How to use this Turns to Milli-radians Converter 🤔
Follow these steps to convert given angle from the units of Turns to the units of Milli-radians.
Enter the input Turns value in the text field.
The calculator converts the given Turns into Milli-radians in realtime ⌚ using the conversion formula, and displays under the Milli-radians label. You do not need to click any button. If the input changes, Milli-radians value is re-calculated, just like that.
You may copy the resulting Milli-radians value using the Copy button.
To view a detailed step by step calculation of the conversion, click on the View Calculation button.
You can also reset the input by clicking on Reset button present below the input field.
What is the Formula to convert Turns to Milli-radians?
The formula to convert given angle from Turns to Milli-radians is:
Angle(Milli-radians) = Angle(Turns) × 2000 × π
Substitute the given value of angle in turns, i.e., Angle(Turns) in the above formula and simplify the right-hand side value. The resulting value is the angle in milli-radians, i.e., Angle(Milli-radians).
Calculation
Calculation will be done after you enter a valid input.
Examples
1
Consider that a turntable rotates by 0.25 turns to play a vinyl record. Convert this rotation from turns to Milli-radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 0.25
Formula:
The formula to convert angle from turns to milli-radians is:
Angle(Milli-radians) = Angle(Turns) × 2000 × π
Substitution:
Substitute given weight Angle(Turns) = 0.25 in the above formula.
Consider that a wind turbine completes 2 turns in a light breeze. Convert this rotation from turns to Milli-radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 2
Formula:
The formula to convert angle from turns to milli-radians is:
Angle(Milli-radians) = Angle(Turns) × 2000 × π
Substitution:
Substitute given weight Angle(Turns) = 2 in the above formula.
Angle(Milli-radians) = 2 × 2000 × 3.14159265359
Angle(Milli-radians) = 12566.3706
Final Answer:
Therefore, 2 turn is equal to 12566.3706 mrad.
The angle is 12566.3706 mrad, in milli-radians.
Turns to Milli-radians Conversion Table
The following table gives some of the most used conversions from Turns to Milli-radians.
Turns (turn)
Milli-radians (mrad)
0 turn
0 mrad
1 turn
6283.1853mrad
10 turn
62831.8531mrad
45 turn
282743.3388mrad
90 turn
565486.6776mrad
180 turn
1130973.3553mrad
360 turn
2261946.7106mrad
1000 turn
6283185.3072mrad
Turns
A turn, also known as a revolution or full circle, represents a complete rotation around a central point and is equal to 360 degrees or 2π radians. Turns are used in various disciplines, including engineering, navigation, and geometry, to describe full rotations. The concept of turns is deeply rooted in both mathematical theory and practical applications, such as in the design of gears and wheels.
Milli-radians
Milli-radians (mrad) are a unit of angular measurement equal to one-thousandth of a radian. This small unit is used in fields such as ballistics, gunnery, and optics, where precise angular measurements are critical. Milli-radians allow for the calculation of minute angular displacements, distances, and target adjustments.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Turns to Milli-radians in Angle?
The formula to convert Turns to Milli-radians in Angle is:
Turns * 2000 * π
2. Is this tool free or paid?
This Angle conversion tool, which converts Turns to Milli-radians, is completely free to use.
3. How do I convert Angle from Turns to Milli-radians?
To convert Angle from Turns to Milli-radians, you can use the following formula:
Turns * 2000 * π
For example, if you have a value in Turns, you substitute that value in place of Turns in the above formula, and solve the mathematical expression to get the equivalent value in Milli-radians.
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"examples": "<div class=\"example\">\n <div class=\"example_head\"><span class=\"example_n\">1</span>\n <h3 class=\"question\">Consider that a turntable rotates by 0.25 turns to play a vinyl record.<br>Convert this rotation from turns to Milli-radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in turns is:</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = 0.25</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from turns to milli-radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Milli-radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2000 × π</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Turns)</sub> = 0.25</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Milli-radians)</sub></span> = <span>0.25</span> × 2000 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Milli-radians)</sub></span> = 1570.7963</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.25 turn</strong> is equal to <strong>1570.7963 mrad</strong>.</p>\n <p>The angle is <strong>1570.7963 mrad</strong>, in milli-radians.</p>\n </div>\n <div class=\"example\">\n <div class=\"example_head\"><span class=\"example_n\">2</span>\n <h3 class=\"question\">Consider that a wind turbine completes 2 turns in a light breeze.<br>Convert this rotation from turns to Milli-radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in turns is:</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = 2</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from turns to milli-radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Milli-radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2000 × π</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Turns)</sub> = 2</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Milli-radians)</sub></span> = <span>2</span> × 2000 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Milli-radians)</sub></span> = 12566.3706</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>2 turn</strong> is equal to <strong>12566.3706 mrad</strong>.</p>\n <p>The angle is <strong>12566.3706 mrad</strong>, in milli-radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Turns</span> to <span class=\"y\">Milli-radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Turns to Milli-radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Turns (<span class=\"unit\">turn</span>)</th><th scope=\"column\" role=\"columnheader\">Milli-radians (<span class=\"unit\">mrad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">turn</span></td><td>0 <span class=\"unit\">mrad</span></td></tr><tr><td>1 <span class=\"unit\">turn</span></td><td>6283<span>.1853</span> <span class=\"unit\">mrad</span></td></tr><tr><td>10 <span class=\"unit\">turn</span></td><td>62831<span>.8531</span> <span class=\"unit\">mrad</span></td></tr><tr><td>45 <span class=\"unit\">turn</span></td><td>282743<span>.3388</span> <span class=\"unit\">mrad</span></td></tr><tr><td>90 <span class=\"unit\">turn</span></td><td>565486<span>.6776</span> <span class=\"unit\">mrad</span></td></tr><tr><td>180 <span class=\"unit\">turn</span></td><td>1130973<span>.3553</span> <span class=\"unit\">mrad</span></td></tr><tr><td>360 <span class=\"unit\">turn</span></td><td>2261946<span>.7106</span> <span class=\"unit\">mrad</span></td></tr><tr><td>1000 <span class=\"unit\">turn</span></td><td>6283185<span>.3072</span> <span class=\"unit\">mrad</span></td></tr></table>",
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