How to use this Diameter Parts to Radians Converter 🤔
Follow these steps to convert given angle from the units of Diameter Parts to the units of Radians.
Enter the input Diameter Parts value in the text field.
The calculator converts the given Diameter Parts 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 Diameter Parts to Radians?
The formula to convert given angle from Diameter Parts to Radians is:
Substitute the given value of angle in diameter parts, i.e., Angle(Diameter Parts) 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 mechanical watch's gear rotates by 12 diameter parts. Convert this rotation from diameter parts to Radians.
Answer:
Given:
The angle in diameter parts is:
Angle(Diameter Parts) = 12
Formula:
The formula to convert angle from diameter parts to radians is:
Substitute given weight Angle(Diameter Parts) = 16 in the above formula.
Angle(Radians) = 16 × 2 × 3.14159265359 / 376.991
Angle(Radians) = 0.2667
Final Answer:
Therefore, 16 diameter part is equal to 0.2667 rad.
The angle is 0.2667 rad, in radians.
Diameter Parts to Radians Conversion Table
The following table gives some of the most used conversions from Diameter Parts to Radians.
Diameter Parts (diameter part)
Radians (rad)
0 diameter part
0 rad
1 diameter part
0.0166666719rad
10 diameter part
0.1667rad
45 diameter part
0.75rad
90 diameter part
1.5rad
180 diameter part
3 rad
360 diameter part
6 rad
1000 diameter part
16.6667rad
Diameter Parts
Diameter parts are a less common unit of angular measurement, historically used to describe angles in terms of the fractional parts of a circle's diameter. This unit was more prevalent in classical geometry and certain types of mechanical design, where direct relationships between linear measurements and angles were essential.
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 Diameter Parts to Radians in Angle?
The formula to convert Diameter Parts to Radians in Angle is:
Diameter Parts * 2 * π / 376.991
2. Is this tool free or paid?
This Angle conversion tool, which converts Diameter Parts to Radians, is completely free to use.
3. How do I convert Angle from Diameter Parts to Radians?
To convert Angle from Diameter Parts to Radians, you can use the following formula:
Diameter Parts * 2 * π / 376.991
For example, if you have a value in Diameter Parts, you substitute that value in place of Diameter Parts in the above formula, and solve the mathematical expression to get the equivalent value in Radians.
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"x": "diameter part",
"y": "rad",
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"y_desc": "Radians",
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"formula": "x * 2 * π / 376.991",
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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 mechanical watch's gear rotates by 12 diameter parts.<br>Convert this rotation from diameter parts to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in diameter parts is:</p>\n <p class=\"step\"><span>Angle<sub>(Diameter Parts)</sub></span> = 12</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from diameter parts to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Diameter Parts)</sub></span> × 2 × π / 376.991</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Diameter Parts)</sub> = 12</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>12</span> × 2 × 3.14159265359 / 376.991</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 0.2</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>12 diameter part</strong> is equal to <strong>0.2 rad</strong>.</p>\n <p>The angle is <strong>0.2 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 precision tool rotates by 16 diameter parts for accurate measurements.<br>Convert this rotation from diameter parts to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in diameter parts is:</p>\n <p class=\"step\"><span>Angle<sub>(Diameter Parts)</sub></span> = 16</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from diameter parts to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Diameter Parts)</sub></span> × 2 × π / 376.991</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Diameter Parts)</sub> = 16</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>16</span> × 2 × 3.14159265359 / 376.991</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 0.2667</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>16 diameter part</strong> is equal to <strong>0.2667 rad</strong>.</p>\n <p>The angle is <strong>0.2667 rad</strong>, in radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Diameter Parts</span> to <span class=\"y\">Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Diameter Parts to Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Diameter Parts (<span class=\"unit\">diameter part</span>)</th><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">diameter part</span></td><td>0 <span class=\"unit\">rad</span></td></tr><tr><td>1 <span class=\"unit\">diameter part</span></td><td>0<span>.0166666719</span> <span class=\"unit\">rad</span></td></tr><tr><td>10 <span class=\"unit\">diameter part</span></td><td>0<span>.1667</span> <span class=\"unit\">rad</span></td></tr><tr><td>45 <span class=\"unit\">diameter part</span></td><td>0<span>.75</span> <span class=\"unit\">rad</span></td></tr><tr><td>90 <span class=\"unit\">diameter part</span></td><td>1<span>.5</span> <span class=\"unit\">rad</span></td></tr><tr><td>180 <span class=\"unit\">diameter part</span></td><td>3 <span class=\"unit\">rad</span></td></tr><tr><td>360 <span class=\"unit\">diameter part</span></td><td>6 <span class=\"unit\">rad</span></td></tr><tr><td>1000 <span class=\"unit\">diameter part</span></td><td>16<span>.6667</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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