Convert Gradians to Arcseconds
1 gradian is 3,240 ″. One gradian is exactly 3240 arcseconds.
One gradian is 3240 arcseconds. To convert gradians to arcseconds, multiply by 3240; to go the other way, divide by 3240 or multiply by 3.0864 × 10^-4. 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 × 3240
1 * 32403,240 ″
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 arcseconds? The converter and the working
- 1.Take the measurement in gradians.
- 2.Multiply by 3240 — that is how many arcseconds fit in one gradian.
- 3.To go back the other way, divide by 3240, or multiply by 3.0864 × 10^-4.
Worked example: 25 gradians to arcseconds
- Formula
- gon × 3240 = ″
- Arithmetic
- 25 × 3240 = 81,000 ″
- Answer
- 25 gon = 81,000 ″
The factor is exact, so this figure is exact too — only the display is rounded.
Gradians to arcseconds conversion table
| Gradians | Arcseconds |
|---|---|
| 1 gon | 3,240 ″ |
| 2 gon | 6,480 ″ |
| 3 gon | 9,720 ″ |
| 4 gon | 12,960 ″ |
| 5 gon | 16,200 ″ |
| 6 gon | 19,440 ″ |
| 7 gon | 22,680 ″ |
| 8 gon | 25,920 ″ |
| 9 gon | 29,160 ″ |
| 10 gon | 32,400 ″ |
| 12 gon | 38,880 ″ |
| 15 gon | 48,600 ″ |
| 20 gon | 64,800 ″ |
| 25 gon | 81,000 ″ |
| 50 gon | 162,000 ″ |
| 100 gon | 324,000 ″ |
| 200 gon | 648,000 ″ |
| 300 gon | 972,000 ″ |
| 500 gon | 1,620,000 ″ |
| 1000 gon | 3,240,000 ″ |
| 2000 gon | 6,480,000 ″ |
| 5000 gon | 16,200,000 ″ |
| 10000 gon | 32,400,000 ″ |
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 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.
How many arcseconds are in a gradian?
One gradian is 3240 arcseconds, exactly. Going the other way, one arcsecond is 3.0864 × 10^-4 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 arcseconds. Rule Calculator. https://rulecalculators.com/convert/gradian-to-arcsecond
- MLA
- "Convert Gradians to arcseconds." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/gradian-to-arcsecond.
- Chicago
- Rule Calculator. "Convert Gradians to arcseconds." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/gradian-to-arcsecond.
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Questions people actually ask
- How many arcseconds are in a gradian?
- 3240. 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.
- How do I convert arcseconds back to gradians?
- Divide by 3240, or multiply by 3.0864 × 10^-4 — they are the same operation.
Other angle conversions
Arcseconds to gradians — the same conversion the other way.