Follow these steps to convert given angle from the units of Radians to the units of Gradians.
Enter the input Radians value in the text field.
The calculator converts the given Radians into Gradians in realtime ⌚ using the conversion formula, and displays under the Gradians label. You do not need to click any button. If the input changes, Gradians value is re-calculated, just like that.
You may copy the resulting Gradians 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 Gradians?
The formula to convert given angle from Radians to Gradians is:
Angle(Gradians) = Angle(Radians) × 200 / 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 gradians, i.e., Angle(Gradians).
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 Gradians.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 1.5
Formula:
The formula to convert angle from radians to gradians is:
Angle(Gradians) = Angle(Radians) × 200 / π
Substitution:
Substitute given weight Angle(Radians) = 1.5 in the above formula.
Angle(Gradians) = 1.5 × 200 / 3.14159265359
Angle(Gradians) = 95.493
Final Answer:
Therefore, 1.5 rad is equal to 95.493 gon.
The angle is 95.493 gon, in gradians.
2
Consider that a satellite dish adjusts by 0.75 radians to align with a signal. Convert this angle from radians to Gradians.
Answer:
Given:
The angle in radians is:
Angle(Radians) = 0.75
Formula:
The formula to convert angle from radians to gradians is:
Angle(Gradians) = Angle(Radians) × 200 / π
Substitution:
Substitute given weight Angle(Radians) = 0.75 in the above formula.
Angle(Gradians) = 0.75 × 200 / 3.14159265359
Angle(Gradians) = 47.7465
Final Answer:
Therefore, 0.75 rad is equal to 47.7465 gon.
The angle is 47.7465 gon, in gradians.
Radians to Gradians Conversion Table
The following table gives some of the most used conversions from Radians to Gradians.
Radians (rad)
Gradians (gon)
0 rad
0 gon
1 rad
63.662gon
10 rad
636.6198gon
45 rad
2864.789gon
90 rad
5729.578gon
180 rad
11459.1559gon
360 rad
22918.3118gon
1000 rad
63661.9772gon
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.
Gradians
Gradians, also known as grads or gon, are a unit of angular measurement where a full circle is divided into 400 gradians. This unit is particularly useful in fields such as surveying and civil engineering, especially in some European countries. One gradian is equivalent to 0.9 degrees, making it convenient for calculating right angles and dividing circles into decimal fractions.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Radians to Gradians in Angle?
The formula to convert Radians to Gradians in Angle is:
Radians * 200 / π
2. Is this tool free or paid?
This Angle conversion tool, which converts Radians to Gradians, is completely free to use.
3. How do I convert Angle from Radians to Gradians?
To convert Angle from Radians to Gradians, you can use the following formula:
Radians * 200 / 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 Gradians.
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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 Gradians.</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 gradians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Gradians)</sub></span> = <span>Angle<sub>(Radians)</sub></span> × 200 / 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>(Gradians)</sub></span> = <span>1.5</span> × 200 / 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Gradians)</sub></span> = 95.493</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>1.5 rad</strong> is equal to <strong>95.493 gon</strong>.</p>\n <p>The angle is <strong>95.493 gon</strong>, in gradians.</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 Gradians.</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 gradians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Gradians)</sub></span> = <span>Angle<sub>(Radians)</sub></span> × 200 / 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>(Gradians)</sub></span> = <span>0.75</span> × 200 / 3.14159265359</p>\n <p class=\"step\"><span>Angle<sub>(Gradians)</sub></span> = 47.7465</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>0.75 rad</strong> is equal to <strong>47.7465 gon</strong>.</p>\n <p>The angle is <strong>47.7465 gon</strong>, in gradians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Radians</span> to <span class=\"y\">Gradians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Radians to Gradians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><th scope=\"column\" role=\"columnheader\">Gradians (<span class=\"unit\">gon</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">rad</span></td><td>0 <span class=\"unit\">gon</span></td></tr><tr><td>1 <span class=\"unit\">rad</span></td><td>63<span>.662</span> <span class=\"unit\">gon</span></td></tr><tr><td>10 <span class=\"unit\">rad</span></td><td>636<span>.6198</span> <span class=\"unit\">gon</span></td></tr><tr><td>45 <span class=\"unit\">rad</span></td><td>2864<span>.789</span> <span class=\"unit\">gon</span></td></tr><tr><td>90 <span class=\"unit\">rad</span></td><td>5729<span>.578</span> <span class=\"unit\">gon</span></td></tr><tr><td>180 <span class=\"unit\">rad</span></td><td>11459<span>.1559</span> <span class=\"unit\">gon</span></td></tr><tr><td>360 <span class=\"unit\">rad</span></td><td>22918<span>.3118</span> <span class=\"unit\">gon</span></td></tr><tr><td>1000 <span class=\"unit\">rad</span></td><td>63661<span>.9772</span> <span class=\"unit\">gon</span></td></tr></table>",
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