Convert Radians to Gradians
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Converting Radians to Gradians
Converting radians to gradians is relevant in specialized engineering and mathematical applications, particularly when working between theoretical calculations in radians and practical surveying measurements in gradians.
Mathematical Relationship
The mathematical relation between radians and gradians is: π radians = 200 gradians. To convert an angle in radians to gradians, multiply the radian value by 200/π.
Common Conversion Values
| Radians | Gradians |
|---|---|
| 0 | 0 |
| 0.7854 | 50 |
| 1.5708 | 100 |
| 3.1416 | 200 |
| 6.2832 | 400 |
Unit Definitions
Radians
The radian (symbol: rad) is the SI unit of angle measurement, defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. One full rotation equals 2π radians.
Gradians
The gradian (symbol: gon or grad) is a unit of angle measurement defined as 1/400 of a full rotation. It was introduced as part of the metric system, with 100 gradians in a right angle, making it convenient for decimal calculations.
Historical Context
The radian was first recognized as a unit of measurement in the mid-18th century and was adopted as the SI unit of angle measurement in 1960. The gradian was introduced during the French Revolution as part of the metric system's decimal approach to measurement.