Follow these steps to convert given angle from the units of Circles to the units of Radians.
Enter the input Circles value in the text field.
The calculator converts the given Circles 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 Circles to Radians?
The formula to convert given angle from Circles to Radians is:
Angle(Radians) = Angle(Circles) × 2 × π
Substitute the given value of angle in circles, i.e., Angle(Circles) 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 Ferris wheel rotates through 0.5 circles during one ride. Convert this rotation from circles to Radians.
Answer:
Given:
The angle in circles is:
Angle(Circles) = 0.5
Formula:
The formula to convert angle from circles to radians is:
Angle(Radians) = Angle(Circles) × 2 × π
Substitution:
Substitute given weight Angle(Circles) = 0.5 in the above formula.
Angle(Radians) = 0.5 × 2 × 3.14159265359
Angle(Radians) = 3.1416
Final Answer:
Therefore, 0.5 circle is equal to 3.1416 rad.
The angle is 3.1416 rad, in radians.
2
Consider that a drone completes 3 circles in the air during a maneuver. Convert this rotation from circles to Radians.
Answer:
Given:
The angle in circles is:
Angle(Circles) = 3
Formula:
The formula to convert angle from circles to radians is:
Angle(Radians) = Angle(Circles) × 2 × π
Substitution:
Substitute given weight Angle(Circles) = 3 in the above formula.
Angle(Radians) = 3 × 2 × 3.14159265359
Angle(Radians) = 18.8496
Final Answer:
Therefore, 3 circle is equal to 18.8496 rad.
The angle is 18.8496 rad, in radians.
Circles to Radians Conversion Table
The following table gives some of the most used conversions from Circles to Radians.
Circles (circle)
Radians (rad)
0 circle
0 rad
1 circle
6.2832rad
10 circle
62.8319rad
45 circle
282.7433rad
90 circle
565.4867rad
180 circle
1130.9734rad
360 circle
2261.9467rad
1000 circle
6283.1853rad
Circles
Circles, in the context of angular measurement, refer to a full rotation or turn, equivalent to 360 degrees or one complete revolution. This unit is often used in discussions of periodic motion, waveforms, and cyclic processes, where the concept of a full rotation is integral to understanding patterns and cycles.
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 Circles to Radians in Angle?
The formula to convert Circles to Radians in Angle is:
Circles * 2 * π
2. Is this tool free or paid?
This Angle conversion tool, which converts Circles to Radians, is completely free to use.
3. How do I convert Angle from Circles to Radians?
To convert Angle from Circles to Radians, you can use the following formula:
Circles * 2 * π
For example, if you have a value in Circles, you substitute that value in place of Circles in the above formula, and solve the mathematical expression to get the equivalent value in Radians.
{
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"y_slug": "radians",
"x": "circle",
"y": "rad",
"x_desc": "Circles",
"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 Ferris wheel rotates through 0.5 circles during one ride.<br>Convert this rotation from circles to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in circles is:</p>\n <p class=\"step\"><span>Angle<sub>(Circles)</sub></span> = 0.5</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from circles to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Circles)</sub></span> × 2 × π</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Circles)</sub> = 0.5</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>0.5</span> × 2 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 3.1416</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.5 circle</strong> is equal to <strong>3.1416 rad</strong>.</p>\n <p>The angle is <strong>3.1416 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 drone completes 3 circles in the air during a maneuver.<br>Convert this rotation from circles to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in circles is:</p>\n <p class=\"step\"><span>Angle<sub>(Circles)</sub></span> = 3</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from circles to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Circles)</sub></span> × 2 × π</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Circles)</sub> = 3</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>3</span> × 2 × 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 18.8496</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>3 circle</strong> is equal to <strong>18.8496 rad</strong>.</p>\n <p>The angle is <strong>18.8496 rad</strong>, in radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Circles</span> to <span class=\"y\">Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Circles to Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Circles (<span class=\"unit\">circle</span>)</th><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">circle</span></td><td>0 <span class=\"unit\">rad</span></td></tr><tr><td>1 <span class=\"unit\">circle</span></td><td>6<span>.2832</span> <span class=\"unit\">rad</span></td></tr><tr><td>10 <span class=\"unit\">circle</span></td><td>62<span>.8319</span> <span class=\"unit\">rad</span></td></tr><tr><td>45 <span class=\"unit\">circle</span></td><td>282<span>.7433</span> <span class=\"unit\">rad</span></td></tr><tr><td>90 <span class=\"unit\">circle</span></td><td>565<span>.4867</span> <span class=\"unit\">rad</span></td></tr><tr><td>180 <span class=\"unit\">circle</span></td><td>1130<span>.9734</span> <span class=\"unit\">rad</span></td></tr><tr><td>360 <span class=\"unit\">circle</span></td><td>2261<span>.9467</span> <span class=\"unit\">rad</span></td></tr><tr><td>1000 <span class=\"unit\">circle</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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