Angle Converter

Worked example

180° is written ≈ 3.141592654 rad, and underneath it says the exact value is π rad. 45° is ≈ 0.7853981634 rad, exactly π/4 rad. 90° = 0.25 turn, 100 gon = 90° and 1° = 60 arcminutes, all exactly.

How it works

Degrees, gradians (gon), turns, arcminutes and arcseconds are exact fractions of a turn: 360° = 400 gon = 1 turn, 60 arcminutes = 1° and 60 arcseconds = 1 arcminute. The radian is different, because a full turn is 2π radians and π is irrational. Any non-zero conversion into or out of radians is therefore rounded (shown with “≈”), even though the true value is an exact multiple of π when you start from degrees, gradians, turns or arcminutes. In that case the exact multiple, such as “Exactly π/4 rad”, is shown underneath.

Type numbers only: the symbol π is not accepted. A radian value you type is used as the decimal you entered, so 3.14159265358979 rad converts to ≈ 180°, not to exactly 180°. Signed values are accepted: a negative angle indicates the opposite direction. This tool converts angle units only and does not do trigonometry.

A result written as a plain number is exact. A result starting with “≈” has been rounded to 10 significant figures, because its exact decimal never ends or is too long to read comfortably. When an exact value is long, its full digits are shown underneath. The calculation itself is never rounded: only the display is.