Convert Degree to Gradian
1 degree = 1.111111 gradian (gon). For example, 10 degree = 11.11111 gradian and 100 degree = 111.1111 gradian. Type any value below to convert degree to gradian both ways — it runs entirely in your browser.
Quick answer: Degree to Gradian
1 Degree = 1.111111Gradian (° → gon). To convert degree to gradian, multiply by 1.111111. To convert gradian to degree, multiply by 0.9. 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 degree-to-gradian questions.
How to convert Degree to Gradian
To convert degree to gradian, multiply the number of degree by the conversion factor 1.111111, because 1 ° = 1.111111gon. The conversion is linear, so the same factor works for any value — whole numbers, decimals or fractions. For the reverse direction, 1 gon = 0.9°, so you divide by 1.111111 (or multiply by 0.9) to turn gradian back into degree.
gon = ° × 1.111111 ·
° = gon × 0.9
- Write down the value you want to convert, in degree.
- Multiply it by 1.111111.
- The result is the same area/length/quantity expressed in gradian.
Degree to Gradian — worked examples
Each row shows the exact arithmetic so you can follow the conversion step by step. For example, 5degree is 5.555556gradian because 5 ° × 1.111111 = 5.555556 gon.
| Degree | Calculation | Gradian |
|---|---|---|
| 1° | 1 ° × 1.111111 = 1.111111 gon | 1.111111gon |
| 2° | 2 ° × 1.111111 = 2.222222 gon | 2.222222gon |
| 3° | 3 ° × 1.111111 = 3.333333 gon | 3.333333gon |
| 5° | 5 ° × 1.111111 = 5.555556 gon | 5.555556gon |
| 7° | 7 ° × 1.111111 = 7.777778 gon | 7.777778gon |
| 10° | 10 ° × 1.111111 = 11.11111 gon | 11.11111gon |
| 12° | 12 ° × 1.111111 = 13.33333 gon | 13.33333gon |
| 15° | 15 ° × 1.111111 = 16.66667 gon | 16.66667gon |
| 20° | 20 ° × 1.111111 = 22.22222 gon | 22.22222gon |
| 25° | 25 ° × 1.111111 = 27.77778 gon | 27.77778gon |
| 50° | 50 ° × 1.111111 = 55.55556 gon | 55.55556gon |
| 100° | 100 ° × 1.111111 = 111.1111 gon | 111.1111gon |
Common Degree to Gradian conversions
These are the degree-to-gradian values people look up most often. Every figure is computed from the exact factor, so you can rely on them for quick reference:
- 1 degree = 1.111111 gradian
- 2 degree = 2.222222 gradian
- 2.5 degree = 2.777778 gradian
- 3 degree = 3.333333 gradian
- 4 degree = 4.444444 gradian
- 5 degree = 5.555556 gradian
- 6 degree = 6.666667 gradian
- 7 degree = 7.777778 gradian
- 8 degree = 8.888889 gradian
- 9 degree = 10 gradian
- 10 degree = 11.11111 gradian
- 12 degree = 13.33333 gradian
- 15 degree = 16.66667 gradian
- 20 degree = 22.22222 gradian
- 25 degree = 27.77778 gradian
- 30 degree = 33.33333 gradian
- 50 degree = 55.55556 gradian
- 75 degree = 83.33333 gradian
- 100 degree = 111.1111 gradian
- 200 degree = 222.2222 gradian
- 500 degree = 555.5556 gradian
- 1000 degree = 1,111.111 gradian
Degree to Gradian conversion chart (both directions)
The chart below converts degree to gradian and gradian to degree side by side, so it works whichever way you need. 1 degree = 1.111111gradian, and 1 gradian = 0.9degree.
| Degree → Gradian | Gradian → Degree |
|---|---|
| 0.25° = 0.2777778gon | 0.25gon = 0.225° |
| 0.5° = 0.5555556gon | 0.5gon = 0.45° |
| 1° = 1.111111gon | 1gon = 0.9° |
| 2° = 2.222222gon | 2gon = 1.8° |
| 3° = 3.333333gon | 3gon = 2.7° |
| 4° = 4.444444gon | 4gon = 3.6° |
| 5° = 5.555556gon | 5gon = 4.5° |
| 6° = 6.666667gon | 6gon = 5.4° |
| 7° = 7.777778gon | 7gon = 6.3° |
| 8° = 8.888889gon | 8gon = 7.2° |
| 9° = 10gon | 9gon = 8.1° |
| 10° = 11.11111gon | 10gon = 9° |
| 12° = 13.33333gon | 12gon = 10.8° |
| 15° = 16.66667gon | 15gon = 13.5° |
| 20° = 22.22222gon | 20gon = 18° |
| 25° = 27.77778gon | 25gon = 22.5° |
| 30° = 33.33333gon | 30gon = 27° |
| 40° = 44.44444gon | 40gon = 36° |
| 50° = 55.55556gon | 50gon = 45° |
| 75° = 83.33333gon | 75gon = 67.5° |
| 100° = 111.1111gon | 100gon = 90° |
| 150° = 166.6667gon | 150gon = 135° |
| 200° = 222.2222gon | 200gon = 180° |
| 250° = 277.7778gon | 250gon = 225° |
| 500° = 555.5556gon | 500gon = 450° |
| 1000° = 1,111.111gon | 1000gon = 900° |
Degree vs Gradian: 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 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.
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.
Convert 1 Degree to other units
It can help to see a degree next to the other units it is commonly compared with. One degree (°) is equal to:
| 1 Degree equals | Unit |
|---|---|
| 0.01745329rad | Radian |
| 1.111111gon | Gradian |
| 0.002777778turn | Turn |
| 60′ | Arcminute |
| 3,600″ | Arcsecond |
Convert 1 Gradian to other units
One gradian (gon) is equal to:
| 1 Gradian equals | Unit |
|---|---|
| 0.01570796rad | Radian |
| 0.9° | Degree |
| 0.0025turn | Turn |
| 54′ | Arcminute |
| 3,240″ | Arcsecond |
Tips for converting Degree to Gradian
- To go from degree to gradian, multiply by 1.111111; to go back, divide by 1.111111 (or multiply by 0.9).
- For a quick mental estimate, remember that 1 degree ≈ 1.111111 gradian, so 10 degree ≈ 11.11111 gradian.
- 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 Degree to Gradian converter
Type a number into the Degree field and the equivalent in Gradian 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 Gradian field to convert the other way (gradian to degree). 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 ° = 1.111111gon), 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 degree-to-gradian 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 gradian are in 1 degree?
- 1 degree = 1.111111 gradian (gon). To convert any number of degree to gradian, multiply by 1.111111.
- How do I convert degree to gradian?
- Multiply the number of degree by 1.111111. For example, 10 degree = 10 × 1.111111 = 11.11111 gradian, and 25 degree = 27.77778 gradian.
- How many degree are in 1 gradian?
- 1 gradian = 0.9 degree. So to convert gradian back to degree, multiply by 0.9.
- What is the formula to convert degree to gradian?
- gradian = degree × 1.111111. The reverse formula is degree = gradian × 0.9.
- How much is 100 degree in gradian?
- 100 degree = 111.1111 gradian. (And 1000 degree = 1,111.111 gradian.)
- Which is bigger, a degree or a gradian?
- A degree is larger: 1 degree = 1.111111 gradian.
- Is this degree to gradian converter accurate?
- Yes — every value is computed from the exact 1.111111 gon per ° factor (not rounded look-up tables), and the factors are re-verified automatically on every update.
- Can I convert gradian to degree too?
- Yes. The converter works both ways — enter a value in either field. 1 gradian = 0.9 degree.