What is an angle converter?
An angle converter is an online tool that lets you quickly and accurately convert between angle units. It supports degrees, radians, gradians, arcminutes, arcseconds and turns.
What are angles?
An angle is a figure formed by two rays sharing a common endpoint called the vertex. Angles are measured in several units: degrees are the most common in everyday use, radians are standard in mathematics and physics, and gradians are used in surveying.
What are the angle conversion formulas?
Key angle conversion formulas:
- 180 degrees = π radians
- 1 full turn = 360 degrees = 2π radians
- 1 degree = π/180 radians ≈ 0.01745 radians
- 1 radian = 180/π degrees ≈ 57.2958 degrees
- 1 gradian = 0.9 degrees
- 360 degrees = 400 gradians
- 1 degree = 60 arcminutes = 3600 arcseconds
Angle conversion examples
Mathematics: 90 degrees = π/2 radians. A right angle, one of the most fundamental angles in geometry.
Navigation: 45 degrees = 50 gradians. A northeast bearing on a compass.
Astronomy: 0.5 degrees = 30 arcminutes. The approximate angular diameter of the Moon as seen from Earth.
When to use an angle converter?
An angle converter is useful in mathematics when switching between degrees and radians for trigonometric calculations, in navigation and surveying for bearing conversions, in astronomy for angular measurements, and in construction for setting precise angles.