Convert Gradian to Degree
1 gradian = 0.9 degree (°). For example, 10 gradian = 9 degree and 100 gradian = 90 degree. Type any value below to convert gradian to degree both ways — it runs entirely in your browser.
Quick answer: Gradian to Degree
1 Gradian = 0.9Degree (gon → °). To convert gradian to degree, multiply by 0.9. To convert degree to gradian, multiply by 1.111111. The converter at the top does this instantly and both ways; the sections below give the formula, worked examples, a full conversion chart and answers to the most common gradian-to-degree questions.
How to convert Gradian to Degree
To convert gradian to degree, multiply the number of gradian by the conversion factor 0.9, because 1 gon = 0.9°. The conversion is linear, so the same factor works for any value — whole numbers, decimals or fractions. For the reverse direction, 1 ° = 1.111111gon, so you divide by 0.9 (or multiply by 1.111111) to turn degree back into gradian.
° = gon × 0.9 ·
gon = ° × 1.111111
- Write down the value you want to convert, in gradian.
- Multiply it by 0.9.
- The result is the same area/length/quantity expressed in degree.
Gradian to Degree — worked examples
Each row shows the exact arithmetic so you can follow the conversion step by step. For example, 5gradian is 4.5degree because 5 gon × 0.9 = 4.5 °.
| Gradian | Calculation | Degree |
|---|---|---|
| 1gon | 1 gon × 0.9 = 0.9 ° | 0.9° |
| 2gon | 2 gon × 0.9 = 1.8 ° | 1.8° |
| 3gon | 3 gon × 0.9 = 2.7 ° | 2.7° |
| 5gon | 5 gon × 0.9 = 4.5 ° | 4.5° |
| 7gon | 7 gon × 0.9 = 6.3 ° | 6.3° |
| 10gon | 10 gon × 0.9 = 9 ° | 9° |
| 12gon | 12 gon × 0.9 = 10.8 ° | 10.8° |
| 15gon | 15 gon × 0.9 = 13.5 ° | 13.5° |
| 20gon | 20 gon × 0.9 = 18 ° | 18° |
| 25gon | 25 gon × 0.9 = 22.5 ° | 22.5° |
| 50gon | 50 gon × 0.9 = 45 ° | 45° |
| 100gon | 100 gon × 0.9 = 90 ° | 90° |
Common Gradian to Degree conversions
These are the gradian-to-degree values people look up most often. Every figure is computed from the exact factor, so you can rely on them for quick reference:
- 1 gradian = 0.9 degree
- 2 gradian = 1.8 degree
- 2.5 gradian = 2.25 degree
- 3 gradian = 2.7 degree
- 4 gradian = 3.6 degree
- 5 gradian = 4.5 degree
- 6 gradian = 5.4 degree
- 7 gradian = 6.3 degree
- 8 gradian = 7.2 degree
- 9 gradian = 8.1 degree
- 10 gradian = 9 degree
- 12 gradian = 10.8 degree
- 15 gradian = 13.5 degree
- 20 gradian = 18 degree
- 25 gradian = 22.5 degree
- 30 gradian = 27 degree
- 50 gradian = 45 degree
- 75 gradian = 67.5 degree
- 100 gradian = 90 degree
- 200 gradian = 180 degree
- 500 gradian = 450 degree
- 1000 gradian = 900 degree
Gradian to Degree conversion chart (both directions)
The chart below converts gradian to degree and degree to gradian side by side, so it works whichever way you need. 1 gradian = 0.9degree, and 1 degree = 1.111111gradian.
| Gradian → Degree | Degree → Gradian |
|---|---|
| 0.25gon = 0.225° | 0.25° = 0.2777778gon |
| 0.5gon = 0.45° | 0.5° = 0.5555556gon |
| 1gon = 0.9° | 1° = 1.111111gon |
| 2gon = 1.8° | 2° = 2.222222gon |
| 3gon = 2.7° | 3° = 3.333333gon |
| 4gon = 3.6° | 4° = 4.444444gon |
| 5gon = 4.5° | 5° = 5.555556gon |
| 6gon = 5.4° | 6° = 6.666667gon |
| 7gon = 6.3° | 7° = 7.777778gon |
| 8gon = 7.2° | 8° = 8.888889gon |
| 9gon = 8.1° | 9° = 10gon |
| 10gon = 9° | 10° = 11.11111gon |
| 12gon = 10.8° | 12° = 13.33333gon |
| 15gon = 13.5° | 15° = 16.66667gon |
| 20gon = 18° | 20° = 22.22222gon |
| 25gon = 22.5° | 25° = 27.77778gon |
| 30gon = 27° | 30° = 33.33333gon |
| 40gon = 36° | 40° = 44.44444gon |
| 50gon = 45° | 50° = 55.55556gon |
| 75gon = 67.5° | 75° = 83.33333gon |
| 100gon = 90° | 100° = 111.1111gon |
| 150gon = 135° | 150° = 166.6667gon |
| 200gon = 180° | 200° = 222.2222gon |
| 250gon = 225° | 250° = 277.7778gon |
| 500gon = 450° | 500° = 555.5556gon |
| 1000gon = 900° | 1000° = 1,111.111gon |
Gradian vs Degree: which is bigger?
