Tool to convert angles unit. Geometric angles can be described using different units (degrees, radian, degrees minutes and seconds, etc.)
Convert Angle Units - dCode
Tag(s) : Geometry
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Convert Angle Units
Convert angular units
Answers to Questions (FAQ)
What is an angle unit? (Definition)
The measure of an angle (or an angular sector) is a number (real and positive number) that can be displayed in several units: generally the radian or the degree.
A full turn is $ 2 \pi $ radians or $ 360 $ degrees.
How to convert degrees to radian?
Conversion of degrees to radians uses the angular formula:
$$ \mbox{ Rad} = \mbox{ Deg} \times \pi / 180 $$
To remember it, keep in mind that the Radians measure a circle over $ 2 \pi $ while the degrees measure a circle over $ 360 ° $. The relationship between the two angles is $ \frac{2\pi}{360}=\frac{\pi}{180} $.
Example: $$ 90° \times \pi / 180 = \frac{\pi}{2} \mbox{ Rad} $$
How to convert degrees to gradians?
Conversion of degrees to gradians uses the formula:
$$ Grad = Deg / 360 \times 400 $$
Example: $$ 90° / 360 \times 400 = 100 \mbox{ Grad} $$
How to convert degrees to arc seconds?
Converting from degrees to arc seconds:
$$ Deg = D + M/60 + S/3600 $$
Example: 1′ (arcminute) = 1°/60 = 0.0166°
Example: 1″ (arcsecond) = 1°/3600 = 0.000277°
How to convert radian to degrees?
Conversion of radians to degrees uses the formula:
$$ Deg = Rad \times 180 / \pi $$
Example: $$ \frac{\pi}{2} \times \frac{180}{\pi} = 90° $$
How to convert gradians to degrees?
Conversion of gradians to degrees uses the formula:
$$ Deg = Grad / 400 \times 360 $$
What are the relationships between degrees, minutes and seconds of arc?
The relationships between these angle subunits are as follows:
— 1 degree = 60 arc minutes
— 1 arc minute = 60 arc seconds
— 1 degree = 3600 arc seconds
Source code
dCode retains ownership of the "Convert Angle Units" source code. Any algorithm for the "Convert Angle Units" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "Convert Angle Units" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) or any database download or API access for "Convert Angle Units" or any other element are not public (except explicit open source licence). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Convert Angle Units" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source (Creative Commons CC-BY free distribution license).
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Convert Angle Units on dCode.fr [online website], retrieved on 2025-07-08,
- Convert angular units
- What is an angle unit? (Definition)
- How to convert degrees to radian?
- How to convert degrees to gradians?
- How to convert degrees to arc seconds?
- How to convert radian to degrees?
- How to convert gradians to degrees?
- What are the relationships between degrees, minutes and seconds of arc?
