Convert Radians to Gradians
1 radian is 63.66 gon. One radian is exactly 63.6619772368 gradians.
One radian is 63.661977 gradians. To convert radians to gradians, multiply by 63.661977; to go the other way, divide by 63.661977 or multiply by 0.015707963. 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. The angle subtending an arc equal to the radius.
Factor checked against the defining standard · How we check
- Radians × 63.661977
1 * 63.66197763.662 gon
1 radian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians (as entered) | 1 rad | — |
| degrees | 57.29577951 ° | × 57.2957795131 |
| gradians | 63.66197724 gon | × 63.6619772368 |
| arcminutes | 3,437.746771 ′ | × 3,437.74677078 |
| arcseconds | 206,264.8062 ″ | × 206,264.806247 |
| turns | 0.1591549431 turn | × 0.159154943092 |
| milliradians | 1,000 mrad | × 1,000 |
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 radians to gradians? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 63.661977 — that is how many gradians fit in one radian.
- 3.To go back the other way, divide by 63.661977, or multiply by 0.015707963.
Worked example: 25 radians to gradians
- Formula
- rad × 63.661977 = gon
- Arithmetic
- 25 × 63.661977 = 1,591.55 gon
- Answer
- 25 rad = 1,591.55 gon
The factor is rounded for display; the figure above is computed from the full value.
Radians to gradians conversion table
| Radians | Gradians |
|---|---|
| 1 rad | 63.66 gon |
| 2 rad | 127.32 gon |
| 3 rad | 190.99 gon |
| 4 rad | 254.65 gon |
| 5 rad | 318.31 gon |
| 6 rad | 381.97 gon |
| 7 rad | 445.63 gon |
| 8 rad | 509.3 gon |
| 9 rad | 572.96 gon |
| 10 rad | 636.62 gon |
| 12 rad | 763.94 gon |
| 15 rad | 954.93 gon |
| 20 rad | 1,273.24 gon |
| 25 rad | 1,591.55 gon |
| 50 rad | 3,183.1 gon |
| 100 rad | 6,366.2 gon |
| 200 rad | 12,732.4 gon |
| 300 rad | 19,098.59 gon |
| 500 rad | 31,830.99 gon |
| 1000 rad | 63,661.98 gon |
| 2000 rad | 127,323.95 gon |
| 5000 rad | 318,309.89 gon |
| 10000 rad | 636,619.77 gon |
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.
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 radian?
One radian is 63.661977 gradians. Going the other way, one gradian is 0.015707963 radians. 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 radian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Radians to gradians. Rule Calculator. https://rulecalculators.com/convert/radian-to-gradian
- MLA
- "Convert Radians to gradians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-gradian.
- Chicago
- Rule Calculator. "Convert Radians to gradians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-gradian.
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 gradians are in a radian?
- 63.661977. 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 radians?
- Divide by 63.661977, or multiply by 0.015707963 — they are the same operation.
Other angle conversions
Gradians to radians — the same conversion the other way.