Gradians to Degrees
Convert any value from gradian to degree with full precision. Use the converter above for instant results, or read on for the exact formula, worked examples, common uses, and answers to frequently asked questions.
📊 Quick Conversion Table
About the Gradian to Degree conversion
Angle conversions are needed in mathematics, engineering, navigation, astronomy, and surveying. The radian is the SI unit and is defined as the angle made by an arc equal in length to the radius. The degree, arcminute, and arcsecond are older units that survive in navigation, geography, and astronomy.
This page focuses specifically on converting gradian to degree. Use the converter above for instant results, or read on for the exact formula, a worked example, and answers to common questions.
Where this conversion is used
Mathematicians and physicists use radians for calculus and trigonometry. Engineers convert between degrees and radians for control systems and signal processing. Astronomers measure small angles in arcseconds and milliarcseconds. Surveyors and navigators use degrees, minutes, and seconds.
If you frequently convert gradian to degree, bookmark this page — the exact URL gives you instant access without searching, and the conversion widget is ready to use the moment the page loads.
Conversion formula
The exact mathematical relationship between gradian and degree is:
1 gradian = 0.9 degree
So to convert a value V from gradian to degree, use:
Vdegree = Vgradian × 0.9
To go in the opposite direction:
Vgradian = Vdegree × 1.11111111
These factors come from the international definitions published by NIST, BIPM, and ISO 80000 and are exact within their respective standard systems. The converter applies them with full floating-point precision.
Worked example
Using the formula above, here are some common values converted from Gradian to Degree:
| Gradian | Degree |
|---|---|
| 1 | 0.9 |
| 5 | 4.5 |
| 10 | 9 |
| 25 | 22.5 |
| 50 | 45 |
| 100 | 90 |
Sources and accuracy
One full revolution equals 2π radians = 360 degrees = 400 gradians. The degree is traditionally divided into 60 arcminutes, each of 60 arcseconds. The radian is dimensionless but is given its own unit by the SI (BIPM).
This page was reviewed against multiple authoritative references. Conversion factors are cross-checked with the NIST SP 811 guide, the BIPM SI brochure, ISO 80000, and where applicable, the historical references for older unit systems. If you spot an inconsistency or have a suggested improvement, please let us know via the contact page.
Important disclaimer: for mission-critical work — medical dosing, legal-for-trade measurements, aerospace, large-scale engineering, and financial calculations — always verify independently with the original source. This converter is intended for everyday conversions, education, and quick reference.
Practical tips
When entering values for trigonometric functions in spreadsheets or code, use radians unless the function explicitly accepts degrees. Most calculators have a "DRG" or "MODE" button to switch between degrees, radians, and gradians.
If you are converting large lists of values, use the swap button to instantly reverse direction without retyping. For decimal-heavy values you can paste them directly into the From field — the input accepts standard decimal notation, including negative values and scientific notation (for example, 1.23e-5).
Frequently asked questions
How accurate is this gradian to degree converter?
It uses the official international conversion factors from NIST and BIPM with full double-precision floating-point accuracy. For everyday use the result is precise to many more decimal places than any practical measurement requires.
Can I convert in both directions?
Yes. Use the ⇄ button above to swap the From and To fields. You can also change either dropdown to any unit in the angle category.
Do I need an internet connection?
Only for the first page load. Once the converter is loaded it runs entirely in your browser, so it works offline as well.
Is my data private?
Yes. The conversion calculation happens locally in your browser. The values you enter are never sent to any server.