Follow these steps to convert given angle from the units of Radians to the units of Circles.
Enter the input Radians value in the text field.
The calculator converts the given Radians into Circles in realtime ⌚ using the conversion formula, and displays under the Circles label. You do not need to click any button. If the input changes, Circles value is re-calculated, just like that.
You may copy the resulting Circles 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 Circles?
The formula to convert given angle from Radians to Circles is:
Angle(Circles) = 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 circles, i.e., Angle(Circles).
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 Circles.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 1.5
Formula:
The formula to convert angle from radians to circles is:
Angle(Circles) = Angle(Radians) / (2 × π)
Substitution:
Substitute given weight Angle(Radians) = 1.5 in the above formula.
Angle(Circles) = 1.5 / (2 × 3.14159265359)
Angle(Circles) = 0.2387
Final Answer:
Therefore, 1.5 rad is equal to 0.2387 circle.
The angle is 0.2387 circle, in circles.
2
Consider that a satellite dish adjusts by 0.75 radians to align with a signal. Convert this angle from radians to Circles.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 0.75
Formula:
The formula to convert angle from radians to circles is:
Angle(Circles) = Angle(Radians) / (2 × π)
Substitution:
Substitute given weight Angle(Radians) = 0.75 in the above formula.
Angle(Circles) = 0.75 / (2 × 3.14159265359)
Angle(Circles) = 0.1194
Final Answer:
Therefore, 0.75 rad is equal to 0.1194 circle.
The angle is 0.1194 circle, in circles.
Radians to Circles Conversion Table
The following table gives some of the most used conversions from Radians to Circles.
Radians (rad)
Circles (circle)
0 rad
0 circle
1 rad
0.1592circle
10 rad
1.5915circle
45 rad
7.162circle
90 rad
14.3239circle
180 rad
28.6479circle
360 rad
57.2958circle
1000 rad
159.1549circle
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.
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.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Radians to Circles in Angle?
The formula to convert Radians to Circles in Angle is:
Radians / (2 * π)
2. Is this tool free or paid?
This Angle conversion tool, which converts Radians to Circles, is completely free to use.
3. How do I convert Angle from Radians to Circles?
To convert Angle from Radians to Circles, 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 Circles.
{
"conversion": "radians-circles",
"x_slug": "radians",
"y_slug": "circles",
"x": "rad",
"y": "circle",
"x_desc": "Radians",
"y_desc": "Circles",
"category": "Angle",
"symbol": "m",
"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 Circles.</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 circles is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Circles)</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>(Circles)</sub></span> = <span>1.5</span> / (2 × 3.14159265359)</p>\n <p class=\"step\"><span>Angle<sub>(Circles)</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 circle</strong>.</p>\n <p>The angle is <strong>0.2387 circle</strong>, in circles.</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 Circles.</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 circles is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Circles)</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>(Circles)</sub></span> = <span>0.75</span> / (2 × 3.14159265359)</p>\n <p class=\"step\"><span>Angle<sub>(Circles)</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 circle</strong>.</p>\n <p>The angle is <strong>0.1194 circle</strong>, in circles.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Radians</span> to <span class=\"y\">Circles</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Radians to Circles.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><th scope=\"column\" role=\"columnheader\">Circles (<span class=\"unit\">circle</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">rad</span></td><td>0 <span class=\"unit\">circle</span></td></tr><tr><td>1 <span class=\"unit\">rad</span></td><td>0<span>.1592</span> <span class=\"unit\">circle</span></td></tr><tr><td>10 <span class=\"unit\">rad</span></td><td>1<span>.5915</span> <span class=\"unit\">circle</span></td></tr><tr><td>45 <span class=\"unit\">rad</span></td><td>7<span>.162</span> <span class=\"unit\">circle</span></td></tr><tr><td>90 <span class=\"unit\">rad</span></td><td>14<span>.3239</span> <span class=\"unit\">circle</span></td></tr><tr><td>180 <span class=\"unit\">rad</span></td><td>28<span>.6479</span> <span class=\"unit\">circle</span></td></tr><tr><td>360 <span class=\"unit\">rad</span></td><td>57<span>.2958</span> <span class=\"unit\">circle</span></td></tr><tr><td>1000 <span class=\"unit\">rad</span></td><td>159<span>.1549</span> <span class=\"unit\">circle</span></td></tr></table>",
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