The degree
The degree (°) divides a full rotation into 360 equal parts, a convention traced to Babylonian sexagesimal astronomy. It is the everyday unit for angles in navigation, geography (latitude/longitude), construction, and general use.
Degrees to Gradians Converter
1 ° = 1.11111 grad (degree → gradian)
1 ° = 1.11111 grad
1 degree equals 1.11111 gradians. To convert degrees to gradians, multiply the degree value by 1.11111. For quick reference: 1 ° = 1.11111 grad, 5 ° = 5.55556 grad, 10 ° = 11.1111 grad, 100 ° = 111.111 grad.
Formula
Gradians = Degrees × 1.11111Quick
How to convert degrees to gradians
Take your value
Start with your value in degrees.
Multiply by 1.11111
Multiply the degree value by 1.11111. This is the exact conversion factor from degrees to gradians.
Read the result
The product is your value in gradians. For example, 5 ° × 1.11111 = 5.55556 grad.
Conversion formula
The exact factor from degrees to gradians is 1.11111.
Gradians = Degrees × 1.11111
Degrees to Gradians conversion table
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Degrees (°) | Gradians (grad) |
|---|---|
| 0.1 ° | 0.11111 grad |
| 0.25 ° | 0.27778 grad |
| 0.5 ° | 0.55556 grad |
| 1 ° | 1.1111 grad |
| 2 ° | 2.2222 grad |
| 3 ° | 3.3333 grad |
| 4 ° | 4.4444 grad |
| 5 ° | 5.5556 grad |
| 6 ° | 6.6667 grad |
| 7 ° | 7.7778 grad |
| 8 ° | 8.8889 grad |
| 9 ° | 10 grad |
| 10 ° | 11.111 grad |
| 11 ° | 12.222 grad |
| 12 ° | 13.333 grad |
| 13 ° | 14.444 grad |
| 14 ° | 15.556 grad |
| 15 ° | 16.667 grad |
| 16 ° | 17.778 grad |
| 18 ° | 20 grad |
| 20 ° | 22.222 grad |
| 22 ° | 24.444 grad |
| 24 ° | 26.667 grad |
| 25 ° | 27.778 grad |
| 28 ° | 31.111 grad |
| 30 ° | 33.333 grad |
| 32 ° | 35.556 grad |
| 36 ° | 40 grad |
| 40 ° | 44.444 grad |
| 45 ° | 50 grad |
| 48 ° | 53.333 grad |
| 50 ° | 55.556 grad |
| 60 ° | 66.667 grad |
| 70 ° | 77.778 grad |
| 75 ° | 83.333 grad |
| 80 ° | 88.889 grad |
| 90 ° | 100 grad |
| 100 ° | 111.11 grad |
| 125 ° | 138.89 grad |
| 150 ° | 166.67 grad |
| 200 ° | 222.22 grad |
| 250 ° | 277.78 grad |
| 300 ° | 333.33 grad |
| 400 ° | 444.44 grad |
| 500 ° | 555.56 grad |
| 600 ° | 666.67 grad |
| 750 ° | 833.33 grad |
| 800 ° | 888.89 grad |
| 900 ° | 1000 grad |
| 1000 ° | 1111.1 grad |
Real-world reference
A right angle is 90°. A straight line is 180°. In gradians, that gives you: 1 ° = 1.11111 grad, 10 ° = 11.1111 grad, 100 ° = 111.111 grad.
Frequently asked questions
- How many gradians are in 1 degree?
- 1 degree equals 1.11111 gradians.
- How do I convert degrees to gradians?
- Multiply the degree value by 1.11111. So x ° × 1.11111 = the equivalent in grad.
- What is 5 degrees in gradians?
- 5 degrees equals 5.55556 gradians.
- What is 10 degrees in gradians?
- 10 degrees equals 11.1111 gradians.
- What is 100 degrees in gradians?
- 100 degrees equals 111.111 gradians.
- How do I convert back from gradians to degrees?
- Multiply the gradian value by 0.9. For example, 1 grad = 0.9 °.
- Is the degree bigger than the gradian?
- Yes. 1 degree is larger than 1 gradian — specifically 1.11111 times larger.
- Are these conversion factors exact?
- The factor is derived directly from the SI definitions of degree and gradian; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.
About the degree and the gradian
The gradian
The gradian (grad), also called the gon, divides a full rotation into 400 equal parts, making a right angle exactly 100 gradians. It was introduced with the metric system for surveying and civil engineering, where its decimal relationship to a right angle simplifies calculations.