4 tools
Degrees, radians and complete turns.
Choose a conversion below. Every tool includes an instant result, an example and a short explanation.
Angles can be expressed as degrees, radians or complete turns. A full revolution is 360 degrees, 2π radians or one turn. Radians measure the ratio of arc length to radius, which makes them natural in trigonometry and calculus; degrees are familiar in diagrams, navigation and everyday directions.
The conversion is proportional, but factors containing π cannot be written as finite decimals. Calculator output is therefore an approximation even when the geometric relationship is exact. Negative angles describe the opposite rotation direction under a chosen sign convention. More than one complete turn can be useful when counting rotation rather than final orientation.
A complete turn is 360 degrees or 2π radians. Degrees divide a circle into 360 parts; radians relate an angle to arc length and radius. Choose the unit expected by your calculator, programming API or drawing, and use enough precision for π when checking a result.
Yes, if the function expects a different unit from your input. Many programming libraries expect radians, while a handheld calculator may be set to degrees. The sine of a numerical value changes dramatically when the mode is wrong. Confirm the function’s angle mode first, convert if needed, and then evaluate it.