Angle Converter

Convert angles between degrees, radians, gradians, turns and arc units — for math, engineering and navigation.

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Quick answer

Angle is a free, private online tool that lets you convert angles between degrees, radians, gradians, turns, arcminutes and arcseconds. It runs entirely in your browser, so nothing you enter is uploaded to a server.

How to use the Angle

Enter the number you want to convert in the Value field.
Pick the unit you're converting From and the unit you want To.
Read the converted result, or use ⇅ to swap the two units.
Check the All units table to see your value expressed in every supported unit at once.

Privacy: this tool runs entirely in your browser. Your input is never sent to, received by, or stored on any server — there are no uploads and no tracking of what you enter.

About Angle

Common angle units

Degrees (everyday and navigation), radians (math and physics), gradians (surveying) and turns (full rotations).

Key conversions

180 degrees = pi radians. 1 turn = 360 degrees = 2 pi radians = 400 gradians.

Where it helps

Trigonometry, programming (most languages use radians), CAD and surveying.

Frequently asked questions

How do I convert degrees to radians?

Multiply by pi/180 (about 0.01745).

What is a gradian?

A unit where a right angle is 100 gradians; a full circle is 400.

What is a turn?

One full rotation = 360 degrees.

Understanding Angle in depth

What angle units measure

An angle measures rotation or the 'opening' between two lines. The everyday unit is the degree, where a full circle is 360°, but mathematics and programming usually use radians, and surveying sometimes uses gradians. This converter translates a value between all of them.

Degrees, radians and the role of pi

A full turn is 360 degrees, 2π radians, or 400 gradians. The radian is the 'natural' unit because it is defined by the circle itself: one radian is the angle where the arc length equals the radius. That is why the conversion factor involves π — 180° = π radians, so to convert degrees to radians you multiply by π/180 (about 0.01745).

How the conversion works

Each unit is expressed relative to the degree, and the tool converts to and from that base. So radians are scaled by 180/π, gradians by 0.9 (since 400 gradians = 360°), and a full turn equals 360°. Fine subdivisions of a degree — arcminutes (1/60 of a degree) and arcseconds (1/3600) — are included for navigation and astronomy.

Why programmers care

Most programming languages' trigonometric functions (Math.sin, Math.cos) expect radians, not degrees. Feeding them degrees is a classic bug. If you think in degrees but your code needs radians, converting first — or multiplying by π/180 — fixes results that otherwise look completely wrong.

Everyday uses

Convert angles for trigonometry homework, prepare values for code that expects radians, work with CAD and 3D rotations, and handle surveying or navigation bearings. It runs entirely in your browser.