Gradian to Degree Conversion Chart
| Gradian (grad) | Degree (deg) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 1 grad | 0.9 deg | Base Definition Ratio of One Gradian to Degree | 1 × 0.9 = 0.9 deg |
| 10 grad | 9 deg | Ten Gradians Decimal Metric Angular Sub-Division | 10 × 0.9 = 9 deg |
| 20 grad | 18 deg | Twenty Gradians Centesimal Surveying Angle Benchmark | 20 × 0.9 = 18 deg |
| 40 grad | 36 deg | Forty Gradians Tenth of Circle Revolution Coordinate | 40 × 0.9 = 36 deg |
| 50 grad | 45 deg | Half Right Angle Forty-Five Degrees Isosceles Vector | 50 × 0.9 = 45 deg |
| 60 grad | 54 deg | Sixty Gradians European Topographic Mapping Angle | 60 × 0.9 = 54 deg |
| 80 grad | 72 deg | Eighty Gradians Regular Pentagon Radial Angle | 80 × 0.9 = 72 deg |
| 100 grad | 90 deg | Perpendicular Right Angle Exactly 100 Centesimal Gradians | 100 × 0.9 = 90 deg |
| 150 grad | 135 deg | One Hundred Fifty Gradians Obtuse Symmetrical Vector | 150 × 0.9 = 135 deg |
| 200 grad | 180 deg | Straight Semicircle Angle Exactly 200 Gradians Line | 200 × 0.9 = 180 deg |
| 250 grad | 225 deg | Two Hundred Fifty Gradians Third Quadrant Symmetry | 250 × 0.9 = 225 deg |
| 300 grad | 270 deg | Three-Quarter Circle Perpendicular Exactly 300 Gradians | 300 × 0.9 = 270 deg |
| 350 grad | 315 deg | Three Hundred Fifty Gradians Fourth Quadrant Vector | 350 × 0.9 = 315 deg |
| 400 grad | 360 deg | Full Circle Geometric Revolution Exactly 400 Gradians | 400 × 0.9 = 360 deg |
| 800 grad | 720 deg | Two Complete Angular Revolutions Eight Hundred Gradians | 800 × 0.9 = 720 deg |
Gradian to Degree Formula & Unit Definitions
The conversion from gradians to degrees is governed by the exact decimal factor of 0.9 (1 grad = 9/10° = 0.9°). To convert gradians into degrees, multiply the gradian value by 0.9 (or multiply by 9 and divide by 10). Conversely, to convert degrees back into gradians, multiply degrees by 10/9 (≈ 1.111111).
Quick Estimation: Subtract 10% from the gradian value (or multiply by 9 and divide by 10). For instance: 50 grad minus 5 = 45°; 100 grad minus 10 = 90°; 200 grad minus 20 = 180°; 400 grad minus 40 = 360°.
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.
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.
Frequently Asked Questions
Q.How many degrees are in one gradian?
One gradian equals exactly 0.9 degrees (1 grad = 9/10° = 0.9°).
Q.What is the reverse conversion from degrees to gradians?
To convert back, use the Degree to Gradian Converter where 1° equals 1.111111 grad.
Q.How many degrees is 100 gradians?
100 gradians equals exactly 90 degrees (one perpendicular right angle).
Q.How many degrees is 200 gradians?
200 gradians equals exactly 180 degrees (a straight line angle).
Q.How do you convert gradians to degrees in your head?
Subtract 10% from the gradian value (e.g. 80 grad - 8 = 72°).