Tools4Day
Converters

Angle Converter

Convert angles accurately between degrees, radians, gradians (gon), revolutions, arcminutes and arcseconds. Example: 180 degrees equals π radians.

Example: an angle of 180 degrees. How many radians is that?
Result 3.141593 rad 180° = 3.141593 rad Display rounded to 6 decimal places when needed.
One-unit equivalent 1° = 0.017453 rad The converter preserves the angle you enter and does not force it into the 0–360° range.

✓ Conversion relationships match the SI definitions (BIPM) and NIST angle conversion tables

How is the conversion calculated? The converter uses the degree as the internal reference for rational angle units. The key radian relation is 1° = π/180 rad; one arcminute is 1/60 of a degree, one arcsecond is 1/3600 of a degree, and one revolution is 360°.

This calculation runs in your browser. Your values are not sent to our server.

How it works

  1. Enter the angle value, then choose the current unit and the unit you want to convert to.
  2. Example: 180 degrees equals π radians, displayed as 3.141593 radians at six decimal places.
  3. Use the swap button to reverse the units without re-entering the value.
  4. The exact SI relationship is 1° = π/180 rad. Arcminutes and arcseconds are exact fractions of a degree.
  5. Signed and multi-turn angles are supported. The converter does not automatically normalize values into the 0–360° range.

FAQ

How many radians are in 180 degrees?

180 degrees equals exactly π radians, approximately 3.141592653589793 radians.

How many degrees are in 1 radian?

1 radian equals 180/π degrees, approximately 57.29577951308232 degrees.

How many arcminutes are in 1 degree?

1 degree equals exactly 60 arcminutes.

How many arcseconds are in 1 degree?

1 degree equals exactly 3,600 arcseconds.

What is a gon or gradian?

A gon, also called a gradian, is an angle unit where 400 gon make a full revolution. Therefore 1 gon equals exactly 0.9 degree.

Does the converter force angles into 0–360 degrees?

No. Negative angles and angles larger than one full revolution are preserved and converted as entered.

You may also find one of these tools useful.

Area Converter Convert square meters, square feet, hectares, acres and other area units. Kitchen Measurement Converter Convert U.S. cups, spoons and fluid ounces to milliliters and liters and back. Length Converter Convert meters, kilometers, inches, feet, miles and other length units. Weight & Mass Converter Convert kilograms, pounds, ounces, tonnes and other common mass units.