degrees to gradians conversion

How to convert degrees to gradians?

To convert degrees to gradians, you can use the conversion factor between these units. There are 400 gradians in a full circle (which is 360 degrees). Therefore, 1 degree is equivalent to:

$1 \text{ degree} \times \left( \frac{400 \text{ gradians}}{360 \text{ degrees}} \right) = \frac{400}{360} \text{ gradians}$ $1 \text{ degree} = \frac{10}{9} \text{ gradians}$ $1 \text{ degree} \approx 1.1111 \text{ gradians}$

Now let’s go through some real-world examples for converting other quantities of degrees to gradians:

Example 1: 90 degrees

90 degrees corresponds to a right angle, which is one-quarter of the full circle. $90 \text{ degrees} \times \left( \frac{400 \text{ gradians}}{360 \text{ degrees}} \right) = 100 \text{ gradians}$

Example 2: 45 degrees

45 degrees is half of a right angle. $45 \text{ degrees} \times \left( \frac{400 \text{ gradians}}{360 \text{ degrees}} \right) = 50 \text{ gradians}$

Example 3: 180 degrees

180 degrees is a straight angle, or half a full circle. $180 \text{ degrees} \times \left( \frac{400 \text{ gradians}}{360 \text{ degrees}} \right) = 200 \text{ gradians}$

Example 4: 360 degrees

360 degrees makes a full circle. $360 \text{ degrees} \times \left( \frac{400 \text{ gradians}}{360 \text{ degrees}} \right) = 400 \text{ gradians}$

By understanding these conversions, you're able to convert any number of degrees into gradians using simple multiplication. This can be useful in various fields such as surveying, civil engineering, and navigation where the gradian system is sometimes preferred for its decimal-friendly format.