Radians to Degrees Calculator
How to use this Radians to Degrees Converter 🤔
Follow these steps to convert given angle from the units of Radians to the units of Degrees.
- Enter the input Radians value in the text field.
- The calculator converts the given Radians into Degrees in realtime ⌚ using the conversion formula, and displays under the Degrees label. You do not need to click any button. If the input changes, Degrees value is re-calculated, just like that.
- You may copy the resulting Degrees value using the Copy button.
- You can also reset the input by clicking on Reset button present below the input field.
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 Degrees.
Answer
Given:
Angle in Radians = 1.5 rad
Converting Angle from Radians to Degrees...
The formula to convert from Radians to Degrees is:
Angle(Degrees) = Angle(Radians) × 180 / π
Substitute given Angle(Radians) = 1.5 in the above formula.
Angle(Degrees) = 1.5 × 180 / 3.14159265359
Angle(Degrees) = 85.9437
Therefore, 1.5 rad is equal to 85.9437 °.
2
Consider that a satellite dish adjusts by 0.75 radians to align with a signal.
Convert this angle from radians to Degrees.
Answer
Given:
Angle in Radians = 0.75 rad
Converting Angle from Radians to Degrees...
The formula to convert from Radians to Degrees is:
Angle(Degrees) = Angle(Radians) × 180 / π
Substitute given Angle(Radians) = 0.75 in the above formula.
Angle(Degrees) = 0.75 × 180 / 3.14159265359
Angle(Degrees) = 42.9718
Therefore, 0.75 rad is equal to 42.9718 °.
Radians to Degrees Conversion Table
The following table gives some of the most used conversions from Radians to Degrees.
| Radians (rad) | Degrees (°) |
|---|
|
| 0 rad | 0 ° |
| 1 rad | 57.2958 ° |
| 10 rad | 572.9578 ° |
| 45 rad | 2578.3101 ° |
| 90 rad | 5156.6202 ° |
| 180 rad | 10313.2403 ° |
| 360 rad | 20626.4806 ° |
| 1000 rad | 57295.7795 ° |
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.
Degrees
Degrees are a widely used unit of angular measurement, especially in geometry, trigonometry, and everyday applications. A full circle is divided into 360 degrees, with each degree further divided into 60 minutes and each minute into 60 seconds. Degrees offer an intuitive way to express angles, and they are prevalent in fields ranging from navigation to astronomy, as well as in common day-to-day measurements.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Radians to Degrees in Angle?
The formula to convert Radians to Degrees in Angle is:
Radians * 180 / π
2. Is this tool free or paid?
This Angle conversion tool, which converts Radians to Degrees, is completely free to use.
3. How do I convert Angle from Radians to Degrees?
To convert Angle from Radians to Degrees, you can use the following formula:
Radians * 180 / 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 Degrees.
{
"conversion": "radians-degrees",
"x_slug": "radians",
"y_slug": "degrees",
"x": "rad",
"y": "°",
"x_desc": "Radians",
"y_desc": "Degrees",
"category": "Angle",
"symbol": "m",
"formula": "x * 180 / 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 robotic arm rotates by 1.5 radians to position an object accurately.<br>Convert this angle from radians to Degrees.</h3></div>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <p class=\"step\">Angle in Radians = 1.5 rad</p>\n <p>Converting Angle from Radians to Degrees...</p>\n <p>The formula to convert from Radians to Degrees is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Degrees)</sub></span> = <span>Angle<sub>(Radians)</sub></span> × 180 / π</p>\n <p>Substitute given <strong>Angle<sub>(Radians)</sub> = 1.5</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Degrees)</sub></span> = <span>1.5</span> × 180 / 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Degrees)</sub></span> = 85.9437</p>\n <p class=\"answer\">Therefore, <strong>1.5 rad</strong> is equal to <strong>85.9437 °</strong>.</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 Degrees.</h3></div>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <p class=\"step\">Angle in Radians = 0.75 rad</p>\n <p>Converting Angle from Radians to Degrees...</p>\n <p>The formula to convert from Radians to Degrees is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Degrees)</sub></span> = <span>Angle<sub>(Radians)</sub></span> × 180 / π</p>\n <p>Substitute given <strong>Angle<sub>(Radians)</sub> = 0.75</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Degrees)</sub></span> = <span>0.75</span> × 180 / 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Degrees)</sub></span> = 42.9718</p>\n <p class=\"answer\">Therefore, <strong>0.75 rad</strong> is equal to <strong>42.9718 °</strong>.</p>\n </div>\n ",
"table1n": "<h2><span class=\"x\">Radians</span> to <span class=\"y\">Degrees</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Radians to Degrees.</p><table><thead><tr><th>Radians (<span class=\"unit\">rad</span>)</th><th>Degrees (<span class=\"unit\">°</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">rad</span></td><td>0 <span class=\"unit\">°</span></td></tr><tr><td>1 <span class=\"unit\">rad</span></td><td>57<span>.2958</span> <span class=\"unit\">°</span></td></tr><tr><td>10 <span class=\"unit\">rad</span></td><td>572<span>.9578</span> <span class=\"unit\">°</span></td></tr><tr><td>45 <span class=\"unit\">rad</span></td><td>2578<span>.3101</span> <span class=\"unit\">°</span></td></tr><tr><td>90 <span class=\"unit\">rad</span></td><td>5156<span>.6202</span> <span class=\"unit\">°</span></td></tr><tr><td>180 <span class=\"unit\">rad</span></td><td>10313<span>.2403</span> <span class=\"unit\">°</span></td></tr><tr><td>360 <span class=\"unit\">rad</span></td><td>20626<span>.4806</span> <span class=\"unit\">°</span></td></tr><tr><td>1000 <span class=\"unit\">rad</span></td><td>57295<span>.7795</span> <span class=\"unit\">°</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",
"π Radians",
"π radians"
],
[
"zam",
"Zam",
"zam"
]
],
"y_long_desc": "Degrees are a widely used unit of angular measurement, especially in geometry, trigonometry, and everyday applications. A full circle is divided into 360 degrees, with each degree further divided into 60 minutes and each minute into 60 seconds. Degrees offer an intuitive way to express angles, and they are prevalent in fields ranging from navigation to astronomy, as well as in common day-to-day measurements.",
"x_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."
}
ConvertOnline