while radian is a relatively modern mathematical concept introduced in 1714 by Roger Cotes.

Degree

Degree is the most commonly used, elementary unit of angular measurement. Even though it is the most common unit in practice it is not the SI unit of angular measurement.

A degree (arc degree) is defined as 1/360th of the total angle of a circle. It is further divided into minutes (arc minutes) and seconds (arc seconds). One arc minute is 1/60th of a degree, and an arc second is 1/60th of an arc minute. Another method of subdivision is decimal degree, where one arc degree is divided into 100. One hundredth of a degree is known and symbolized by the term grad.

A radian is defined as the plane angle subtended by a circular arc of length which is equal to its radius.

Radian is the standard unit of angular measurement, and it’s used in many areas of mathematics and its applications. Radian is also a derived SI unit of angular measurement, and it is dimensionless. Radians are symbolized using the term rad behind the numeric values.

A circle subtends an angle of 2π rad at the center and a semicircle subtends π rad. A right angle is π/2 rad.

These relations allow conversion from degrees to radians and vice versa.

1° = π/180 rad   ↔   1 rad = 180°/π

Compared to other units, radian is preferred because of its natural nature. When applied, radian allows more interpretation in mathematics than other units. Except in practical geometry, in calculus, analysis, and other sub disciplines of mathematics radian is used.

What is the difference between Radians and Degrees?

• A degree is a unit purely based on the amount of rotation or turn while radian is based on the arc length produced by each angle.

• A degree is 1/360th of the angle of a circle while radian is the angle subtended by a circular arc which has the same length as its radius. It follows that a circle subtends 3600 or 2π radians.

• Degrees are further divided into arc minutes and arc seconds, while radians have no subdivision, but uses decimals for smaller angles and fractional angles.

• Radian supports the easier interpretation of concepts in mathematics; therefore, allowing application in physics and other pure sciences (for example consider the definitions of tangential velocity).

• Both degrees and radians are dimensionless units.

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