Convert Arcseconds to Gradians
1 arcsecond is 0.0003086 gon. One arcsecond is exactly 0.000308641975309 gradians.
One arcsecond is 3.0864 × 10^-4 gradians. To convert arcseconds to gradians, multiply by 3.0864 × 10^-4; to go the other way, divide by 3.0864 × 10^-4 or multiply by 3240. 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 3,600th of a degree.
Factor checked against the defining standard · How we check
- Arcseconds × 3.0864 × 10^-4
1 * 0.00030860 gon
1 arcsecond in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.000004848136811 rad | × 0.0000048481368111 |
| degrees | 0.0002777777778 ° | × 0.000277777777778 |
| gradians | 0.0003086419753 gon | × 0.000308641975309 |
| arcminutes | 0.01666666667 ′ | × 0.0166666666667 |
| arcseconds (as entered) | 1 ″ | — |
| turns | 0.0000007716049383 turn | × 0.000000771604938272 |
| milliradians | 0.004848136811 mrad | × 0.0048481368111 |
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 arcseconds to gradians? The converter and the working
- 1.Take the measurement in arcseconds.
- 2.Multiply by 3.0864 × 10^-4 — that is how many gradians fit in one arcsecond.
- 3.To go back the other way, divide by 3.0864 × 10^-4, or multiply by 3240.
Worked example: 25 arcseconds to gradians
- Formula
- ″ × 3.0864 × 10^-4 = gon
- Arithmetic
- 25 × 3.0864 × 10^-4 = 0.01 gon
- Answer
- 25 ″ = 0.01 gon
The factor is rounded for display; the figure above is computed from the full value.
Arcseconds to gradians conversion table
| Arcseconds | Gradians |
|---|---|
| 1 ″ | 0.0003086 gon |
| 2 ″ | 0.0006173 gon |
| 3 ″ | 0.0009259 gon |
| 4 ″ | 0.001235 gon |
| 5 ″ | 0.001543 gon |
| 6 ″ | 0.001852 gon |
| 7 ″ | 0.00216 gon |
| 8 ″ | 0.002469 gon |
| 9 ″ | 0.002778 gon |
| 10 ″ | 0.003086 gon |
| 12 ″ | 0.003704 gon |
| 15 ″ | 0.00463 gon |
| 20 ″ | 0.01 gon |
| 25 ″ | 0.01 gon |
| 50 ″ | 0.02 gon |
| 100 ″ | 0.03 gon |
| 200 ″ | 0.06 gon |
| 300 ″ | 0.09 gon |
| 500 ″ | 0.15 gon |
| 1000 ″ | 0.31 gon |
| 2000 ″ | 0.62 gon |
| 5000 ″ | 1.54 gon |
| 10000 ″ | 3.09 gon |
What is an arcsecond?
A 3,600th of a degree. Stellar parallax is measured in these: a star one arcsecond of parallax away is one parsec from Earth, which is where the name comes from.
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 an arcsecond?
One arcsecond is 3.0864 × 10^-4 gradians. Going the other way, one gradian is 3240 arcseconds. 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 an arcsecond.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Arcseconds to gradians. Rule Calculator. https://rulecalculators.com/convert/arcsecond-to-gradian
- MLA
- "Convert Arcseconds to gradians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/arcsecond-to-gradian.
- Chicago
- Rule Calculator. "Convert Arcseconds to gradians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/arcsecond-to-gradian.
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Questions people actually ask
- How many gradians are in an arcsecond?
- 3.0864 × 10^-4. 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 arcseconds?
- Divide by 3.0864 × 10^-4, or multiply by 3240 — they are the same operation.
Other angle conversions
Gradians to arcseconds — the same conversion the other way.