Angle Converter

Free angle converter. Convert between degrees, radians, gradians, and turns (full rotations) with exact, round-trippable conversions.

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This tool has a free JSON API. Copy a prompt or skill below to use it with ChatGPT, Claude, or any AI agent โ€” no API key needed.

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How angle converter works

Angles can be measured in several units. Degrees split a full circle into 360 parts; radians express an angle as the ratio of arc length to radius (a full circle is 2ฯ€ radians); gradians split a circle into 400; and a turn is one full rotation (1). Each converts to the others by a fixed ratio.

This converter passes the value through turns as a common intermediate โ€” 1 turn = 360 degrees = 2ฯ€ radians = 400 gradians โ€” so conversions are exact and round-trip cleanly. It supports degrees, radians, gradians, and turns.

Enter a value, choose the source and target units, and the tool returns the converted angle. Use it for trigonometry homework, geometry, navigation, and any time you need to move between the common angle units.

Frequently asked questions

How many radians are in a degree?
ฯ€/180, about 0.01745. So 180 degrees equal ฯ€ radians (about 3.14159), and 360 degrees equal 2ฯ€ radians.
What is a gradian?
A unit where a full circle is 400 gradians, so 100 gradians is a right angle. It is used in surveying and some European engineering. 90 degrees equal 100 gradians.
What is a turn?
One full rotation โ€” 360 degrees, 2ฯ€ radians, or 400 gradians. It is a convenient unit for fractions of a circle (a quarter turn is 90 degrees).
Do the conversions round-trip exactly?
Yes. Because all conversions go through turns with exact ratios, converting to a unit and back gives the original value (up to floating-point rounding).