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Convert Angle Units

Tool to convert angles unit. Geometric angles can be described using different units (degrees, radian, degrees minutes and seconds, etc.)

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Convert Angle Units -

Tag(s) : Geometry

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# Convert Angle Units

## Convert angular units

### 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:

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

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:

$$Grad = Deg / 360 * 400$$

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

### How to convert degrees to arc seconds

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

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:

$$Deg = Grad / 400 * 360$$

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