Angle Converter
Convert between degrees, radians, gradians, turns and degrees-minutes-seconds. Enter an angle in one unit and see it expressed in all the others, including the DMS breakdown surveyors and astronomers use.
Degrees versus radians matters in CSS too — the CSS Clip Path generator accepts either, and Number Base covers the numeric side.
How to use the Angle Converter
- 1 Enter the angle you want to convert.
- 2 Choose the source unit — degrees, radians, gradians or turns.
- 3 Read the equivalent in the other units, plus the reference values for common angles.
- 4 Swap direction to convert the other way.
How It Works
All units are defined relative to the degree. The calculator also decomposes the result into whole degrees, minutes and seconds, and prints the radians as an exact multiple of π where possible.
- Degrees, radians and gradians
- Turns (full revolutions)
- Milliradians and arcminutes
- Degrees / minutes / seconds output
- Radians as a fraction of π
Frequently asked questions
What exactly is a radian?
The angle you get when the arc length equals the radius. That makes a full circle 2π radians rather than 360°, so one radian is about 57.2958°. It looks awkward but removes constants from calculus and physics, which is why it is the SI unit.
Why do programming languages use radians?
Because their maths libraries are built on the SI convention — sin, cos and tan in JavaScript, Python and C all take radians. Passing degrees produces plausible-looking but wrong answers rather than an error, which makes it a particularly easy bug to miss.
What are gradians for?
A metric attempt at angle measurement: 400 gradians to a full turn, so a right angle is exactly 100. It divides neatly by ten, which appealed to surveyors and the military, but degrees and radians won out almost everywhere else.
Related Unit & Data Converters
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