Angle Converter
The angle converter lets you quickly and accurately convert between degrees, radians, gradians, turns, arcminutes, and arcseconds. Whether you're working in trigonometry, navigation, or engineering, this tool handles the math instantly.
Angle conversions are fundamental in mathematics, physics, surveying, astronomy, and computer graphics. Different fields and software tools use different angle units, making a reliable converter essential for accurate calculations.
How it works
Angle conversions use standardized factors with degrees as the base unit. Key relationships: 360° = 2π radians = 400 gradians = 1 turn. Subdivisions: 1° = 60 arcminutes (′), 1 arcminute = 60 arcseconds (″). To convert, multiply by the appropriate factor.
Use cases
- Converting between degrees and radians for trigonometric calculations
- Translating survey measurements between gradians and degrees
- Converting astronomical coordinates from degrees to arcminutes/arcseconds
- Working with rotation values in computer graphics and game development
Frequently asked questions
How do I convert degrees to radians?
Multiply the angle in degrees by π/180 (approximately 0.0174533). For example, 90° × π/180 = π/2 ≈ 1.5708 radians. To go the other way, multiply the value in radians by 180/π.
What is the difference between degrees and gradians?
A full circle is 360 degrees but 400 gradians, so one gradian equals 0.9 degrees. Gradians (also called gons) are mainly used in surveying because a right angle is exactly 100 gradians, which makes decimal calculations simpler.
How many arcminutes and arcseconds are in one degree?
One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so one degree equals 3,600 arcseconds. These subdivisions are widely used in astronomy, navigation, and geographic coordinates.
Why do programming languages use radians instead of degrees?
Most math libraries expect radians because they are the natural unit for trigonometric functions — identities like sin(x) ≈ x for small angles only hold when x is in radians. If your input is in degrees, multiply it by π/180 before calling sin, cos, or tan.
What is a turn and when is it used?
A turn represents one complete rotation, equal to 360°, 2π radians, or 400 gradians. Turns are convenient in computer graphics and animation, where rotations are often expressed as fractions of a full revolution, such as 0.25 turn for a quarter rotation.