Gon to Radian Converter
Enter the value that you want to convert gon to radian (rad) or radian to gon.
1 gon = 0.0157080 radian
Formula: radian = gon value × 0.0157080
gon to radian
10 gon = 0.15708 radian
Popular Degree Converters:
Gon to Radian: The Essentials
The Gon: History & Usage
Gon (gon) is a unit of degree measurement. 1 gon is equal to 0.0157080 radian.
The Radian: History & Usage
The radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
Adopted as the SI unit of angular measure, the radian makes calculus and physics equations significantly simpler because it eliminates conversion constants. One full revolution equals 2π radians (≈ 6.2832 rad). Radians are essential in signal processing, robotics, computer graphics (3D rotations), oscillation analysis, and any domain where angular velocity or frequency calculations are performed.
Why Angle Conversions Matter
Angle conversions bridge the gap between everyday measurement (degrees) and mathematical computation (radians). A mechanical engineer designing a robotic arm needs radians for inverse kinematics. A pilot reads compass headings in degrees. A surveyor might work in gradians. Game developers convert between degrees (artist-friendly) and radians (GPU shaders) hundreds of times per frame. Understanding these conversions is essential across STEM fields, navigation, and digital media production.
gon to radian metric conversion table
| 0.01 gon | = | 0.00016 rad |
| 0.1 gon | = | 0.00157 rad |
| 1 gon | = | 0.01571 rad |
| 2 gon | = | 0.03142 rad |
| 3 gon | = | 0.04712 rad |
| 4 gon | = | 0.06283 rad |
| 5 gon | = | 0.07854 rad |
| 6 gon | = | 0.09425 rad |
| 7 gon | = | 0.10996 rad |
| 8 gon | = | 0.12566 rad |
| 9 gon | = | 0.14137 rad |
| 10 gon | = | 0.15708 rad |
| 11 gon | = | 0.17279 rad |
| 12 gon | = | 0.18850 rad |
| 13 gon | = | 0.20420 rad |
| 14 gon | = | 0.21991 rad |
| 15 gon | = | 0.23562 rad |
| 16 gon | = | 0.25133 rad |
| 17 gon | = | 0.26704 rad |
| 18 gon | = | 0.28274 rad |
| 19 gon | = | 0.29845 rad |
| 20 gon | = | 0.31416 rad |
| 30 gon | = | 0.47124 rad |
| 40 gon | = | 0.62832 rad |
| 50 gon | = | 0.78540 rad |
| 60 gon | = | 0.94248 rad |
| 70 gon | = | 1.09956 rad |
| 80 gon | = | 1.25664 rad |
| 90 gon | = | 1.41372 rad |
| 100 gon | = | 1.57080 rad |
| 200 gon | = | 3.14159 rad |
| 300 gon | = | 4.71239 rad |
| 400 gon | = | 6.28319 rad |
| 500 gon | = | 7.85398 rad |
| 600 gon | = | 9.42478 rad |
| 700 gon | = | 10.99557 rad |
| 800 gon | = | 12.56637 rad |
| 900 gon | = | 14.13717 rad |
| 1000 gon | = | 15.70796 rad |
How to Convert Gon to Radian?
We can convert gon to radian by using an example.
Example:
Convert 20 Gon to Radian?
We know 1 Gon = 0.0157080 radian; 1 Radian = 63.6619772 gon.
20 gon = ___rad
20 × 0.0157080 = 0.31416 rad (we know 1 gon = 0.0157080 radian)
Answer:
20 gon = 0.31416 radian
How to Convert Gradians to Radians
Since 400 gradians = 2π radians, the conversion factor is π/200 ≈ 0.015708:
- Write down the angle in gradians.
- Multiply by π/200 (≈ 0.015708).
- The result is the angle in radians.
Solved Examples
Question 1: Convert 100 gradians to radians.
Solution:
Radians = 100 × (π/200)
= π/2
≈ 1.5708
Answer: 100 gradians = π/2 radians (right angle)
Question 2: Convert 150 gradians to radians.
Solution:
Radians = 150 × (π/200)
= 3π/4
≈ 2.3562
Answer: 150 gradians = 3π/4 radians
Question 3: A surveyor records 66.667 gon. Convert to radians.
Solution:
Radians = 66.667 × (π/200)
= 66.667π/200
≈ 1.0472
Answer: 66.667 gon ≈ π/3 ≈ 1.047 radians
Practice Questions
Try solving these on your own to test your understanding:
- Convert 50 gradians to radians. (Answer: π/4 ≈ 0.785 rad)
- What is 300 gon in radians? (Answer: 3π/2 ≈ 4.712 rad)
- Express 250 gon in radians. (Answer: 5π/4 ≈ 3.927 rad)
- Convert 33.333 gon to radians. (Answer: π/6 ≈ 0.524 rad)
Importing Survey Data into Scientific Software
Surveying instruments record angles in gradians, but scientific computing libraries (NumPy, MATLAB, R) expect radians for trigonometric functions. When processing survey data programmatically, every angle must be converted: radians = gradians × π/200. Forgetting this conversion is a common source of bugs in GIS scripts and surveying software, producing wildly incorrect coordinates or distances.
Key Takeaways
- Multiply gradians by π/200 (≈ 0.015708) to get radians.
- 100 gon = π/2 rad, 200 gon = π rad, 400 gon = 2π rad.
- Essential when importing surveying data into scientific computing.
- All trig functions in programming require radians, not gradians.
Gon to Radian Conversion Formula
radian = gon × 0.0157080
1 gon = 0.0157080 radian
1 radian = 63.6619772 gon
Reverse: gon = radian × 63.6619772
Frequently Asked Questions
How many radian are in 1 gon?
There are 0.0157080 radian in 1 gon. To convert gon to radian, multiply the value by 0.0157080.
How do I convert gon to radian?
Multiply your gon value by 0.0157080 to get the equivalent in radian. For example, 5 gon = 5 × 0.0157080 = 0.07854 radian.
How do I convert radian to gon?
Multiply your radian value by 63.6619772 to get the equivalent in gon. Alternatively, divide by 0.0157080.
What is 10 gon in radian?
10 gon is equal to 0.15708 radian.
What is 100 gon in radian?
100 gon is equal to 1.57080 radian.