Grads to Radians Converter
Convert Grads to Radians
Quick Conversions
How to Convert Grads to Radians
To convert from grads to radians, you multiply the angle in grads by π/200. For more information about grads as a unit of measurement, visit our grads page.
Formula
Radians = Grads × (π / 200)
or
rad = gon × 0.015708
Step-by-step process
- Take the angle in grads.
- Multiply it by 0.015708 (or π/200).
- The result is the equivalent angle in radians.
Examples
- 50 gon = 50 × (π / 200) = 0.7854 rad (π/4)
- 100 gon = 100 × (π / 200) = 1.5708 rad (π/2)
- 200 gon = 200 × (π / 200) = 3.1416 rad (π)
- 400 gon = 400 × (π / 200) = 6.2832 rad (2π)
When to Convert Grads to Radians
This conversion is useful when you need to use surveying data in mathematical or scientific calculations that require radians.
Mathematics
Radians are the standard unit of angular measure in calculus and other higher mathematics.
Physics and Engineering
Many formulas in physics and engineering, particularly those involving rotational motion, require angles to be in radians.
Common Grads to Radians Conversions
Here is a table of common conversions for quick reference:
| Grads (gon) | Radians (rad) | Grads (gon) | Radians (rad) |
|---|---|---|---|
| 10 | 0.1571 | 150 | 2.3562 |
| 20 | 0.3142 | 200 | 3.1416 |
| 30 | 0.4712 | 250 | 3.927 |
| 40 | 0.6283 | 300 | 4.7124 |
| 50 | 0.7854 | 350 | 5.4978 |
| 60 | 0.9425 | 400 | 6.2832 |
| 70 | 1.0996 | 500 | 7.854 |
| 80 | 1.2566 | 1000 | 15.708 |
| 90 | 1.4137 | ||
| 100 | 1.5708 |
Frequently Asked Questions
What is a grad?
A grad, also known as a gon, is a unit of angle equal to 1/400 of a full circle. A right angle is 100 grads.
What is a radian?
A radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. There are 2π radians in a full circle.
How do I convert radians to grads?
To convert from radians to grads, you multiply the angle in radians by 200/π. For example, π/2 radians is equal to (π/2) * (200/π) = 100 gon.