Angle Unit Conversion

FAQ

• What is the difference between degrees and radians?
  Degrees are based on dividing a circle into 360 equal parts, while radians are based on the radius of the circle. One radian equals approximately 57.3 degrees. Radians are the standard unit in mathematics and engineering calculations.
• How do I convert degrees to radians?
  To convert degrees to radians, multiply by π/180. For example: 90° × π/180 = π/2 radians ≈ 1.571 radians. The formula is: radians = degrees × π/180.
• What are arc minutes and arc seconds used for?
  Arc minutes and arc seconds are used for precise angular measurements in astronomy, navigation, surveying, and cartography. They provide finer precision than degrees alone. 1 degree = 60 arc minutes = 3600 arc seconds.
• How do I read DMS (Degree-Minute-Second) notation?
  DMS notation expresses angles as degrees, minutes, and seconds. For example, 45°30'15" means 45 degrees, 30 arc minutes, and 15 arc seconds. This equals 45.50417 decimal degrees.
• When should I use each angle unit?
  Use degrees for general measurements and everyday applications. Use radians for mathematical calculations, trigonometry, and engineering. Use arc minutes/seconds for precise measurements in astronomy, GPS coordinates, and surveying.
• What is the relationship between π and angle measurements?
  π (pi) represents half a circle in radians. A full circle is 2π radians = 360 degrees. Common angles: π/2 rad = 90°, π rad = 180°, 3π/2 rad = 270°, 2π rad = 360°.