Convert Gradians to Degrees
1 gradian is 0.9 °. One gradian is exactly 0.9 degrees.
One gradian is 0.9 degrees. To convert gradians to degrees, multiply by 0.9; to go the other way, divide by 0.9 or multiply by 1.1111111. The factor is exact rather than rounded: it follows from NIST Special Publication 811. A 400th of a turn, so a right angle is exactly 100.
Factor checked against the defining standard · How we check
- Gradians × 0.9
1 * 0.90.9 °
1 gradian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.01570796327 rad | × 0.0157079632679 |
| degrees | 0.9 ° | × 0.9 |
| gradians (as entered) | 1 gon | — |
| arcminutes | 54 ′ | × 54 |
| arcseconds | 3,240 ″ | × 3,240 |
| turns | 0.0025 turn | × 0.0025 |
| milliradians | 15.70796327 mrad | × 15.7079632679 |
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 gradians to degrees? The converter and the working
- 1.Take the measurement in gradians.
- 2.Multiply by 0.9 — that is how many degrees fit in one gradian.
- 3.To go back the other way, divide by 0.9, or multiply by 1.1111111.
Worked example: 25 gradians to degrees
- Formula
- gon × 0.9 = °
- Arithmetic
- 25 × 0.9 = 22.5 °
- Answer
- 25 gon = 22.5 °
The factor is exact, so this figure is exact too — only the display is rounded.
Gradians to degrees conversion table
| Gradians | Degrees |
|---|---|
| 1 gon | 0.9 ° |
| 2 gon | 1.8 ° |
| 3 gon | 2.7 ° |
| 4 gon | 3.6 ° |
| 5 gon | 4.5 ° |
| 6 gon | 5.4 ° |
| 7 gon | 6.3 ° |
| 8 gon | 7.2 ° |
| 9 gon | 8.1 ° |
| 10 gon | 9 ° |
| 12 gon | 10.8 ° |
| 15 gon | 13.5 ° |
| 20 gon | 18 ° |
| 25 gon | 22.5 ° |
| 50 gon | 45 ° |
| 100 gon | 90 ° |
| 200 gon | 180 ° |
| 300 gon | 270 ° |
| 500 gon | 450 ° |
| 1000 gon | 900 ° |
| 2000 gon | 1,800 ° |
| 5000 gon | 4,500 ° |
| 10000 gon | 9,000 ° |
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 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.
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.
How many degrees are in a gradian?
One gradian is 0.9 degrees, exactly. Going the other way, one degree is 1.1111111 gradians. 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 gradian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Gradians to degrees. Rule Calculator. https://rulecalculators.com/convert/gradian-to-degree
- MLA
- "Convert Gradians to degrees." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/gradian-to-degree.
- Chicago
- Rule Calculator. "Convert Gradians to degrees." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/gradian-to-degree.
The date is when the figures on this page were last checked against their source, not the day you opened it. Add your own access date if your style needs one.
Questions people actually ask
- How many degrees are in a gradian?
- 0.9. 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.
- How do I convert degrees back to gradians?
- Divide by 0.9, or multiply by 1.1111111 — they are the same operation.
Other angle conversions
Degrees to gradians — the same conversion the other way.