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.
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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 what each unit is, the exact formula, a worked example, and answers to common questions.
Understanding gradian and degree
What is a gradian?
The gradian, also called the gon, divides a right angle into 100 parts, so a full circle is 400 gradians. It is used in surveying and some engineering fields because it fits the decimal system neatly.
What is a degree?
The degree divides a full circle into 360 equal parts, a convention inherited from ancient Babylonian astronomy and its base-60 counting. It is the everyday unit for angles in geometry, navigation, and construction.
How a gradian compares to a degree
The degree is the larger of the two units: it takes about 1.11111111 gradian to make a single degree. Because the gradian is smaller, the same length or quantity works out to a larger number when you measure it with that unit. Knowing which unit is larger is a quick way to sanity-check a conversion: if the numbers move in the wrong direction, the two units have probably been swapped.
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).
Conversion factors are cross-checked against the NIST SP 811 guide, the BIPM SI brochure, and ISO 80000, plus published historical references for older unit systems. For mission-critical work such as medical dosing, legal-for-trade measurement, aerospace, or large-scale engineering, always verify independently with the original source.
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.
Frequently asked questions
How many degree are in one gradian?
One gradian equals 0.9 degree. To convert, multiply your gradian value by 0.9.
Which is bigger, a gradian or a degree?
The degree is bigger. One gradian is only about 0.9 degree.
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 degree back to gradian as well?
Yes. Use the swap button above to reverse the From and To fields, or change either dropdown to any unit in the angle category. The calculation runs entirely in your browser, so it also works offline once the page has loaded.