Angle Converter
Convert between degrees, radians, gradians, arcminutes, and arcseconds instantly.
Conversions run locally in your browser — nothing is uploaded or stored.
About Angle Units
This converter handles five units commonly used in mathematics, engineering, surveying, navigation, and astronomy. Select your starting unit, enter a value, choose the target format, and read the converted result immediately.
Quick Reference Table
| Unit | Symbol | Full Circle Value |
|---|---|---|
| Degree | ° | 360° |
| Radian | rad | 2π ≈ 6.28319 |
| Gradian | grad (or gon) | 400 grad |
| Arcminute | ′ | 21,600′ |
| Arcsecond | ″ | 1,296,000″ |
Common Use Cases by Field
- Mathematics & Trigonometry: Converting between degrees and radians for calculus functions, sine/cosine calculations, and geometry problems
- Programming: Most programming languages use radians for trig functions (Math.sin, Math.cos), so converting degree inputs is essential
- Surveying & Civil Engineering: Gradians are standard in some European countries and surveying equipment because they simplify right-angle calculations
- Navigation & Cartography: Latitude and longitude traditionally use degrees with arcminute/arcsecond precision for GPS coordinates
- Astronomy: Celestial coordinates and angular separation between stars use arcminutes and arcseconds for high precision
- Ballistics & Optics: Small angular measurements (milliradians) for aiming systems and lens field-of-view calculations
Frequently Asked Questions
How many radians are in a full circle?
A full circle equals 2π radians, approximately 6.28319, which corresponds to 360 degrees. The radian is the SI unit for angles and is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
What is a gradian?
A gradian (also called a gon or metric degree) divides a right angle into 100 equal parts, making a full circle 400 gradians. It was introduced in France as part of the metric system and is still used in some surveying equipment and European countries.
How many arcminutes are in a degree?
One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds. This sexagesimal subdivision mirrors how time is measured (60 seconds per minute). Arcminutes and arcseconds allow precise angular measurements without using decimals.
Can I convert degrees to radians for programming?
Absolutely. Select degrees as your source unit and radians as the target. The result can be copied directly into code. For reference, the conversion formula is: radians = degrees × (π / 180).
Is this useful for astronomy calculations?
Yes. Astronomers frequently work with very small angles — the apparent size of planets, angular distance between stars, or parallax measurements — all expressed in arcminutes and arcseconds rather than decimal degrees.
Related Converters
Unit Converter · Length Converter · Frequency Converter · Speed Converter