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To convert from gradian (grad) to degree (deg), use the following formula:
Let's convert 5 gradian (grad) to degree (deg).
Using the formula:
Therefore, 5 gradian (grad) is equal to degree (deg).
Here are some quick reference conversions from gradian (grad) to degree (deg):
| gradians | degrees |
|---|---|
| 0.000001 grad | deg |
| 0.001 grad | deg |
| 0.1 grad | deg |
| 1 grad | deg |
| 2 grad | deg |
| 3 grad | deg |
| 4 grad | deg |
| 5 grad | deg |
| 6 grad | deg |
| 7 grad | deg |
| 8 grad | deg |
| 9 grad | deg |
| 10 grad | deg |
| 20 grad | deg |
| 30 grad | deg |
| 40 grad | deg |
| 50 grad | deg |
| 100 grad | deg |
| 1000 grad | deg |
| 10000 grad | deg |
While most of us learn about measuring angles in degrees, there's another unit of angle measurement called the gradian.
A gradian (often abbreviated as grad) is a unit of angle equal to 0.9 (or 9/10) of a degree. It's an alternative to degrees and radians, designed to make some calculations simpler.
Unlike the familiar 360-degree system, a full circle is divided into 400 gradians.
This base-100 system simplifies many geometric calculations:
This makes it an intuitive framework for certain types of angular math.
The conversion between gradians and degrees is straightforward.
Here is the simple gradians to degrees formula:
For example, to convert 200 gradians to degrees, you would calculate: .
When comparing radians vs. gradians, the relationship is key for trigonometry and higher math.
A full circle is 400 gradians or 2π radians.
This means that 200 gradians are equal to π radians. The conversion factor, π/200, is fundamental for calculations that bridge these two systems.
So, why use this system at all?
Gradians are primarily used in specific professional fields like surveying and some branches of engineering, especially in Europe.
The decimal-based nature of the 400-gradian circle simplifies calculations involving right angles, making fieldwork and topographical analysis more efficient.
In geometry and everyday life, we measure angles using degrees.
A degree (represented by the universal symbol °) is the basic unit for measuring rotation. It helps us describe the amount of turn between two lines that meet at a point.
For instance, a perfect corner, like the edge of a book, is a 90° right angle, and one complete, full-circle rotation measures 360°.
The standard of a circle containing 360 degrees (360°) originated with the ancient Babylonians.
They used a base-60 (sexagesimal) number system, and 360 was a perfect number for them because it is highly divisible. Its large number of factors made it incredibly easy to perform fractional calculations in fields like astronomy and geometry.
For fields that require extreme precision, like astronomy, cartography (map-making), and GPS navigation, a single degree is broken down into even smaller units:
This system ensures that even the tiniest angles can be measured with high accuracy.