Follow these steps to convert given angle from the units of Turns to the units of Radians.
Enter the input Turns value in the text field.
The calculator converts the given Turns into Radians in realtime ⌚ using the conversion formula, and displays under the Radians label. You do not need to click any button. If the input changes, Radians value is re-calculated, just like that.
You may copy the resulting 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 Radians?
The formula to convert given angle from Turns to Radians is:
Angle(Radians) = Angle(Turns) × 2 × 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 radians, i.e., Angle(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 Radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 0.25
Formula:
The formula to convert angle from turns to radians is:
Angle(Radians) = Angle(Turns) × 2 × π
Substitution:
Substitute given weight Angle(Turns) = 0.25 in the above formula.
Angle(Radians) = 0.25 × 2 × 3.14159265359
Angle(Radians) = 1.5708
Final Answer:
Therefore, 0.25 turn is equal to 1.5708 rad.
The angle is 1.5708 rad, in radians.
2
Consider that a wind turbine completes 2 turns in a light breeze. Convert this rotation from turns to Radians.
Answer:
Given:
The angle in turns is:
Angle(Turns) = 2
Formula:
The formula to convert angle from turns to radians is:
Angle(Radians) = Angle(Turns) × 2 × π
Substitution:
Substitute given weight Angle(Turns) = 2 in the above formula.
Angle(Radians) = 2 × 2 × 3.14159265359
Angle(Radians) = 12.5664
Final Answer:
Therefore, 2 turn is equal to 12.5664 rad.
The angle is 12.5664 rad, in radians.
Turns to Radians Conversion Table
The following table gives some of the most used conversions from Turns to Radians.
Turns (turn)
Radians (rad)
0 turn
0 rad
1 turn
6.2832rad
10 turn
62.8319rad
45 turn
282.7433rad
90 turn
565.4867rad
180 turn
1130.9734rad
360 turn
2261.9467rad
1000 turn
6283.1853rad
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.
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.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Turns to Radians in Angle?
The formula to convert Turns to Radians in Angle is:
Turns * 2 * π
2. Is this tool free or paid?
This Angle conversion tool, which converts Turns to Radians, is completely free to use.
3. How do I convert Angle from Turns to Radians?
To convert Angle from Turns to Radians, you can use the following formula:
Turns * 2 * 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 Radians.
{
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"y_slug": "radians",
"x": "turn",
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"y_desc": "Radians",
"category": "Angle",
"symbol": "m",
"formula": "x * 2 * π",
"precision": 11,
"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 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 radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2 × 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>(Radians)</sub></span> = <span>0.25</span> × 2 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 1.5708</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.25 turn</strong> is equal to <strong>1.5708 rad</strong>.</p>\n <p>The angle is <strong>1.5708 rad</strong>, in 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 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 radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Turns)</sub></span> × 2 × 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>(Radians)</sub></span> = <span>2</span> × 2 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 12.5664</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>2 turn</strong> is equal to <strong>12.5664 rad</strong>.</p>\n <p>The angle is <strong>12.5664 rad</strong>, in radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Turns</span> to <span class=\"y\">Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Turns to Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Turns (<span class=\"unit\">turn</span>)</th><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">turn</span></td><td>0 <span class=\"unit\">rad</span></td></tr><tr><td>1 <span class=\"unit\">turn</span></td><td>6<span>.2832</span> <span class=\"unit\">rad</span></td></tr><tr><td>10 <span class=\"unit\">turn</span></td><td>62<span>.8319</span> <span class=\"unit\">rad</span></td></tr><tr><td>45 <span class=\"unit\">turn</span></td><td>282<span>.7433</span> <span class=\"unit\">rad</span></td></tr><tr><td>90 <span class=\"unit\">turn</span></td><td>565<span>.4867</span> <span class=\"unit\">rad</span></td></tr><tr><td>180 <span class=\"unit\">turn</span></td><td>1130<span>.9734</span> <span class=\"unit\">rad</span></td></tr><tr><td>360 <span class=\"unit\">turn</span></td><td>2261<span>.9467</span> <span class=\"unit\">rad</span></td></tr><tr><td>1000 <span class=\"unit\">turn</span></td><td>6283<span>.1853</span> <span class=\"unit\">rad</span></td></tr></table>",
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"y_long_desc": "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.",
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