A degree is the larger unit: one degree equals 1.111111 gradians. Put another way, you need 1.111111 gradians to make a single degree.
What is a Gradian? History, origin and usage
The gradian (also called the gon or “grade”) was born of the French Revolution’s drive to decimalise everything, dividing the right angle into 100 parts so a full circle is 400 gradians. Sometimes called the “metric degree,” it was meant to fit the new metric system but never displaced the ordinary degree.
The gradian survives mainly in surveying and some civil-engineering and cartography work in continental Europe, where a right angle being exactly 100 gon simplifies slope and bearing calculations. Many scientific calculators still offer a “grad” mode alongside degrees and radians.
Because a quarter-circle is exactly 100 gradians, the gradian meshes neatly with the percentage conventions surveyors use for gradients. The international name “gon” was adopted to avoid clashing with the German word Grad (degree) in northern Europe.
What is a Degree? History, origin and usage
Dividing a circle into 360 degrees traces back to Babylonian astronomy and its base-60 (sexagesimal) number system, reinforced by the roughly 360-day ancient year in which the Sun seemed to advance about one degree each day. The number 360 was also prized for being divisible by so many factors.
The degree is the everyday angle unit for navigation, geography (latitude and longitude), construction, geometry teaching and most practical measurement. Its symbol is the small raised circle (°), and it subdivides into arcminutes and arcseconds.
360 is unusually divisible — it splits evenly by every whole number from 1 to 10 except 7 — which made it convenient long before modern arithmetic. A full circle is 360°, a right angle is 90°, and a single degree divides into 60 arcminutes.
Convert 1 Gradian to other units
It can help to see a gradian next to the other units it is commonly compared with. One gradian (gon) is equal to:
| 1 Gradian equals | Unit |
|---|---|
| 0.01570796rad | Radian |
| 0.9° | Degree |
| 0.0025turn | Turn |
| 54′ | Arcminute |
| 3,240″ | Arcsecond |
Convert 1 Degree to other units
One degree (°) is equal to:
| 1 Degree equals | Unit |
|---|---|
| 0.01745329rad | Radian |
| 1.111111gon | Gradian |
| 0.002777778turn | Turn |
| 60′ | Arcminute |
| 3,600″ | Arcsecond |
Tips for converting Gradian to Degree
- To go from gradian to degree, multiply by 0.9; to go back, divide by 0.9 (or multiply by 1.111111).
- For a quick mental estimate, remember that 1 gradian ≈ 0.9 degree, so 10 gradian ≈ 9 degree.
- The converter above keeps full precision; the tables round for readability, so use the tool for exact figures.
- Both fields update live as you type — change either side to convert in that direction.
How to use this Gradian to Degree converter
Type a number into the Gradian field and the equivalent in Degree appears instantly — there is no “convert” button to press and nothing is sent to a server, so it works offline once the page has loaded and is safe for any data. You can also type into the Degree field to convert the other way (degree to gradian). Use the swap control to flip the two units, and copy the result with a single click. Because the calculation runs in your browser with full floating-point precision, the converter is more exact than the rounded figures shown in the reference chart above — use the chart for quick look-ups and the tool for precise work.
Accuracy and method
Every figure on this page — the formula, the worked examples, the conversion chart and the “convert to other units” tables — is computed from a single verified conversion factor (1 gon = 0.9°), never copied from a hand-typed lookup table that could drift. That factor is derived from each unit’s definition in terms of a common base unit, and an automated check re-verifies all of the site’s factors on every update, so the numbers here stay correct over time. This matters for gradian-to-degree conversions because a small rounding error in a published table compounds quickly at larger quantities; computing from the exact factor avoids that.
Angle factors are exact, anchored to the radian: a full turn = 2π rad = 360° = 400 gon, 1° = 60 arcminutes, 1 arcminute = 60 arcseconds. So the live tool and every number on this page always agree.
Frequently asked questions
- How many degree are in 1 gradian?
- 1 gradian = 0.9 degree (°). To convert any number of gradian to degree, multiply by 0.9.
- How do I convert gradian to degree?
- Multiply the number of gradian by 0.9. For example, 10 gradian = 10 × 0.9 = 9 degree, and 25 gradian = 22.5 degree.
- How many gradian are in 1 degree?
- 1 degree = 1.111111 gradian. So to convert degree back to gradian, multiply by 1.111111.
- What is the formula to convert gradian to degree?
- degree = gradian × 0.9. The reverse formula is gradian = degree × 1.111111.
- How much is 100 gradian in degree?
- 100 gradian = 90 degree. (And 1000 gradian = 900 degree.)
- Which is bigger, a gradian or a degree?
- A degree is larger: 1 degree = 1.111111 gradian.
- Is this gradian to degree converter accurate?
- Yes — every value is computed from the exact 0.9 ° per gon factor (not rounded look-up tables), and the factors are re-verified automatically on every update.
- Can I convert degree to gradian too?
- Yes. The converter works both ways — enter a value in either field. 1 degree = 1.111111 gradian.