A degree is pi/180 radians.
Degrees to Gradians Converter — deg to gon
Convert Degree (deg) to Gradian (gon) using the exact conversion factor (1 degree = 1.111111111 gradian). See the formula, worked examples, conversion table, history, and common uses.
Degrees to Gradians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
A gradian is 1/400 of a turn.
Result = input x 0.01745329252 / 0.01570796327.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Degrees to Gradians
Degree and Gradian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Degree is most often used for navigation and cartography (latitude/longitude).
Formula
gradians = degrees × 1.11111111111
This factor comes from each unit's defined relationship to the category's base unit: 1 degree equals 0.0174532925199 base units, and 1 gradian equals 0.0157079632679 base units, so dividing one by the other gives the direct degree-to-gradian factor of 1.11111111111.
Simple example
1 deg × 1.111111111 = 1.111111111 gon
1 degree = 1.111111111 gradians.
Real-world example
90 deg × 1.111111111 = 100 gon
90 degrees = 100 gradians.
Conversion table
| Degree (deg) | Gradian (gon) |
|---|---|
| 0 deg | 0 gon |
| 30 deg | 33.33333333 gon |
| 45 deg | 50 gon |
| 90 deg | 100 gon |
| 180 deg | 200 gon |
| 360 deg | 400 gon |
Reverse conversion: Gradian to Degree
1.111111111 gon × 0.9 = 0.9999999999 deg
1.111111111 gradians = 0.9999999999 degrees.
degrees = gradians × 0.9
For a page dedicated to this direction, see Gradian to Degree.
Understanding the Degree
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Where it's used: Used worldwide for navigation, geography, and everyday angle measurement.
Uses of the Degree today
- Navigation and cartography (latitude/longitude)
- Construction and surveying
- Everyday angle measurement (protractors, sports)
History of the Degree
The 360-degree circle traces to ancient Babylonian astronomy, whose base-60 (sexagesimal) number system made 360 — divisible by many small numbers — a practical choice for dividing a circle. The convention passed through Greek astronomy (Hipparchus, Ptolemy) into common use.
Historical origin. Degree was not the invention of a single named person; it developed through the process described above.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many gradians are in 1 degree?
1 degree equals 1.111111111 gradians, using the exact defined conversion factor rather than an estimate.
How do I convert degree to gradian?
Multiply the degree value by 1.111111111. The converter above does this instantly to whatever precision you set.
How do I convert gradian back to degree?
Use the reverse factor: 1 gradian equals 0.9 degrees. You can also use the swap control in the converter above to flip the direction instantly.
What is a degree?
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
What is a gradian?
Gradian (gon) is a unit of angle.
Is the degree to gradian conversion exact?
Yes. Both degree and gradian are defined by fixed standards rather than physical artifacts, so the factor of 1.111111111 used above is exact to as many digits as you choose to display.
Where is the degree still used today?
Used worldwide for navigation, geography, and everyday angle measurement.