Degree to Gradian Conversion Chart
| Degree (deg) | Gradian (grad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.9 deg | 1 grad | Base Definition Ratio of One Gradian to Degree | 0.9 × 1.111111 = 1 grad |
| 9 deg | 10 grad | Ten Gradians Decimal Metric Angular Sub-Division | 9 × 1.111111 = 10 grad |
| 18 deg | 20 grad | Twenty Gradians Centesimal Surveying Angle Benchmark | 18 × 1.111111 = 20 grad |
| 36 deg | 40 grad | Forty Gradians Tenth of Circle Revolution Coordinate | 36 × 1.111111 = 40 grad |
| 45 deg | 50 grad | Half Right Angle Forty-Five Degrees Isosceles Vector | 45 × 1.111111 = 50 grad |
| 54 deg | 60 grad | Sixty Gradians European Topographic Mapping Angle | 54 × 1.111111 = 60 grad |
| 72 deg | 80 grad | Eighty Gradians Regular Pentagon Radial Angle | 72 × 1.111111 = 80 grad |
| 90 deg | 100 grad | Perpendicular Right Angle Exactly 100 Centesimal Gradians | 90 × 1.111111 = 100 grad |
| 135 deg | 150 grad | One Hundred Fifty Gradians Obtuse Symmetrical Vector | 135 × 1.111111 = 150 grad |
| 180 deg | 200 grad | Straight Semicircle Angle Exactly 200 Gradians Line | 180 × 1.111111 = 200 grad |
| 225 deg | 250 grad | Two Hundred Fifty Gradians Third Quadrant Symmetry | 225 × 1.111111 = 250 grad |
| 270 deg | 300 grad | Three-Quarter Circle Perpendicular Exactly 300 Gradians | 270 × 1.111111 = 300 grad |
| 315 deg | 350 grad | Three Hundred Fifty Gradians Fourth Quadrant Vector | 315 × 1.111111 = 350 grad |
| 360 deg | 400 grad | Full Circle Geometric Revolution Exactly 400 Gradians | 360 × 1.111111 = 400 grad |
| 720 deg | 800 grad | Two Complete Angular Revolutions Eight Hundred Gradians | 720 × 1.111111 = 800 grad |
Degree to Gradian Formula & Unit Definitions
The conversion from degrees to gradians is governed by the exact rational factor of 10/9 (1° = 10/9 grad ≈ 1.111111 grad). To convert degrees into gradians, multiply the degree value by 10 and divide by 9 (or multiply by ~1.111111). Conversely, to convert gradians back into degrees, multiply gradians by 0.9 (or multiply by 9 and divide by 10).
Quick Estimation: Add one-ninth to the degree value (or multiply degrees by 10 and divide by 9). For example, 90° × (10/9) = 100 grad; 180° × (10/9) = 200 grad; 360° × (10/9) = 400 grad.
Degree Angle (°)
Sexagesimal Circle Division- Creator & Origin: Originated in ancient Babylon based on a base-60 sexagesimal astronomical calendar circle.
- Standard Definition: Defined as exactly 1/360 of a full geometric circle or revolution (90° = 1 right angle).
- Everyday Focus: Compass headings, architectural drafting, mechanical engineering, and school geometry.
Gradian Unit (grad / gon)
Centesimal Metric Division- Creator & Origin: Conceived during the French Revolution (1790s) as part of decimal metric system reforms.
- Standard Definition: Defined as exactly 1/400 of a complete circle (100 grad = 1 right angle, 0.9° = 1 grad).
- Everyday Focus: European cadastral surveying, Alpine tunneling alignment, civil road grading, and total stations.
Frequently Asked Questions
Q.How many gradians are in one degree?
One degree equals exactly 10/9 gradians (approximately 1.111111 gradians or gon).
Q.What is the reverse conversion from gradians to degrees?
To convert in reverse, use the Gradian to Degree Converter where 1 grad equals exactly 0.9°.
Q.How many gradians is 90 degrees?
90 degrees equals exactly 100 gradians (a metric centesimal right angle).
Q.How many gradians is a full circle?
A full circle (360°) equals exactly 400 gradians (400 gon).
Q.What formula converts degrees to gradians?
Multiply degrees by 10 and divide by 9: Gradians = Degrees × (10 / 9).