Degrees to Radians Converter

About this tool

Angles appear in different unit systems depending on the field: degrees for everyday geometry, radians for calculus and programming, gradians for some European surveying, and arcminutes and arcseconds for astronomy, optics and map coordinates. Converting between them manually is a constant source of errors — the degree-to-radian step trips up every programmer who forgets that JavaScript trig functions expect radians. This converter handles five units: degrees, radians, gradians, arcminutes and arcseconds. Enter a value, choose the From and To units, and the result appears instantly to fourteen significant digits. Underneath, the same angle is always echoed in radians as a quick sanity check. To turn a degrees-minutes-seconds reading into decimal degrees, convert the whole reading to arcseconds first (degrees × 3600 + minutes × 60 + seconds) and then convert arcseconds to degrees.

Why use it

• Five Angle Units: Converts between degrees, radians, gradians, arcminutes and arcseconds in a single interface, covering geometry, programming, surveying and astronomy.

• Radian Echo: Every conversion also shows the angle in radians, so you can confirm the value you are about to pass to a trig function without a second conversion.

• High Precision: Results carry up to fourteen significant digits, so 90° reads as 1.5707963267949 rad rather than a rounded 1.57.

• Live Conversion: The result updates on every keystroke or unit change — no submit button required.

• Offline Capable: All conversions run as plain browser JavaScript. No network request is needed, so the tool works in the field or in labs where internet access is restricted.

How to use

1. Type the angle in the Value field
2. Choose the source unit in the From dropdown: Degrees, Radians, Gradians, Arcminutes or Arcseconds
3. Choose the target unit in the To dropdown (it starts on Radians)
4. Read the converted value and the radian echo underneath it, which update as you type

When it helps

• Converting degrees to radians before passing an angle to JavaScript's Math.sin() or Math.cos() functions.
• Translating a DMS coordinate (37° 25′ 30″) to decimal degrees via arcseconds for a mapping API.
• Understanding a gradian value in a civil engineering or European surveying document.
• Converting an arcminute or arcsecond measurement from a telescope or optics spec into degrees.
• Verifying that a full rotation (360°) equals exactly 2π rad and 400 grad.

Examples

Tips

• JavaScript's Math.sin(), Math.cos(), and Math.atan2() all use radians — always convert from degrees before passing values into these functions.
• DMS notation uses minutes (1/60 of a degree) and seconds (1/3600 of a degree) — convert the whole reading to arcseconds to use it here.
• Gradians make right angles a clean 100 grad — useful in some surveying contexts where 90° produces less convenient arithmetic.
• One full rotation = 360° = 2π rad = 400 grad — handy for checking any conversion.
• The tool does not wrap angles, so 450° stays 450°; subtract 360° yourself if your code expects 0–360°.

Frequently Asked Questions

Glossary

Degree (°)

The most common unit of angle measurement, dividing a full circle into 360 parts. The 360-degree convention originates from ancient Babylonian astronomy and has been the dominant angular unit in navigation and everyday geometry ever since.

Radian (rad)

The SI unit of angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle is 2π radians. Radians are the natural unit for trigonometric functions and calculus.

Gradian (grad)

Also called a gon, the gradian divides a right angle into 100 parts and a full circle into 400 parts. Introduced during the French Revolution as part of the metric system, it simplifies some surveying calculations and is still used in parts of European civil engineering.

Turn (full revolution)

A unit equal to one complete rotation, equivalent to 360°, 2π radians, or 400 gradians. The turn is increasingly favoured in computer graphics and animation because it expresses rotations without requiring knowledge of π.

Degrees-Minutes-Seconds (DMS)

A notation for angles that subdivides degrees into 60 minutes (′) and each minute into 60 seconds (″). Used in geographic coordinates, navigation charts, and astronomical positions. 1 arcsecond ≈ 1/3600 of a degree.

Arc Length

The distance along a curved line or arc. For a circle of radius r, the arc length s subtended by an angle θ in radians is s = rθ. This direct relationship between arc length and radians is why radians are the natural angular unit in mathematics.