Radian to Gradian Conversion Chart
| Radian (rad) | Gradian (grad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.0157 rad | 0.9995 grad | Base Gradian Benchmark Centesimal Angular Increment | 0.0157 × 63.662 = 0.9995 grad |
| 0.0785 rad | 4.9975 grad | Five Gradians Metric Surveying Deflection Increment | 0.0785 × 63.662 = 4.9975 grad |
| 0.1571 rad | 10.0013 grad | Ten Gradians Topographic Mapping Traverse Station | 0.1571 × 63.662 = 10.0013 grad |
| 0.3142 rad | 20.0026 grad | Twenty Gradians Centesimal Cadastral Angular Vector | 0.3142 × 63.662 = 20.0026 grad |
| 0.7854 rad | 50.0001 grad | Exact Half Right Angle Fifty Gradians Metric Octant | 0.7854 × 63.662 = 50.0001 grad |
| 1 rad | 63.662 grad | One Natural Radian Unit Arc-to-Radius Equality in Gradians | 1 × 63.662 = 63.662 grad |
| 1.5708 rad | 100.0003 grad | Exact Perpendicular Right Angle 100 Centesimal Gradians | 1.5708 × 63.662 = 100.0003 grad |
| 2.3562 rad | 150.0004 grad | One Hundred Fifty Gradians Obtuse Symmetrical Vector | 2.3562 × 63.662 = 150.0004 grad |
| 3.1416 rad | 200.0005 grad | Exact Straight Semicircle 200 Centesimal Gradians | 3.1416 × 63.662 = 200.0005 grad |
| 3.927 rad | 250.0007 grad | Two Hundred Fifty Gradians Third Quadrant Vector | 3.927 × 63.662 = 250.0007 grad |
| 4.7124 rad | 300.0008 grad | Three-Quarter Circle Turn 300 Centesimal Gradians | 4.7124 × 63.662 = 300.0008 grad |
| 5.4978 rad | 350.0009 grad | Three Hundred Fifty Gradians Fourth Quadrant Diagonal | 5.4978 × 63.662 = 350.0009 grad |
| 6.2832 rad | 400.0011 grad | Full Geometric Circle Revolution 400 Centesimal Gradians | 6.2832 × 63.662 = 400.0011 grad |
| 9.4248 rad | 600.0016 grad | One and a Half Circle Turns Six Hundred Gradians | 9.4248 × 63.662 = 600.0016 grad |
| 12.5664 rad | 800.0021 grad | Two Complete Angular Revolutions Eight Hundred Gradians | 12.5664 × 63.662 = 800.0021 grad |
Radian to Gradian Formula & Unit Definitions
The conversion from radians to gradians is governed by the exact formula: Gradians = Radians × (200 / π) ≈ Radians × 63.661977. Conversely, to convert gradians into radians, multiply by π / 200 ≈ 0.01570796.
Quick Estimation: Remember that π radians equals 200 gradians and π/2 radians equals 100 gradians. For quick estimates, multiply radians by 64 (or multiply by 200 and divide by 3.1416). For example, 1 rad ≈ 63.66 grad; 1.57 rad ≈ 100 grad; 3.14 rad ≈ 200 grad.
Radian Unit (rad)
SI Pure Geometric Unit- Creator & Origin: Formalized by Roger Cotes (1714) and James Thomson (1873) in mathematical physics.
- Standard Definition: Subtends an arc equal in length to the circle radius (2π rad = 1 full circle).
- Everyday Focus: Calculus derivatives, harmonic wave oscillators, rotational dynamics, and computer graphics.
Gradian Unit (grad / gon)
Centesimal Metric Division- Creator & Origin: Established during the French Revolutionary metrication movement of the 1790s.
- Standard Definition: Defined as exactly 1/400 of a complete circle (100 grad = 1 right angle = π/2 rad).
- Everyday Focus: Alpine tunneling, total station surveying, civil road grading, and cadastral mapping.
Frequently Asked Questions
Q.How many gradians are in one radian?
One radian equals approximately 63.661977 gradians (exactly 200/π grad or gon).
Q.What is the reverse conversion from gradians to radians?
To convert back, use the Gradian to Radian Converter where 1 grad equals approximately 0.015708 rad.
Q.How many gradians is π radians?
π radians (180°) equals exactly 200 gradians (200 gon).
Q.How many gradians is π/2 radians?
π/2 radians (90°) equals exactly 100 gradians (100 gon).
Q.What formula converts radians to gradians?
Multiply radians by 200 and divide by π: Gradians = Radians × (200 / π).