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To convert from gradian (grad) to radian (rad), use the following formula:
To convert from gradian (grad) to degree (deg), use the following formula:
To convert from gradian (grad) to arcminute (arcmin), use the following formula:
To convert from gradian (grad) to arcsecond (arcsec), use the following formula:
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.