gradians (grad) | radians (rad) |
---|---|
0 | 0 |
1 | 0.01570796326795 |
2 | 0.0314159265359 |
3 | 0.04712388980385 |
4 | 0.0628318530718 |
5 | 0.07853981633974 |
6 | 0.09424777960769 |
7 | 0.1099557428756 |
8 | 0.1256637061436 |
9 | 0.1413716694115 |
10 | 0.1570796326795 |
20 | 0.314159265359 |
30 | 0.4712388980385 |
40 | 0.628318530718 |
50 | 0.7853981633974 |
60 | 0.9424777960769 |
70 | 1.0995574287564 |
80 | 1.2566370614359 |
90 | 1.4137166941154 |
100 | 1.5707963267949 |
1000 | 15.707963267949 |
Here's a breakdown of how to convert between gradians and radians, focusing on clarity, conciseness, and SEO best practices.
Gradians (also called "grades" or "gons") and radians are both units used to measure angles. A gradian is defined as of a circle, while a radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. These units are part of the broader topic of angular measurement, crucial in fields like navigation, engineering, and physics.
To convert gradians to radians, you can use the following formula:
So, to convert 1 gradian to radians:
To convert radians to gradians, use the reciprocal of the above conversion factor:
Therefore, to convert 1 radian to gradians:
The French Revolution: The gradian (or grade) was introduced during the French Revolution as part of the metric system, with the aim of simplifying calculations. The idea was to divide a right angle into 100 grades, making calculations more decimal-friendly.
Radian's Natural Significance: Radians are preferred in many mathematical and scientific contexts because they are directly linked to the circle's radius and circumference, simplifying many formulas in calculus, physics, and engineering.
While gradians aren't as widely used as degrees or radians, here are some examples where you might encounter conversions:
Example Scenario:
An engineer is using a surveying tool that gives an angle of 50 gradians. To perform calculations in a system that uses radians, they need to convert:
See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the radians to other unit conversions.
Gradians, also known as gons, are a unit of angular measurement primarily used in surveying, civil engineering, and some European countries. This section explores the definition, formation, and applications of gradians.
A gradian is defined as of a full circle. This means there are 400 gradians in a complete rotation. It's an alternative to degrees (360 in a full circle) and radians ( in a full circle). The symbol for gradian is "gon" or "grad".
The gradian system was introduced in France around the time of the French Revolution as part of the metric system, aiming for a decimal-based approach to angle measurement.
The appeal of gradians lies in their decimal-friendly nature. A right angle is exactly 100 gradians, which can simplify calculations in certain contexts.
While the gradian system was intended to integrate seamlessly with the metric system, it didn't achieve widespread adoption globally. While no single individual is directly credited with "discovering" or "inventing" the gradian in the same way someone might discover a physical law, its creation is associated with the general movement towards decimalization that occurred during the French Revolution. The French committee that developed the metric system advocated for its use.
Gradians to Degrees:
Degrees to Gradians:
Gradians to Radians:
Radians to Gradians:
Radians are a fundamental unit for measuring angles, particularly useful in mathematics and physics. They provide a natural way to relate angles to the radius of a circle and are essential for various calculations involving circular motion, trigonometry, and calculus.
A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. In simpler terms, imagine taking the radius of a circle and bending it along the circumference. The angle formed at the center of the circle by this arc is one radian.
To visualize how radians are formed:
Since the circumference of a circle is , there are radians in a full circle (). Therefore:
Degrees to Radians: To convert an angle from degrees to radians, multiply the angle in degrees by :
Radians to Degrees: To convert an angle from radians to degrees, multiply the angle in radians by :
One of the most important applications of radians is in calculating arc length. The arc length of a circle is given by:
Where:
Circular Motion: In physics, radians are used to describe angular velocity () and angular acceleration () in circular motion. For instance, angular velocity is often measured in radians per second (rad/s).
Navigation: Radians are used in navigation systems, particularly in calculations involving latitude and longitude on the Earth's surface.
Signal Processing: Radians are used in Fourier analysis and signal processing to represent frequencies and phases of signals.
Computer Graphics: Radians are used extensively in computer graphics to specify rotations and angles for objects and transformations.
Pendulums: In the analysis of simple harmonic motion, such as a pendulum's swing, the angle of displacement is often expressed in radians for simpler mathematical treatment. For small angles, when is in radians.
Convert 1 grad to other units | Result |
---|---|
gradians to radians (grad to rad) | 0.01570796326795 |
gradians to degrees (grad to deg) | 0.9 |
gradians to arcminutes (grad to arcmin) | 54 |
gradians to arcseconds (grad to arcsec) | 3240 |