Follow these steps to convert given Circles value from Circles units to Radians units.
Enter the input Circles value in the text field.
The given Circles is converted to Radians in realtime ⌚ using the formula, and displayed under the Radians label.
You may copy the resulting Radians value using the Copy button.
Formula
To convert given angle from Circles to Radians, use the following formula.
Radians = Circles * 2 * π
Calculation
Calculation will be done after you enter a valid input.
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.
{
"conversion": "circles-radians",
"x_slug": "circles",
"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 × Ï€</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 × Ï€</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 ",
"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>",
"units": [
[
"degrees",
"Degrees",
"°"
],
[
"radians",
"Radians",
"rad"
],
[
"gradians",
"Gradians",
"gon"
],
[
"minutes",
"Minutes",
"'"
],
[
"seconds",
"Seconds",
"\""
],
[
"turns",
"Turns",
"turn"
],
[
"circles",
"Circles",
"circle"
],
[
"binary_degrees",
"Binary Degrees",
"°"
],
[
"compass_points",
"Compass Points",
"compass point"
],
[
"diameter_part",
"Diameter Parts",
"diameter part"
],
[
"hexacontades",
"Hexa-Contades",
"hexacontade"
],
[
"hour_angles",
"Hour Angles",
"hour angle"
],
[
"right_angles",
"Right Angles",
"right angle"
],
[
"milliradians",
"Milli-radians",
"mrad"
],
[
"quadrants",
"Quadrants",
"quadrant"
],
[
"sextants",
"Sextants",
"sextant"
],
[
"pi_radians",
"Ï€ Radians",
"Ï€ radians"
],
[
"zam",
"Zam",
"zam"
]
],
"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.",
"x_long_desc": "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."
}
ConvertOnline