Angle Converter

Convert between all common angle units including degrees, radians, gradians, arcminutes, arcseconds, turns, and milliradians.

Angle Converter 7 units

From

—

Common Angle Conversions

All Angle Conversions

Browse all unit combinations — each page has a dedicated converter and conversion table.

Degrees → Radians Degrees → Gradians Degrees → Arcminutes Degrees → Arcseconds Degrees → Turns Degrees → Milliradians Radians → Degrees Radians → Gradians Radians → Arcminutes Radians → Arcseconds Radians → Turns Radians → Milliradians Gradians → Degrees Gradians → Radians Gradians → Arcminutes Gradians → Arcseconds Gradians → Turns Gradians → Milliradians Arcminutes → Degrees Arcminutes → Radians Arcminutes → Gradians Arcminutes → Arcseconds Arcminutes → Turns Arcminutes → Milliradians Arcseconds → Degrees Arcseconds → Radians Arcseconds → Gradians Arcseconds → Arcminutes Arcseconds → Turns Arcseconds → Milliradians Turns → Degrees Turns → Radians Turns → Gradians Turns → Arcminutes Turns → Arcseconds Turns → Milliradians Milliradians → Degrees Milliradians → Radians Milliradians → Gradians Milliradians → Arcminutes Milliradians → Arcseconds Milliradians → Turns

📐 How to Use

Pick the angle unit you are starting from in the From list and the one you want in the To list.
Enter the angle in the input below From; the converted value and a plain-language result line refresh with every keystroke.
Click the swap button to exchange the two units, and Copy to send the result to your clipboard.
The Common Angle Conversions grid loads frequent pairs such as degrees to radians in one click, while All Angle Conversions links every pair to a dedicated page carrying a full conversion table.

❓ Frequently Asked Questions

QHow many degrees are in 1 radian?

1 radian is 57.2958 degrees, stored here as 57.29577951. Going the other way, 1 degree is 0.01745329 radians. The factor is 180 divided by pi, so neither direction produces an exact decimal, and a right angle is 1.570796 radians.

QWhat is 1 degree in gradians?

1 degree is 1.111111 gradians, and 1 gradian is exactly 0.9 degrees. The gradian splits the right angle into 100 units, so a full circle is 400 gradians instead of 360 degrees. Surveying instruments and some calculators label the mode gon or grad.

QHow many degrees are in a full turn?

One turn is 360 degrees, 400 gradians or about 6.283185 radians. The turn is handy for rotation counts and for phase, where half a turn is 180 degrees and a quarter turn is the familiar right angle.

QWhy does 1 degree convert to 59.9988 arcminutes rather than 60?

A degree does contain exactly 60 arcminutes and 3600 arcseconds, but the arcminute is stored as 0.016667 degrees, a rounded sixth decimal. The returned 59.9988 is that rounding showing through, so round arcminute and arcsecond results to whole numbers where precision matters.

ℹ️ About Angle Conversion

An angle is a ratio of arc length to radius, so its units are pure convention. The 360-degree circle descends from Babylonian base-60 astronomy. The radian comes out of the geometry itself, which is why one full turn is 2 pi radians and degree-to-radian results never land on round numbers. The gradian, which divides a right angle into 100 parts, is a metric reform that survives in European surveying. Arcminutes and arcseconds split the degree by 60 and 3600 for astronomy and navigation, while milliradians are used in optics and marksmanship.

Seven units are supported, with the degree as the base: values are multiplied by the source unit's degree factor and divided by the target's. Rounding tightens as numbers shrink, from four decimal places at ten and above to eight below one. Conversion runs in the browser the moment you change a field.

📏 7 Supported Units

Degree (°), Radian (rad), Gradian (gon), Arcminute ('), Arcsecond ("), Turn (tr), Milliradian (mrad).