Convert Degrees to Gradians
1 degree is 1.11 gon. One degree is exactly 1.11111111111 gradians.
One degree is 1.1111111 gradians. To convert degrees to gradians, multiply by 1.1111111; to go the other way, divide by 1.1111111 or multiply by 0.9. The relation is exact but the figure is not: it is a rounding of a number that does not terminate, and it follows from NIST Special Publication 811. A 360th of a full turn, inherited from Babylonian astronomy and its base-60 arithmetic.
Factor checked against the defining standard · How we check
- Degrees × 1.1111111
1 * 1.11111111.111 gon
1 degree in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.01745329252 rad | × 0.0174532925199 |
| degrees (as entered) | 1 ° | — |
| gradians | 1.111111111 gon | × 1.11111111111 |
| arcminutes | 60 ′ | × 60 |
| arcseconds | 3,600 ″ | × 3,600 |
| turns | 0.002777777778 turn | × 0.00277777777778 |
| milliradians | 17.45329252 mrad | × 17.4532925199 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert degrees to gradians? The converter and the working
- 1.Take the measurement in degrees.
- 2.Multiply by 1.1111111 — that is how many gradians fit in one degree.
- 3.To go back the other way, divide by 1.1111111, or multiply by 0.9.
Worked example: 25 degrees to gradians
- Formula
- ° × 1.1111111 = gon
- Arithmetic
- 25 × 1.1111111 = 27.78 gon
- Answer
- 25 ° = 27.78 gon
The factor is rounded for display; the figure above is computed from the full value.
Degrees to gradians conversion table
| Degrees | Gradians |
|---|---|
| 1 ° | 1.11 gon |
| 2 ° | 2.22 gon |
| 3 ° | 3.33 gon |
| 4 ° | 4.44 gon |
| 5 ° | 5.56 gon |
| 6 ° | 6.67 gon |
| 7 ° | 7.78 gon |
| 8 ° | 8.89 gon |
| 9 ° | 10 gon |
| 10 ° | 11.11 gon |
| 12 ° | 13.33 gon |
| 15 ° | 16.67 gon |
| 20 ° | 22.22 gon |
| 25 ° | 27.78 gon |
| 50 ° | 55.56 gon |
| 100 ° | 111.11 gon |
| 200 ° | 222.22 gon |
| 300 ° | 333.33 gon |
| 500 ° | 555.56 gon |
| 1000 ° | 1,111.11 gon |
| 2000 ° | 2,222.22 gon |
| 5000 ° | 5,555.56 gon |
| 10000 ° | 11,111.11 gon |
A right angle is 100 gradians, not 90
The gradian divides a full turn into 400 rather than 360, so a right angle is exactly 100 and the factor to degrees is 0.9. It was the metric system’s attempt on the circle, and it survives in European surveying and in the GRAD mode on a calculator — which is the usual reason a trigonometry answer comes out wrong by a factor nobody can find.
NIST Special Publication 811 — Guide for the Use of the International System of Units
What is a degree?
A 360th of a full turn, inherited from Babylonian astronomy and its base-60 arithmetic. 360 survives because it divides evenly by everything from 2 to 12 except 7.
What is a gradian?
A 400th of a turn, so a right angle is exactly 100. Invented with the metric system and still used in European surveying and on calculators with a GRAD mode nobody means to press.
How many gradians are in a degree?
One degree is 1.1111111 gradians. Going the other way, one gradian is 0.9 degrees. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to a degree.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Degrees to gradians. Rule Calculator. https://rulecalculators.com/convert/degree-to-gradian
- MLA
- "Convert Degrees to gradians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/degree-to-gradian.
- Chicago
- Rule Calculator. "Convert Degrees to gradians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/degree-to-gradian.
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Questions people actually ask
- How many gradians are in a degree?
- 1.1111111. A 400th of a turn, so a right angle is exactly 100. Invented with the metric system and still used in European surveying and on calculators with a GRAD mode nobody means to press.
- How do I convert gradians back to degrees?
- Divide by 1.1111111, or multiply by 0.9 — they are the same operation.
Other angle conversions
Gradians to degrees — the same conversion the other way.