Angle Converter
Convert between different angle units: degree, radian, gradian, turn.
Angle Converter
Instant conversion between angle units
⚡ Popular Conversions
About Angle Conversion
Degree (°)
Most common angle measurement.
- • 360° - Full circle
- • 180° - Half circle
- • 90° - Right angle
- • 45° - Half right angle
Radian (rad)
SI unit for angle measurement.
- • 2π rad - Full circle
- • π rad - Half circle (180°)
- • π/2 rad - Right angle (90°)
- • π/4 rad - 45°
Gradian (grad)
Metric angle unit (gon).
- • 400 grad - Full circle
- • 200 grad - Half circle
- • 100 grad - Right angle
- • 50 grad - 45°
Applications
Where angles are used.
- • Mathematics - Radians preferred
- • Navigation - Degrees common
- • Surveying - Gradians used
- • Engineering - Context dependent
Understanding Angle Units
Angles measure the rotation between two lines or surfaces, with radians (rad) serving as the fundamental unit in mathematical and scientific applications. Understanding angle conversions is essential for navigation, engineering, astronomy, computer graphics, and trigonometric calculations requiring precise angular measurements.
The degree system divides a full circle into 360 equal parts, providing intuitive measurements for everyday applications. This ancient Babylonian system remains standard in navigation, surveying, and general education, with familiar reference points like 90° for right angles and 180° for straight lines.
Radians offer mathematical elegance by relating angle measurement directly to arc length and radius. One radian equals the angle subtended by an arc length equal to the radius, making 2π radians equal to 360°. This natural unit simplifies calculus operations and trigonometric functions in advanced mathematics and physics.
The gradian system (also called gons) divides a circle into 400 parts, providing decimal-friendly measurements for surveying and military applications. While less common than degrees or radians, gradians offer advantages in certain technical fields requiring metric-system compatibility and decimal calculations.
Modern applications demand precise angle conversions across diverse fields. GPS navigation requires degree-minute-second precision, computer graphics use radians for rotation calculations, and engineering projects need exact angular specifications for component alignment, structural design, and mechanical system functionality.