Converting from Radians to Gradians
Multiply by 63.662, or to be precise by 200/π. A full turn is 2π radians and 400 gradians, so π radians is 200 gradians, and that ratio is the whole conversion.
1.5 radians comes to 95.49 gradians. Because π is involved there's no tidy shortcut – multiplying by 64 gives 96 gradians, about half a percent high, fine for a sketch and wrong for a survey.
Gradians (also called gons) put a right angle at exactly 100, which is why surveyors in parts of Europe still use them and almost nobody else does.
About Radians
Radians are a unit of measurement used in mathematics and physics to quantify angles. Unlike degrees, which divide a circle into 360 equal parts, radians divide a circle into 2π (approximately 6.28) equal parts. This unit is particularly useful in trigonometry and calculus, as it simplifies many mathematical calculations involving angles.
The concept of radians is based on the relationship between the length of an arc and the radius of a circle. One radian is defined as the angle subtended by an arc that is equal in length to the radius of the circle. In other words, if we were to take a circle with a radius of 1 unit and measure an arc along its circumference that is also 1 unit long, the angle formed at the center of the circle would be 1 radian.
Radians are advantageous because they allow for more straightforward calculations involving angles in trigonometric functions and calculus. Many mathematical formulas and equations involving angles become simpler when expressed in radians. Additionally, radians are dimensionless, meaning they do not have any units associated with them. This property makes it easier to perform calculations and conversions involving angles in various systems of measurement.
About Gradians
Gradians, also known as gons or grads, divide a circle into 400 equal parts. This means that a right angle is equal to 100 gradians, a full circle is 400 gradians, and so on. Gradians were introduced as an alternative to degrees and radians, aiming to provide a more convenient and decimal-based system for measuring angles.
While gradians are not as commonly used as degrees or radians, they do have their applications. For example, they are often used in surveying and navigation, where angles need to be measured and calculated with high precision. Additionally, gradians can be easily converted to degrees or radians, making them a versatile unit of measurement.
While radians are the standard unit for measuring angles in mathematics and physics, gradians offer an alternative system that can be useful in specific fields. Whether it's for precise measurements in surveying or for converting between different angle units, gradians provide a decimal-based approach to quantifying angles.