Follow these steps to convert given angle from the units of Radians to the units of Turns.
Enter the input Radians value in the text field.
The calculator converts the given Radians into Turns in realtime ⌚ using the conversion formula, and displays under the Turns label. You do not need to click any button. If the input changes, Turns value is re-calculated, just like that.
You may copy the resulting Turns 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 Radians to Turns?
The formula to convert given angle from Radians to Turns is:
Angle(Turns) = Angle(Radians) / (2 × π)
Substitute the given value of angle in radians, i.e., Angle(Radians) in the above formula and simplify the right-hand side value. The resulting value is the angle in turns, i.e., Angle(Turns).
Calculation
Calculation will be done after you enter a valid input.
Examples
1
Consider that a robotic arm rotates by 1.5 radians to position an object accurately. Convert this angle from radians to Turns.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 1.5
Formula:
The formula to convert angle from radians to turns is:
Angle(Turns) = Angle(Radians) / (2 × π)
Substitution:
Substitute given weight Angle(Radians) = 1.5 in the above formula.
Angle(Turns) = 1.5 / (2 × 3.14159265359)
Angle(Turns) = 0.2387
Final Answer:
Therefore, 1.5 rad is equal to 0.2387 turn.
The angle is 0.2387 turn, in turns.
2
Consider that a satellite dish adjusts by 0.75 radians to align with a signal. Convert this angle from radians to Turns.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 0.75
Formula:
The formula to convert angle from radians to turns is:
Angle(Turns) = Angle(Radians) / (2 × π)
Substitution:
Substitute given weight Angle(Radians) = 0.75 in the above formula.
Angle(Turns) = 0.75 / (2 × 3.14159265359)
Angle(Turns) = 0.1194
Final Answer:
Therefore, 0.75 rad is equal to 0.1194 turn.
The angle is 0.1194 turn, in turns.
Radians to Turns Conversion Table
The following table gives some of the most used conversions from Radians to Turns.
Radians (rad)
Turns (turn)
0 rad
0 turn
1 rad
0.1592turn
10 rad
1.5915turn
45 rad
7.162turn
90 rad
14.3239turn
180 rad
28.6479turn
360 rad
57.2958turn
1000 rad
159.1549turn
Radians
Radians are a fundamental unit of angular measurement in the International System of Units (SI). One radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. Radians are essential in mathematics and physics, particularly in calculus and trigonometry, where they simplify equations and allow for the natural expression of rotational and periodic phenomena.
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.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Radians to Turns in Angle?
The formula to convert Radians to Turns in Angle is:
Radians / (2 * π)
2. Is this tool free or paid?
This Angle conversion tool, which converts Radians to Turns, is completely free to use.
3. How do I convert Angle from Radians to Turns?
To convert Angle from Radians to Turns, you can use the following formula:
Radians / (2 * π)
For example, if you have a value in Radians, you substitute that value in place of Radians in the above formula, and solve the mathematical expression to get the equivalent value in Turns.
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"formula": "x / (2 * π)",
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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 robotic arm rotates by 1.5 radians to position an object accurately.<br>Convert this angle from radians to Turns.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in radians is:</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 1.5</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from radians to turns is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Turns)</sub></span> = <span>Angle<sub>(Radians)</sub></span> / (2 × π)</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Radians)</sub> = 1.5</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = <span>1.5</span> / (2 × 3.14159265359)</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = 0.2387</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>1.5 rad</strong> is equal to <strong>0.2387 turn</strong>.</p>\n <p>The angle is <strong>0.2387 turn</strong>, in turns.</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 satellite dish adjusts by 0.75 radians to align with a signal.<br>Convert this angle from radians to Turns.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in radians is:</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 0.75</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from radians to turns is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Turns)</sub></span> = <span>Angle<sub>(Radians)</sub></span> / (2 × π)</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Radians)</sub> = 0.75</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = <span>0.75</span> / (2 × 3.14159265359)</p>\n <p class=\"step\"><span>Angle<sub>(Turns)</sub></span> = 0.1194</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.75 rad</strong> is equal to <strong>0.1194 turn</strong>.</p>\n <p>The angle is <strong>0.1194 turn</strong>, in turns.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Radians</span> to <span class=\"y\">Turns</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Radians to Turns.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><th scope=\"column\" role=\"columnheader\">Turns (<span class=\"unit\">turn</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">rad</span></td><td>0 <span class=\"unit\">turn</span></td></tr><tr><td>1 <span class=\"unit\">rad</span></td><td>0<span>.1592</span> <span class=\"unit\">turn</span></td></tr><tr><td>10 <span class=\"unit\">rad</span></td><td>1<span>.5915</span> <span class=\"unit\">turn</span></td></tr><tr><td>45 <span class=\"unit\">rad</span></td><td>7<span>.162</span> <span class=\"unit\">turn</span></td></tr><tr><td>90 <span class=\"unit\">rad</span></td><td>14<span>.3239</span> <span class=\"unit\">turn</span></td></tr><tr><td>180 <span class=\"unit\">rad</span></td><td>28<span>.6479</span> <span class=\"unit\">turn</span></td></tr><tr><td>360 <span class=\"unit\">rad</span></td><td>57<span>.2958</span> <span class=\"unit\">turn</span></td></tr><tr><td>1000 <span class=\"unit\">rad</span></td><td>159<span>.1549</span> <span class=\"unit\">turn</span></td></tr></table>",
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