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To convert from gradian (grad) to radian (rad), use the following formula:
Let's convert 5 gradian (grad) to radian (rad).
Using the formula:
Therefore, 5 gradian (grad) is equal to radian (rad).
Here are some quick reference conversions from gradian (grad) to radian (rad):
| gradians | radians |
|---|---|
| 0.000001 grad | rad |
| 0.001 grad | rad |
| 0.1 grad | rad |
| 1 grad | rad |
| 2 grad | rad |
| 3 grad | rad |
| 4 grad | rad |
| 5 grad | rad |
| 6 grad | rad |
| 7 grad | rad |
| 8 grad | rad |
| 9 grad | rad |
| 10 grad | rad |
| 20 grad | rad |
| 30 grad | rad |
| 40 grad | rad |
| 50 grad | rad |
| 100 grad | rad |
| 1000 grad | rad |
| 10000 grad | rad |
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.
A radian (rad) is the standard unit used to measure angles, and it's part of the International System of Units (SI).
One radian is equal to roughly 57.3 degrees (deg), or more precisely, 180/π degrees.
The radian is the official SI unit for angles, making it the preferred choice in science and engineering.
It is especially common in fields like physics, calculus, and computer graphics. The main advantages of using radians are:
A full circle has 360 degrees (360°), which is equal to 2π radians.
This key relationship gives us the precise formulas for converting between radians and degrees:
Degrees = Radians × (180/π)Radians = Degrees × (π/180)Here are some common angle conversions:
| Degrees | Radians (exact) | Radians (approx.) |
|---|---|---|
| 30° | π/6 rad | 0.524 rad |
| 45° | π/4 rad | 0.785 rad |
| 60° | π/3 rad | 1.047 rad |
| 90° | π/2 rad | 1.571 rad |
| 180° | π rad | 3.142 rad |
| 360° | 2π rad | 6.283 rad |
Geometrically, the definition of a radian is based on a circle's own properties.
Imagine an arc along the edge of a circle that has the same length as the circle's radius. The angle created at the center of the circle by this specific arc is exactly one radian.
Because a radian is a ratio of two lengths (arc length divided by radius), it is technically a dimensionless unit. This unique property is why it integrates so smoothly into advanced math and physics formulas.