Angle Converter
Convert any angle unit to another with this free angle converter. It supports 6 units including degrees, radians, gradians, arcminutes, arcseconds, turns. Pick a conversion below for a dedicated calculator, formula, and reference table. For example, 1 ° = 0.017453293 rad.
All angle conversions
About these units
Degree (°)
- Definition
- A degree (°) is an angle equal to 1/360 of a full turn.
- History
- The 360-degree circle descends from Babylonian astronomy and its base-60 number system.
- Current use
- Degrees measure angles in navigation, geometry, and everyday use.
Radian (rad)
- Definition
- A radian (rad) is the SI angle for which the arc length equals the radius; a full circle is 2π radians.
- History
- The concept was formalised in the 19th century and named in 1873.
- Current use
- Radians are the standard angle unit in mathematics and physics.
Gradian (grad)
- Definition
- A gradian (grad) divides a right angle into 100 parts, so a full circle is 400 gradians.
- History
- It was introduced in France around the time of the metric system to decimalise angles.
- Current use
- Gradians are used in some surveying and civil-engineering contexts.
Arcminute (')
- Definition
- An arcminute (′) is one sixtieth of a degree.
- History
- It comes from the base-60 subdivision of the degree in astronomy.
- Current use
- Arcminutes measure small angles in astronomy, optics, and navigation.
Arcsecond (")
- Definition
- An arcsecond (″) is one sixtieth of an arcminute, or 1/3600 of a degree.
- History
- It continues the base-60 subdivision used since ancient astronomy.
- Current use
- Arcseconds measure very small angles such as star positions and telescope resolution.
Turn (turn)
- Definition
- A turn is one complete rotation, equal to 360 degrees or 2π radians.
- History
- The full turn is the most intuitive angle and underlies the definition of other units.
- Current use
- Turns describe rotations in engineering, mechanics, and everyday language.
Frequently asked questions
What angle units can I convert?
This angle converter supports 6 units: degrees, radians, gradians, arcminutes, arcseconds, turns. Select any pair below to open a dedicated converter with a formula and conversion table.
How accurate is the angle converter?
Conversions use exact definitional factors, so results are accurate to the precision you need for science, engineering, and everyday use. Values are rounded only for display.
Is the angle converter free?
Yes. Every angle conversion is completely free, needs no sign-up, and runs entirely in your browser — your inputs never leave your device.
Free, private, and instant — every conversion runs in your browser.
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