Angle Converter
Degrees, radians, gradians, arcminutes, arcseconds, and full turns.
Common conversions
Angle unit reference
What 1 degree equals in every other unit.
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Why radian is the one angle unit that's never an exact conversion
A full circle is 360 degrees, 400 gradians, or exactly 1 full turn — and every one of those relationships is a clean, exact fraction (1 gradian is exactly 0.9 degrees, no rounding involved). Radian breaks that pattern: a full circle is 2π radians, and π is irrational — it never resolves to a finite decimal, no matter how far out you calculate it.
That means any conversion into or out of radians shown on this page (or anywhere else) is necessarily a rounded value, not an exact one — unlike converting degrees to gradians, which is exact all the way down. This isn't a flaw in the calculation; it's a real property of the unit itself, which is defined by the geometric relationship between a circle's radius and its circumference rather than by dividing a circle into an arbitrary number of equal slices the way degrees and gradians do.
Arcminutes and arcseconds are subdivisions of the degree (60 arcminutes per degree, 60 arcseconds per arcminute) — the same 60-based counting the Babylonians used for degrees, hours, and minutes. They're still the standard way to express fine angular precision in astronomy and geographic coordinates.