A Plane angle conversion calculator is a tool that helps you convert angles from one unit of measure to another. Some common units of Plane angle include degrees, radians, gradians, and revolutions.
Here's some information about these units:
To use a Plane angle conversion calculator, simply input the angle in the unit of measure that you have and select the desired unit of measure for the output. The calculator will then convert the angle for you. There are many online Plane angle conversion calculators available for free, which can be easily found through a search engine.
Here are the general steps for using a Plane angle conversion calculator:
Overall, using a Plane angle conversion calculator is a straightforward process. Just make sure to select the correct units of measure and double-check your input values before performing the conversion.
Here are the formulas for converting between different units of Plane angle:
Note that π (pi) is a mathematical constant approximately equal to 3.14159.
These formulas can be used to convert between different units of Plane angle manually. However, it is much more convenient to use an online Plane angle conversion calculator, as it will perform the conversion automatically and accurately.
Here is a table that shows the conversion factors for common units of Plane angle:
| Input Unit | Output Unit | Conversion Factor |
|---|---|---|
| Degrees | Radians | π / 180 |
| Radians | Degrees | 180 / π |
| Degrees | Gradians | 10 / 9 |
| Gradians | Degrees | 9 / 10 |
| Radians | Gradians | 200 / π |
| Gradians | Radians | π / 200 |
To use this table, simply find the conversion factor for the input and output units of measure that you want to convert between, and multiply the input angle by that factor to get the output angle. For example, to convert 45 degrees to radians, you would multiply 45 by π/180 to get 0.7854 radians. Alternatively, you can use an online Plane angle conversion calculator to perform the conversion automatically.
This table contains conversions between almost all Plane angle units.
| Name of unit | Symbol | Definition | Relation to SI units |
|---|---|---|---|
| Angular mil | µ | ≡ 2π⁄ 6400rad | ≈ 0.981 748×10 −3 rad |
| Arcminute; MOA | ' | ≡ 1°⁄ 60 | ≈ 0.290 888×10 −3 rad |
| Arcsecond | " | ≡ 1°⁄ 3600 | ≈ 4.848 137×10 −6 rad |
| Centesimal minute of arc | ' | ≡ 1⁄ 100grad | ≈ 0.157 080×10 −3 rad |
| Centesimal second of arc | " | ≡ 1⁄ 10 000grad | ≈ 1.570 796×10 −6 rad |
| Degree (of arc) | ° | ≡ 1⁄ 360of a revolution ≡ π⁄ 180rad | ≈ 17.453 293×10 −3 rad |
| Grad; gradian; gon | grad | ≡ 1⁄ 400of a revolution ≡ π⁄ 200rad ≡ 0.9° | ≈ 15.707 963×10 −3 rad |
| Octant | ≡ 45° | ≈ 0.785 398 rad | |
| Quadrant | ≡ 90° | ≈ 1.570 796 rad | |
| Radian(SI unit) | rad | The angle is subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians. | = 1 rad |
| Sextant | ≡ 60° | ≈ 1.047 198 rad | |
| Sign | ≡ 30° | ≈ 0.523 599 rad |
There are several benefits of using a Plane angle conversion calculator:
Summary
Overall, using a Plane angle conversion calculator is a simple and effective way to perform accurate and efficient angle conversions in various fields such as mathematics, physics, engineering, and more. Check more unit conversion calculators like this to solve your daily problems on Drlogy Calculator to get exact solution.
Reference
The formula for plane angle is:
θ = s / r
Where:
θ is the angle in radians. s is the arc length of the sector. r is the radius of the circle.
Alternatively, we can use the formula:
θ = L / (2πr)
Where:
To convert an angle to a length, you need to know the radius of the circle and the measure of the angle in radians.
Length of arc = radius × angle in radians
60 degrees × (π/180) = 1.047 radians
Length of arc = 5 × 1.047 = 5.236 units
So the length of the arc is approximately 5.236 units.
Angle in degrees = Angle in radians × (180/π)
Determine whether the given number is in radians or some other unit of measure.
If the given number is in radians, multiply it by (180/π) to convert it to degrees.
Angle in degrees = 2.5 radians × (180/π) = 143.24 degrees
Therefore, an angle of 2.5 radians is equivalent to 143.24 degrees.
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