How many degrees are in one radian?

One radian (rad) is equivalent to approximately 57.2958 degrees. A full circle (360 degrees) is equivalent to exactly 2*pi radians.

A gradian (grad, gon, or grade) is a unit of angle equal to 1/400 of a full turn. Therefore, a right angle (90 degrees) is exactly 100 gradians. It was introduced during the French Revolution metrication effort.

How are arcminutes and arcseconds related to degrees?

One degree is split into exactly 60 arcminutes (minutes of arc), and one arcminute is split into exactly 60 arcseconds (seconds of arc). Therefore, one degree is equivalent to 3,600 arcseconds. These units are standard in astronomy and rifle scopes calibration (MOA).

Angle Converter

Convert geometric and spatial angles instantly: degrees, radians, gradians, arcminutes, and revolutions online.

Value to Convert From Unit

Converted Value

3.141593

To Unit

What is an Angle? Geometric Space and Rotation

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex. The magnitude of an angle represents the amount of rotation required to superimpose one ray onto the other. The standard SI derived unit for angles is the **Radian (rad)**, which is defined by the arc length of a circle divided by its radius.

Trigonometric calculations, mapping systems, astronomical alignments, mechanical gear ratios, and rifle ballistic calculations all rely on translating angular metrics accurately.

Standard Angle Units Comparison

Our online **angle conversion tool** translates between multiple mathematical scales:

Degree (°): A full circle is divided into 360 degrees. The most common unit for basic education and daily geographic coordinates.
Radian (rad): Standard in calculus and advanced physics. A full circle is exactly 2*pi radians.
Gradian (grad): Splits a right angle into 100 units. Often used in surveying and civil engineering.
Arcminutes / Arcseconds: Used for sub-degree precision in astronomy and shooting ballistics (minutes of angle, or MOA).
Revolution (rev): Represents one full circular turn (360 degrees).

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