Angle Converter

About Angle

An angle is a measure of the rotation between two rays with a common endpoint, that is, the vertex. It is typically measured in degrees, radians, or other circular measures.

• Degree (°) – Most commonly used unit;  a circle = 360°.
• Radian (rad) – SI unit of angle; one complete circle = 2π radians.
• Gradian (gon) – Metric unit; one complete circle = 400 gon.
• Turn (tr) – Equivalent one complete revolution; 1 turn = 360° = 2π rad.
• Arcminute (′) – 1/60 of a degree.
• Arcsecond (″) – 1/60 of an arcminute (or 1/3600 of a degree).
• Milliradian (mrad) – Used for ballistics and the military; 1/1000 of a radian.
• Compass point – Obsolete navigational unit; 1 point = 11.25°.
• Right angle (⊾) – 90° angle, typical in geometry.
• Sextant – Navigation unit; 1 sextant = 60°.

Angle Units

Angle measurement is important in fields such as mathematics, physics, engineering, and navigation. Various units have been defined through the years to denote angles, each suitable for a specific application.

• Radian (rad): The physical and mathematical unit of measurement, which is the central angle of a circle formed by an arc of the same length as the radius. The subdivisions are the milliradian (mrad), microradian (μrad), and nanoradian (nrad), used mainly in precision optics and ballistics.
• Turn (tr): A full revolution or 360°, often used in computer graphics and signal processing. Equivalent units include the circle (360°), the traditional emblem of a full revolution, and derived units like the right angle (90°) and sextant (60°), often used in geometry and navigation.
• Degree (°): Widely used in day-to-day activities and navigation. It is also further subdivided into arcminutes (′) and arcseconds (″) to allow more precise measurements, especially in astronomy and geodesy.
• Gradian (gon): This unit divides a right angle into 100 parts, making a full circle 400 gradians. The milligon (mgon) is typically used in surveying and engineering, favored for its decimal structure.
• Compass-based units: Traditional navigation uses include the quadrant (1/4 turn), octant (1/8 turn), hexacontade (1/60 turn), and compass point (1/32 turn). These units have historical importance in sea and air navigation, offering fine directional resolution.

Together, these angle units form a rich set that suits an extensive variety of scientific, engineering, and navigational uses.