A gradian is 1/400 of a turn.
Gradians to Degrees Converter — gon to deg
Convert Gradian (gon) to Degree (deg) using the exact conversion factor (1 gradian = 0.9 degree). See the formula, worked examples, conversion table, history, and common uses.
Gradians to Degrees 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 degree is pi/180 radians.
Result = input x 0.01570796327 / 0.01745329252.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Gradians to Degrees
Gradian and Degree 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. Specifically: A gradian is 1/400 of a turn, and a degree is pi/180 radians.
Formula
degrees = gradians × 0.9
This factor comes from each unit's defined relationship to the category's base unit: 1 gradian equals 0.0157079632679 base units, and 1 degree equals 0.0174532925199 base units, so dividing one by the other gives the direct gradian-to-degree factor of 0.9.
Simple example
1 gon × 0.9 = 0.9 deg
1 gradian = 0.9 degrees.
Real-world example
90 gon × 0.9 = 81 deg
90 gradians = 81 degrees.
Conversion table
| Gradian (gon) | Degree (deg) |
|---|---|
| 0 gon | 0 deg |
| 30 gon | 27 deg |
| 45 gon | 40.5 deg |
| 90 gon | 81 deg |
| 180 gon | 162 deg |
| 360 gon | 324 deg |
Reverse conversion: Degree to Gradian
0.9 deg × 1.111111111 = 1 gon
0.9 degrees = 1 gradian.
gradians = degrees × 1.11111111111
For a page dedicated to this direction, see Degree to Gradian.
Understanding the Gradian (gon)
A gradian is 1/400 of a turn.
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.
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 degrees are in 1 gradian?
1 gradian equals 0.9 degrees, using the exact defined conversion factor rather than an estimate.
How do I convert gradian to degree?
Multiply the gradian value by 0.9. The converter above does this instantly to whatever precision you set.
How do I convert degree back to gradian?
Use the reverse factor: 1 degree equals 1.111111111 gradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a gradian?
Gradian (gon) is a unit of angle.
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.
Is the gradian to degree conversion exact?
Yes. Both gradian and degree are defined by fixed standards rather than physical artifacts, so the factor of 0.9 used above is exact to as many digits as you choose to display.