Convert Radians to Arcseconds
1 radian is 206,264.81 ″. One radian is exactly 206264.806247 arcseconds.
One radian is 206264.81 arcseconds. To convert radians to arcseconds, multiply by 206264.81; to go the other way, divide by 206264.81 or multiply by 4.8481 × 10^-6. 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 × 206264.81
1 * 206264.81206,264.806 ″
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 arcseconds? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 206264.81 — that is how many arcseconds fit in one radian.
- 3.To go back the other way, divide by 206264.81, or multiply by 4.8481 × 10^-6.
Worked example: 25 radians to arcseconds
- Formula
- rad × 206264.81 = ″
- Arithmetic
- 25 × 206264.81 = 5,156,620.16 ″
- Answer
- 25 rad = 5,156,620.16 ″
The factor is rounded for display; the figure above is computed from the full value.
Radians to arcseconds conversion table
| Radians | Arcseconds |
|---|---|
| 1 rad | 206,264.81 ″ |
| 2 rad | 412,529.61 ″ |
| 3 rad | 618,794.42 ″ |
| 4 rad | 825,059.22 ″ |
| 5 rad | 1,031,324.03 ″ |
| 6 rad | 1,237,588.84 ″ |
| 7 rad | 1,443,853.64 ″ |
| 8 rad | 1,650,118.45 ″ |
| 9 rad | 1,856,383.26 ″ |
| 10 rad | 2,062,648.06 ″ |
| 12 rad | 2,475,177.67 ″ |
| 15 rad | 3,093,972.09 ″ |
| 20 rad | 4,125,296.12 ″ |
| 25 rad | 5,156,620.16 ″ |
| 50 rad | 10,313,240.31 ″ |
| 100 rad | 20,626,480.62 ″ |
| 200 rad | 41,252,961.25 ″ |
| 300 rad | 61,879,441.87 ″ |
| 500 rad | 103,132,403.12 ″ |
| 1000 rad | 206,264,806.25 ″ |
| 2000 rad | 412,529,612.49 ″ |
| 5000 rad | 1,031,324,031.24 ″ |
| 10000 rad | 2,062,648,062.47 ″ |
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 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 radian?
One radian is 206264.81 arcseconds. Going the other way, one arcsecond is 4.8481 × 10^-6 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 arcseconds. Rule Calculator. https://rulecalculators.com/convert/radian-to-arcsecond
- MLA
- "Convert Radians to arcseconds." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-arcsecond.
- Chicago
- Rule Calculator. "Convert Radians to arcseconds." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-arcsecond.
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Questions people actually ask
- How many arcseconds are in a radian?
- 206264.81. 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 radians?
- Divide by 206264.81, or multiply by 4.8481 × 10^-6 — they are the same operation.
Other angle conversions
Arcseconds to radians — the same conversion the other way.