Follow these steps to convert given angle from the units of Turns to the units of π Radians.
Enter the input Turns value in the text field.
The calculator converts the given Turns into π Radians in realtime ⌚ using the conversion formula, and displays under the π Radians label. You do not need to click any button. If the input changes, π Radians value is re-calculated, just like that.
You may copy the resulting π 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 π Radians?
The formula to convert given angle from Turns to π Radians is:
Angle(π Radians) = Angle(Turns) × 2
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 π radians, i.e., Angle(π 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 π Radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 0.25
Formula:
The formula to convert angle from turns to π radians is:
Angle(π Radians) = Angle(Turns) × 2
Substitution:
Substitute given weight Angle(Turns) = 0.25 in the above formula.
Angle(π Radians) = 0.25 × 2
Angle(π Radians) = 0.5
Final Answer:
Therefore, 0.25 turn is equal to 0.5 π radians.
The angle is 0.5 π radians, in π radians.
2
Consider that a wind turbine completes 2 turns in a light breeze. Convert this rotation from turns to π Radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 2
Formula:
The formula to convert angle from turns to π radians is:
Angle(π Radians) = Angle(Turns) × 2
Substitution:
Substitute given weight Angle(Turns) = 2 in the above formula.
Angle(π Radians) = 2 × 2
Angle(π Radians) = 4
Final Answer:
Therefore, 2 turn is equal to 4 π radians.
The angle is 4 π radians, in π radians.
Turns to π Radians Conversion Table
The following table gives some of the most used conversions from Turns to π Radians.
Turns (turn)
π Radians (π radians)
0 turn
0 π radians
1 turn
2 π radians
10 turn
20 π radians
45 turn
90 π radians
90 turn
180 π radians
180 turn
360 π radians
360 turn
720 π radians
1000 turn
2000 π radians
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.
π Radians
π radians represent a half-circle or 180 degrees. This unit is fundamental in mathematics, particularly in trigonometry and calculus, where the relationship between angles and the properties of circles is central to many concepts. The use of π radians simplifies the representation of angles and the formulation of trigonometric functions.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Turns to π Radians in Angle?
The formula to convert Turns to π Radians in Angle is:
Turns * 2
2. Is this tool free or paid?
This Angle conversion tool, which converts Turns to π Radians, is completely free to use.
3. How do I convert Angle from Turns to π Radians?
To convert Angle from Turns to π Radians, you can use the following formula:
Turns * 2
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 π 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 π 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 π radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(π Radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2</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>(π Radians)</sub></span> = <span>0.25</span> × 2</p>\n <p class=\"step\"><span>Angle<sub>(π Radians)</sub></span> = 0.5</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.25 turn</strong> is equal to <strong>0.5 π radians</strong>.</p>\n <p>The angle is <strong>0.5 π radians</strong>, in π 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 π 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 π radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(π Radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2</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>(π Radians)</sub></span> = <span>2</span> × 2</p>\n <p class=\"step\"><span>Angle<sub>(π Radians)</sub></span> = 4</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>2 turn</strong> is equal to <strong>4 π radians</strong>.</p>\n <p>The angle is <strong>4 π radians</strong>, in π radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Turns</span> to <span class=\"y\">π Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Turns to π Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Turns (<span class=\"unit\">turn</span>)</th><th scope=\"column\" role=\"columnheader\">π Radians (<span class=\"unit\">π radians</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">turn</span></td><td>0 <span class=\"unit\">π radians</span></td></tr><tr><td>1 <span class=\"unit\">turn</span></td><td>2 <span class=\"unit\">π radians</span></td></tr><tr><td>10 <span class=\"unit\">turn</span></td><td>20 <span class=\"unit\">π radians</span></td></tr><tr><td>45 <span class=\"unit\">turn</span></td><td>90 <span class=\"unit\">π radians</span></td></tr><tr><td>90 <span class=\"unit\">turn</span></td><td>180 <span class=\"unit\">π radians</span></td></tr><tr><td>180 <span class=\"unit\">turn</span></td><td>360 <span class=\"unit\">π radians</span></td></tr><tr><td>360 <span class=\"unit\">turn</span></td><td>720 <span class=\"unit\">π radians</span></td></tr><tr><td>1000 <span class=\"unit\">turn</span></td><td>2000 <span class=\"unit\">π radians</span></td></tr></table>",
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