Angle Unit Converter
Convert degrees, radians, gradians, turns, arcminutes, and arcseconds from the same angle value. Choose the source and target units to update the result window and summary cards instantly.
Input
Result
ready to use.
- Visible firstKeep the input and result positions clear.
- Results firstPut the main number up front and keep details secondary.
- Less to askNo sign-up or extra information before using the tool.
Read degrees and radians as the same angle
This converter rewrites one angle between common angle units: degree, radian, gradian, turn, arcminute, and arcsecond. Degrees are familiar in everyday geometry, while radians are the usual input for trigonometry, physics, engineering, and programming.
Use the left window for the value and unit shown in your source. The result window shows the selected target unit, and the summary cards keep degree, radian, gon, and turn visible together. The page is meant for angle magnitude conversion; if a sign or rotation direction matters, keep that context with the copied value.
Use it in screen order
- Enter the angle value first, such as 180 for a half-turn.
- Pick the source unit exactly as it appears in your note or formula.
- Choose the target unit you need. Switch units reverses the source and target direction.
- Use the summary cards to check the same angle in degree, radian, gon, and turn before copying.
Units and basis
- A degree divides one full turn into 360 parts.
- A radian is based on arc length divided by radius. 180° equals π rad and 360° equals 2π rad.
- A gradian, or gon, divides a full turn into 400 parts. 1 gon equals 0.9°.
- An arcminute is 1/60° and an arcsecond is 1/3600°, often used for maps, astronomy, and precision measurement.
Example conversions
The readable unit depends on context. Formulas often need radians even when source material is written in degrees.
Rounding and cautions
- Many programming math functions expect radians. Passing degrees directly can produce a wrong result.
- This page treats the input as a non-negative angle magnitude. Keep a separate sign or clockwise/counterclockwise note when direction matters.
- Radian output is a decimal approximation of values involving π. Keep the exact symbolic form when precision matters.
- Do not confuse arcmin and arcsec in coordinates or observation notes; they differ by a factor of 60.
FAQ
How many radians are in 180 degrees?
180° equals π rad, or about 3.141593 rad. A full 360° turn equals 2π rad.
When should I use radians?
Radians are commonly used in trigonometry, calculus, physics, engineering, and programming language math functions.
How do I convert degrees and gradians?
1 gon equals 0.9°. Convert degrees to gon with degree ÷ 0.9, and gon to degrees with gon × 0.9.
What are arcminutes and arcseconds?
1 arcminute is 1/60° and 1 arcsecond is 1/3600°. They are used for small angles in mapping, astronomy, and surveying.
Can I convert negative angles?
This page is set up for non-negative angle magnitudes. Convert the magnitude, then keep the original sign or direction note with the result.
References used
The angle factors follow the Angle section in NIST SP 811 Appendix B.9, which lists degree and gon conversion factors to radians.