Gradian to Radian Conversion Chart
| Gradian (grad) | Radian (rad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 1 grad | 0.0157 rad | Base Gradian Benchmark Centesimal Angular Increment | 1 × 0.015708 = 0.0157 rad |
| 5 grad | 0.0785 rad | Five Gradians Metric Surveying Deflection Increment | 5 × 0.015708 = 0.0785 rad |
| 10 grad | 0.1571 rad | Ten Gradians Topographic Mapping Traverse Station | 10 × 0.015708 = 0.1571 rad |
| 20 grad | 0.3142 rad | Twenty Gradians Centesimal Cadastral Angular Vector | 20 × 0.015708 = 0.3142 rad |
| 50 grad | 0.7854 rad | Exact Half Right Angle Fifty Gradians Metric Octant | 50 × 0.015708 = 0.7854 rad |
| 63.662 grad | 1 rad | One Natural Radian Unit Arc-to-Radius Equality in Gradians | 63.662 × 0.015708 = 1 rad |
| 100 grad | 1.5708 rad | Exact Perpendicular Right Angle 100 Centesimal Gradians | 100 × 0.015708 = 1.5708 rad |
| 150 grad | 2.3562 rad | One Hundred Fifty Gradians Obtuse Symmetrical Vector | 150 × 0.015708 = 2.3562 rad |
| 200 grad | 3.1416 rad | Exact Straight Semicircle 200 Centesimal Gradians | 200 × 0.015708 = 3.1416 rad |
| 250 grad | 3.927 rad | Two Hundred Fifty Gradians Third Quadrant Vector | 250 × 0.015708 = 3.927 rad |
| 300 grad | 4.7124 rad | Three-Quarter Circle Turn 300 Centesimal Gradians | 300 × 0.015708 = 4.7124 rad |
| 350 grad | 5.4978 rad | Three Hundred Fifty Gradians Fourth Quadrant Diagonal | 350 × 0.015708 = 5.4978 rad |
| 400 grad | 6.2832 rad | Full Geometric Circle Revolution 400 Centesimal Gradians | 400 × 0.015708 = 6.2832 rad |
| 600 grad | 9.4248 rad | One and a Half Circle Turns Six Hundred Gradians | 600 × 0.015708 = 9.4248 rad |
| 800 grad | 12.5664 rad | Two Complete Angular Revolutions Eight Hundred Gradians | 800 × 0.015708 = 12.5664 rad |
Gradian to Radian Formula & Unit Definitions
The conversion from gradians to radians is governed by the exact formula: Radians = Gradians × (π / 200) ≈ Gradians × 0.01570796. Conversely, to convert radians back into gradians, multiply by 200 / π ≈ 63.661977.
Quick Estimation: Divide the gradian value by 200 to find the fraction of π. For instance: 100 grad = 100/200 π = π/2 ≈ 1.5708 rad; 50 grad = π/4 ≈ 0.7854 rad; 200 grad = π ≈ 3.1416 rad; 400 grad = 2π ≈ 6.2832 rad.
Gradian Unit (grad / gon)
Centesimal Metric Division- Creator & Origin: Created in revolutionary France (1790s) to align circular angles with base-10 decimals.
- Standard Definition: Defined as 1/400 of a circle (100 grad = 1 right angle, 200 grad = 1 semicircle).
- Everyday Focus: European land boundary records, electronic theodolites, road banking, and railway gradients.
Radian Unit (rad)
SI Pure Geometric Unit- Creator & Origin: Conceptualized by Roger Cotes and adopted globally as the SI derived unit of plane angle.
- Standard Definition: Subtends a circular arc equal to the radius (π rad = 180° = 200 grad).
- Everyday Focus: Scientific simulations, robotics forward kinematics, angular velocity, and calculus.
Frequently Asked Questions
Q.How many radians are in one gradian?
One gradian equals exactly π/200 radians (approximately 0.01570796 radians).
Q.What is the reverse conversion from radians to gradians?
To convert back, use the Radian to Gradian Converter where 1 rad equals approximately 63.662 grad.
Q.How many radians is 100 gradians?
100 gradians equals exactly π/2 radians (approximately 1.5707963 radians).
Q.How many radians is 200 gradians?
200 gradians equals exactly π radians (approximately 3.14159265 radians).
Q.What formula converts gradians to radians?
Multiply gradians by π and divide by 200: Radians = Gradians × (π / 200).