Follow these steps to convert given angle from the units of Gradians to the units of Radians.
Enter the input Gradians value in the text field.
The calculator converts the given Gradians 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 Gradians to Radians?
The formula to convert given angle from Gradians to Radians is:
Angle(Radians) = Angle(Gradians) × π / 200
Substitute the given value of angle in gradians, i.e., Angle(Gradians) 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 precision engineering tool adjusts by 100 gradians. Convert this angle from gradians to Radians.
Answer:
Given:
The angle in gradians is:
Angle(Gradians) = 100
Formula:
The formula to convert angle from gradians to radians is:
Angle(Radians) = Angle(Gradians) × π / 200
Substitution:
Substitute given weight Angle(Gradians) = 100 in the above formula.
Angle(Radians) = 100 × 3.14159265359 / 200
Angle(Radians) = 1.5708
Final Answer:
Therefore, 100 gon is equal to 1.5708 rad.
The angle is 1.5708 rad, in radians.
2
Consider that a civil engineer designs a slope with an angle of 90 gradians. Convert this angle from gradians to Radians.
Answer:
Given:
The angle in gradians is:
Angle(Gradians) = 90
Formula:
The formula to convert angle from gradians to radians is:
Angle(Radians) = Angle(Gradians) × π / 200
Substitution:
Substitute given weight Angle(Gradians) = 90 in the above formula.
Angle(Radians) = 90 × 3.14159265359 / 200
Angle(Radians) = 1.4137
Final Answer:
Therefore, 90 gon is equal to 1.4137 rad.
The angle is 1.4137 rad, in radians.
Gradians to Radians Conversion Table
The following table gives some of the most used conversions from Gradians to Radians.
Gradians (gon)
Radians (rad)
0 gon
0 rad
1 gon
0.01570796327rad
10 gon
0.1571rad
45 gon
0.7069rad
90 gon
1.4137rad
180 gon
2.8274rad
360 gon
5.6549rad
1000 gon
15.708rad
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.
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 Gradians to Radians in Angle?
The formula to convert Gradians to Radians in Angle is:
Gradians * π / 200
2. Is this tool free or paid?
This Angle conversion tool, which converts Gradians to Radians, is completely free to use.
3. How do I convert Angle from Gradians to Radians?
To convert Angle from Gradians to Radians, you can use the following formula:
Gradians * π / 200
For example, if you have a value in Gradians, you substitute that value in place of Gradians 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 a precision engineering tool adjusts by 100 gradians.<br>Convert this angle from gradians to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in gradians is:</p>\n <p class=\"step\"><span>Angle<sub>(Gradians)</sub></span> = 100</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from gradians to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Gradians)</sub></span> × π / 200</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Gradians)</sub> = 100</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>100</span> × 3.14159265359 / 200</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>100 gon</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 civil engineer designs a slope with an angle of 90 gradians.<br>Convert this angle from gradians to Radians.</h3></div>\n <h4 class=\"answer\">Answer:</h4>\n <p><strong>Given:</strong></p>\n <p>The angle in gradians is:</p>\n <p class=\"step\"><span>Angle<sub>(Gradians)</sub></span> = 90</p>\n <p><strong>Formula:</strong></p>\n <p>The formula to convert angle from gradians to radians is:</p>\n <p class=\"formula step\"><span>Angle<sub>(Radians)</sub></span> = <span>Angle<sub>(Gradians)</sub></span> × π / 200</p>\n <p><strong>Substitution:</strong></p>\n <p>Substitute given weight <strong>Angle<sub>(Gradians)</sub> = 90</strong> in the above formula.</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = <span>90</span> × 3.14159265359 / 200</p>\n <p class=\"step\"><span>Angle<sub>(Radians)</sub></span> = 1.4137</p>\n <p><strong>Final Answer:</strong></p>\n <p>Therefore, <strong>90 gon</strong> is equal to <strong>1.4137 rad</strong>.</p>\n <p>The angle is <strong>1.4137 rad</strong>, in radians.</p>\n </div>\n ",
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"table1n": "<h2><span class=\"x\">Gradians</span> to <span class=\"y\">Radians</span> Conversion Table</h2><p>The following table gives some of the most used conversions from Gradians to Radians.</p><table><thead><tr><th scope=\"column\" role=\"columnheader\">Gradians (<span class=\"unit\">gon</span>)</th><th scope=\"column\" role=\"columnheader\">Radians (<span class=\"unit\">rad</span>)</th><tr></thead><tbody><tr><td>0 <span class=\"unit\">gon</span></td><td>0 <span class=\"unit\">rad</span></td></tr><tr><td>1 <span class=\"unit\">gon</span></td><td>0<span>.01570796327</span> <span class=\"unit\">rad</span></td></tr><tr><td>10 <span class=\"unit\">gon</span></td><td>0<span>.1571</span> <span class=\"unit\">rad</span></td></tr><tr><td>45 <span class=\"unit\">gon</span></td><td>0<span>.7069</span> <span class=\"unit\">rad</span></td></tr><tr><td>90 <span class=\"unit\">gon</span></td><td>1<span>.4137</span> <span class=\"unit\">rad</span></td></tr><tr><td>180 <span class=\"unit\">gon</span></td><td>2<span>.8274</span> <span class=\"unit\">rad</span></td></tr><tr><td>360 <span class=\"unit\">gon</span></td><td>5<span>.6549</span> <span class=\"unit\">rad</span></td></tr><tr><td>1000 <span class=\"unit\">gon</span></td><td>15<span>.708</span> <span class=\"unit\">rad</span></td></tr></table>",
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