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

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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.

Conversion of degrees to radians uses the angular formula:

$$ \mbox{ Rad} = \mbox{ Deg} * \pi / 180 $$

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:__ $$ 90° \times \pi / 180 = \frac{\pi}{2} \mbox{ Rad} $$

Conversion of degrees to gradians uses the formula:

$$ Grad = Deg / 360 * 400 $$

__Example:__ $$ 90° / 360 \times 400 = 100 \mbox{ Grad} $$

Conversion of degrees to arc seconds (used for GPS geolocalization):

__Example:__ 1′ (arcminute) = 1°/60 = 0.0166°

__Example:__ 1″ (arcsecond) = 1°/3600 = 0.000277°

Conversion of radians to degrees uses the formula:

$$ Deg = Rad \times 180 / \pi $$

__Example:__ $$ \frac{\pi}{2} \times \frac{180}{\pi} = 90° $$

Conversion of gradians to degrees uses the formula:

$$ Deg = Grad / 400 * 360 $$

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