Convert Gradians to Radians
1 gradian is 0.02 rad. One gradian is exactly 0.0157079632679 radians.
One gradian is 0.015707963 radians. To convert gradians to radians, multiply by 0.015707963; to go the other way, divide by 0.015707963 or multiply by 63.661977. 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 400th of a turn, so a right angle is exactly 100.
Factor checked against the defining standard · How we check
- Gradians × 0.015707963
1 * 0.0157080.016 rad
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 radians? The converter and the working
- 1.Take the measurement in gradians.
- 2.Multiply by 0.015707963 — that is how many radians fit in one gradian.
- 3.To go back the other way, divide by 0.015707963, or multiply by 63.661977.
Worked example: 25 gradians to radians
- Formula
- gon × 0.015707963 = rad
- Arithmetic
- 25 × 0.015707963 = 0.39 rad
- Answer
- 25 gon = 0.39 rad
The factor is rounded for display; the figure above is computed from the full value.
Gradians to radians conversion table
| Gradians | Radians |
|---|---|
| 1 gon | 0.02 rad |
| 2 gon | 0.03 rad |
| 3 gon | 0.05 rad |
| 4 gon | 0.06 rad |
| 5 gon | 0.08 rad |
| 6 gon | 0.09 rad |
| 7 gon | 0.11 rad |
| 8 gon | 0.13 rad |
| 9 gon | 0.14 rad |
| 10 gon | 0.16 rad |
| 12 gon | 0.19 rad |
| 15 gon | 0.24 rad |
| 20 gon | 0.31 rad |
| 25 gon | 0.39 rad |
| 50 gon | 0.79 rad |
| 100 gon | 1.57 rad |
| 200 gon | 3.14 rad |
| 300 gon | 4.71 rad |
| 500 gon | 7.85 rad |
| 1000 gon | 15.71 rad |
| 2000 gon | 31.42 rad |
| 5000 gon | 78.54 rad |
| 10000 gon | 157.08 rad |
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 radian?
The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
How many radians are in a gradian?
One gradian is 0.015707963 radians. Going the other way, one radian is 63.661977 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 radians. Rule Calculator. https://rulecalculators.com/convert/gradian-to-radian
- MLA
- "Convert Gradians to radians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/gradian-to-radian.
- Chicago
- Rule Calculator. "Convert Gradians to radians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/gradian-to-radian.
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 radians are in a gradian?
- 0.015707963. The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
- How do I convert radians back to gradians?
- Divide by 0.015707963, or multiply by 63.661977 — they are the same operation.
Other angle conversions
Radians to gradians — the same conversion the other way.