∡ Angle Conversion

Convert between angle units for mathematics, navigation, engineering, and astronomy. Supports degrees (°), radians (rad), gradians (gon), arcminutes (′), arcseconds (″), and milliradians (mrad).

Angular conversion calculates rotational displacement across circular division systems. The SI derived unit is the radian (rad). A full circle equals 360 degrees (360°), 2π radians (approx. 6.283185 rad), or 400 gradians (gon). 1 radian equals approximately 57.29578 degrees.

Metrological Standards & Base Equation

π radians = 180°. 1 radian ≈ 57.2958°. 1° = 60 arcminutes = 3,600 arcseconds.

Trigonometric angular factors adhere to ISO 80000-3 (Quantities and Units — Space and Time) and the SI brochure, maintaining double-precision floating-point values of mathematical π for astronomical and geodetic calculations.

Primary References: BIPM SI Brochure (2019) · Standards Directory

Supported Angle Units (6 Total)

Angle Unit Definitions and Scaling Factors
Unit Symbol Unit Name System Equivalent in Degree
deg Degree Metric Reference Standard (1 deg)
rad Radian Scientific 1 rad = 57.29577951 deg
mrad Milliradian Scientific 1 mrad = 0.05729578 deg
grad Gradian Other 1 grad = 0.9 deg
arcmin Arcminute Other 1 arcmin = 0.01666667 deg
arcsec Arcsecond Other 1 arcsec = 0.00027778 deg

Popular Angle Conversions

Degrees to Radians

° → rad — trigonometry & calculus

Radians to Degrees

rad → ° — practical geometry

Degrees to Gradians

° → gon — surveying & land measurement

Arcminutes to Degrees

′ → ° — astronomy & navigation

Radians to mrad

rad → mrad — precision targeting

Common Use Cases

  • Trigonometry (°↔rad)
  • Navigation (°↔′↔″)
  • Surveying (gon↔°)
  • Astronomy (′↔″↔rad)
  • Engineering (rad↔mrad)

Frequently Asked Questions

How do I convert degrees to radians?

Multiply degrees by π/180. For example, 180° × π/180 = π radians, 90° × π/180 = π/2 radians.

What is a gradian?

A gradian (gon) divides a right angle into 100 parts. 100 gradians = 90°, 400 gradians = 360°. Used in surveying and some European engineering.