Plane Angle Conversion Calculator For Angle Units

Plane Angle Conversion Calculator

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Plane Angle Conversion Calculator

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:

Degrees (°): This is the most commonly used unit of Plane angle, where one full revolution is equal to 360 degrees.
Radians (rad): This is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is equal to approximately 57.3 degrees.
Gradians (gon or grad): This unit divides a circle into 400 equal parts, so one full revolution is equal to 400 gradians.
Revolutions (rev or rot): This unit measures the number of complete rotations made around a circle. One revolution is equal to 360 degrees or 2π radians.

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.

Steps For Plane Angle Conversion Calculator

Here are the general steps for using a Plane angle conversion calculator:

Determine the input unit of measure for the angle you want to convert. It could be degrees, radians, gradians, or revolutions.
Input the value of the angle in the input unit of measure. Make sure to use the correct decimal point and sign if needed.
Select the desired output unit of measure for the angle conversion. This will be the unit of measure that you want the angle to be converted to.
The calculator will then display the converted angle in the output unit of measure that you selected.
If needed, you can perform additional conversions by inputting another angle and selecting a different output unit of measure.
Some calculators may have additional features such as rounding, decimal places, or the ability to copy the result to the clipboard.

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.

Plane Angle Conversion Formulas

Here are the formulas for converting between different units of Plane angle:

Degrees to radians: radians = degrees × (π / 180)
Radians to degrees: degrees = radians × (180 / π)
Degrees to gradians: gradians = degrees × (10 / 9)
Gradians to degrees: degrees = gradians × (9 / 10)
Radians to gradians: gradians = radians × (200 / π)
Gradians to radians: radians = gradians × (π / 200)

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.

Plane Angle Conversion Chart

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.

Plane Angle Conversion Chart Table

Plane Angle Unit Conversion Table

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

Plane Angle Conversion Calculator Benefits

There are several benefits of using a Plane angle conversion calculator:

Accuracy: Plane angle conversion calculators perform conversions accurately, eliminating the possibility of human error in manual calculations.
Efficiency: Calculators perform conversions quickly, saving time and effort compared to manual calculations.
Convenience: Plane angle conversion calculators are easily accessible online, making them convenient to use from anywhere with an internet connection.
Versatility: Conversion calculators can handle multiple units of measure, allowing for easy conversions between different units of Plane angle.
Educational: By using a conversion calculator, users can better understand the relationships between different units of Plane angles and how they relate to each other.

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

Category: Units of plane angle [1].
Plane Angle - an overview [2].

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Plane Angle Conversion Calculator FAQ

What is the formula of plane angle?

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:

θ is the angle in radians
L is the length of the arc
r is the radius of the circle
π is the mathematical constant pi, approximately equal to 3.14159.

How do you convert angle to length?

To convert an angle to a length, you need to know the radius of the circle and the measure of the angle in radians.

Once you have these two values, you can use the formula:

Length of arc = radius × angle in radians

For example, if you have a circle with a radius of 5 units and an angle of 60 degrees, you would first convert the angle to radians:

60 degrees × (π/180) = 1.047 radians

Then, you can use the formula to find the length of the arc:

Length of arc = 5 × 1.047 = 5.236 units

So the length of the arc is approximately 5.236 units.

How do you convert numbers to angle degrees?

To convert a number to an angle in degrees, you need to know the relationship between degrees and radians. One full circle is 360 degrees or 2π radians. Therefore, we can use the following formula to convert from radians to degrees:

Angle in degrees = Angle in radians × (180/π)

So to convert a given number to an angle in degrees, follow these steps:

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.