Angle Converter
Convert degrees, radians, gradians, turns, arcminutes and arcseconds.
Angle Converter
| Converted angle | 3.141593 |
| Summary | 180 ° = 3.141593 rad |
180 degrees is exactly π radians (3.14159265…) — a half turn.
Convert angles between the units used in maths, surveying and astronomy. A full turn is 360 degrees, 2π radians or 400 gradians; each degree splits into 60 arcminutes and each arcminute into 60 arcseconds.
Radians dominate mathematics because they make calculus clean (the derivative of sin x is cos x only in radians); gradians survive in European surveying.
The formula
Worked example
180 degrees is exactly π radians (3.14159265…) — a half turn.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180. For example, 90° = π/2 ≈ 1.5708 rad, and a right angle in gradians is exactly 100 gon.
How many arcseconds are in a degree?
3600 — 60 arcminutes per degree × 60 arcseconds per arcminute. Astronomers use arcseconds for star positions and telescope resolution.
Where are gradians used?
Surveying and some European instrumentation: a right angle is a round 100 gon, which makes slope and bearing arithmetic decimal-friendly.
Category: Unit Conversions calculators
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