How to use this Hour Angles to Radians Converter 🤔
Follow these steps to convert given angle from the units of Hour Angles to the units of Radians.
Enter the input Hour Angles value in the text field.
The calculator converts the given Hour Angles 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 Hour Angles to Radians?
The formula to convert given angle from Hour Angles to Radians is:
Angle(Radians) = Angle(Hour Angles) × π / 12
Substitute the given value of angle in hour angles, i.e., Angle(Hour Angles) 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 the position of a celestial body is tracked at 6 hour angles. Convert this angle from hour angles to Radians.
Answer:
Given:
The angle in hour angles is:
Angle(Hour Angles) = 6
Formula:
The formula to convert angle from hour angles to radians is:
Angle(Radians) = Angle(Hour Angles) × π / 12
Substitution:
Substitute given weight Angle(Hour Angles) = 6 in the above formula.
Angle(Radians) = 6 × 3.14159265359 / 12
Angle(Radians) = 1.5708
Final Answer:
Therefore, 6 hour angle is equal to 1.5708 rad.
The angle is 1.5708 rad, in radians.
2
Consider that a sundial shows a time difference of 4 hour angles. Convert this angle from hour angles to Radians.
Answer:
Given:
The angle in hour angles is:
Angle(Hour Angles) = 4
Formula:
The formula to convert angle from hour angles to radians is:
Angle(Radians) = Angle(Hour Angles) × π / 12
Substitution:
Substitute given weight Angle(Hour Angles) = 4 in the above formula.
Angle(Radians) = 4 × 3.14159265359 / 12
Angle(Radians) = 1.0472
Final Answer:
Therefore, 4 hour angle is equal to 1.0472 rad.
The angle is 1.0472 rad, in radians.
Hour Angles to Radians Conversion Table
The following table gives some of the most used conversions from Hour Angles to Radians.
Hour Angles (hour angle)
Radians (rad)
0 hour angle
0 rad
1 hour angle
0.2618rad
10 hour angle
2.618rad
45 hour angle
11.781rad
90 hour angle
23.5619rad
180 hour angle
47.1239rad
360 hour angle
94.2478rad
1000 hour angle
261.7994rad
Hour Angles
Hour angles are a unit of angular measurement used in astronomy to describe the position of celestial objects relative to an observer's local meridian. One hour angle corresponds to 15 degrees, reflecting the Earth's rotation rate of 15 degrees per hour. Hour angles are crucial in celestial navigation and the tracking of astronomical objects.
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 Hour Angles to Radians in Angle?
The formula to convert Hour Angles to Radians in Angle is:
Hour Angles * π / 12
2. Is this tool free or paid?
This Angle conversion tool, which converts Hour Angles to Radians, is completely free to use.
3. How do I convert Angle from Hour Angles to Radians?
To convert Angle from Hour Angles to Radians, you can use the following formula:
Hour Angles * π / 12
For example, if you have a value in Hour Angles, you substitute that value in place of Hour Angles in the above formula, and solve the mathematical expression to get the equivalent value in Radians.
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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 the position of a celestial body is tracked at 6 hour angles.<br>Convert this angle from hour angles to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in hour angles is:</p>\n <p class=\"step\"><span>Angle<sub>(Hour Angles)</sub></span> = 6</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from hour angles to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Hour Angles)</sub></span> × π / 12</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Hour Angles)</sub> = 6</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>6</span> × 3.14159265359 / 12</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>6 hour angle</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 sundial shows a time difference of 4 hour angles.<br>Convert this angle from hour angles to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in hour angles is:</p>\n <p class=\"step\"><span>Angle<sub>(Hour Angles)</sub></span> = 4</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from hour angles to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Hour Angles)</sub></span> × π / 12</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Hour Angles)</sub> = 4</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>4</span> × 3.14159265359 / 12</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 1.0472</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>4 hour angle</strong> is equal to <strong>1.0472 rad</strong>.</p>\n <p>The angle is <strong>1.0472 rad</strong>, in radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Hour Angles</span> to <span class=\"y\">Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Hour Angles to Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Hour Angles (<span class=\"unit\">hour angle</span>)</th><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">hour angle</span></td><td>0 <span class=\"unit\">rad</span></td></tr><tr><td>1 <span class=\"unit\">hour angle</span></td><td>0<span>.2618</span> <span class=\"unit\">rad</span></td></tr><tr><td>10 <span class=\"unit\">hour angle</span></td><td>2<span>.618</span> <span class=\"unit\">rad</span></td></tr><tr><td>45 <span class=\"unit\">hour angle</span></td><td>11<span>.781</span> <span class=\"unit\">rad</span></td></tr><tr><td>90 <span class=\"unit\">hour angle</span></td><td>23<span>.5619</span> <span class=\"unit\">rad</span></td></tr><tr><td>180 <span class=\"unit\">hour angle</span></td><td>47<span>.1239</span> <span class=\"unit\">rad</span></td></tr><tr><td>360 <span class=\"unit\">hour angle</span></td><td>94<span>.2478</span> <span class=\"unit\">rad</span></td></tr><tr><td>1000 <span class=\"unit\">hour angle</span></td><td>261<span>.7994</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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