Gradians to Radians Converter
Quick answer: To convert gradians to radians, multiply by 0.01570796. For example, 10 grad is 0.1570796 rad. One gradian equals 0.01570796 rad.
- Calculator
- Formula
- Examples
- Size compared
- About the units
- Where used
- Step by step
- Popular conversions
- Reading your result
- Mistakes
- FAQ
- Related tools
- Method
Use the Gradians to Radians Converter
Gradians to Radians formula and what each symbol means
rad = grad × 0.01570796
| Symbol | Meaning |
|---|---|
| grad | Gradian |
| rad | Radian |
Gradians to Radians examples
1 grad
1 grad × 0.01570796 = 0.01570796 rad.
10 grad
10 grad × 0.01570796 = 0.1570796 rad.
100 grad
100 grad × 0.01570796 = 1.570796 rad.
Gradians compared with Radians
One rad is 63.66 times as large as one grad, so your number gets smaller when you convert gradians to radians and bigger when you convert back. If the answer is not smaller than what you typed, you multiplied instead of dividing.
About gradians and radians
Gradian (grad): 1/400 of a full turn, also called a gon. Radian (rad): The SI unit of plane angle: the angle subtended by an arc equal to the radius.
Where gradians to radians conversions are used
Navigation and surveying use degrees, while maths, physics and programming use radians. Machining and construction use degrees; some drafting and military work uses gradians or mils.
How to calculate Gradians to Radians step by step
- Enter the value in grad (the starting unit).
- Multiply by 0.01570796, because 1 grad = 0.01570796 rad.
- The product is the value in rad. To go back, divide by 0.01570796 or multiply by 63.66198.
Popular angle conversions
How to read your Gradians to Radians result
Quick estimate: multiply by about 0.016 to get radians from gradians; this is within 1.9% of the exact factor. To convert degrees to radians multiply by π/180, and to convert radians to degrees multiply by 180/π.
| GRADIANS | RADIANS |
|---|---|
| 1 | 0.01570796 |
| 2 | 0.03141593 |
| 5 | 0.07853982 |
| 10 | 0.1570796 |
| 20 | 0.3141593 |
| 50 | 0.7853982 |
| 100 | 1.570796 |
| 1,000 | 15.70796 |
Radians to Gradians: quick table
| RADIANS | GRADIANS |
|---|---|
| 1 | 63.66198 |
| 5 | 318.3099 |
| 10 | 636.6198 |
| 25 | 1,591.549 |
| 50 | 3,183.099 |
| 100 | 6,366.198 |
| 250 | 15,915.49 |
| 500 | 31,830.99 |
Common mistakes when calculating Gradians to Radians
- Leaving a calculator in degree mode when the input is in radians (or the reverse).
- Dividing when you should multiply: from grad to rad multiply by 0.01570796; from rad to grad divide by 0.01570796.
Gradians to Radians FAQ
How many rad are in 1 grad?
1 grad equals 0.01570796 rad.
How many grad are in 1 rad?
1 rad equals 63.66198 grad.
Is 1 grad = 0.01570796 rad an exact conversion?
The factor is shown rounded to 7 significant figures (0.01570796). The calculator above uses more digits.
What is a radian (rad)?
The SI unit of plane angle: the angle subtended by an arc equal to the radius.
How can I estimate gradians to radians in my head?
Quick estimate: multiply by about 0.016 to get radians from gradians; this is within 1.9% of the exact factor.
What is 7 grad in radians?
7 grad = 0.1099557 rad (since 7 × 0.01570796).
What is 40 grad in radians?
40 grad = 0.6283185 rad (since 40 × 0.01570796).
What is 200 grad in radians?
200 grad = 3.141593 rad (since 200 × 0.01570796).
How many decimals should I keep when converting grad to rad?
Match the precision of your original measurement. For example, 0.1570796 rad rounds to 0.157 rad at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angle converters
- Degrees to Radians Converter
- Radians to Revolutions Converter
- Degrees to Gradians Converter
- Revolutions to Degrees Converter
- Revolutions to Gradians Converter
- Revolutions to Radians Converter
See all angle converters tools · All Conversion calculators · Site map
Method, review and disclaimer
Edited by: Hemant Kumar and Anjita Rai, founders of ToolsVault (SEO and content professional, not a licensed adviser). Method: this tool runs in your browser using the formula shown on this page; the numbers you enter are not sent to our servers. Sources: NIST SP 811, Appendix B.8: conversion factors, BIPM: the SI derived units