Convert Arcseconds to Radians
1 arcsecond is 0.000004848 rad. One arcsecond is exactly 0.0000048481368111 radians.
One arcsecond is 4.8481 × 10^-6 radians. To convert arcseconds to radians, multiply by 4.8481 × 10^-6; to go the other way, divide by 4.8481 × 10^-6 or multiply by 206264.81. 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 × 4.8481 × 10^-6
1 * 0.00000480 rad
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 radians? The converter and the working
- 1.Take the measurement in arcseconds.
- 2.Multiply by 4.8481 × 10^-6 — that is how many radians fit in one arcsecond.
- 3.To go back the other way, divide by 4.8481 × 10^-6, or multiply by 206264.81.
Worked example: 25 arcseconds to radians
- Formula
- ″ × 4.8481 × 10^-6 = rad
- Arithmetic
- 25 × 4.8481 × 10^-6 = 0.0001212 rad
- Answer
- 25 ″ = 0.0001212 rad
The factor is rounded for display; the figure above is computed from the full value.
Arcseconds to radians conversion table
| Arcseconds | Radians |
|---|---|
| 1 ″ | 0.000004848 rad |
| 2 ″ | 0.000009696 rad |
| 3 ″ | 0.00001454 rad |
| 4 ″ | 0.00001939 rad |
| 5 ″ | 0.00002424 rad |
| 6 ″ | 0.00002909 rad |
| 7 ″ | 0.00003394 rad |
| 8 ″ | 0.00003879 rad |
| 9 ″ | 0.00004363 rad |
| 10 ″ | 0.00004848 rad |
| 12 ″ | 0.00005818 rad |
| 15 ″ | 0.00007272 rad |
| 20 ″ | 0.00009696 rad |
| 25 ″ | 0.0001212 rad |
| 50 ″ | 0.0002424 rad |
| 100 ″ | 0.0004848 rad |
| 200 ″ | 0.0009696 rad |
| 300 ″ | 0.001454 rad |
| 500 ″ | 0.002424 rad |
| 1000 ″ | 0.004848 rad |
| 2000 ″ | 0.01 rad |
| 5000 ″ | 0.02 rad |
| 10000 ″ | 0.05 rad |
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 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 an arcsecond?
One arcsecond is 4.8481 × 10^-6 radians. Going the other way, one radian is 206264.81 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 radians. Rule Calculator. https://rulecalculators.com/convert/arcsecond-to-radian
- MLA
- "Convert Arcseconds to radians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/arcsecond-to-radian.
- Chicago
- Rule Calculator. "Convert Arcseconds to radians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/arcsecond-to-radian.
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Questions people actually ask
- How many radians are in an arcsecond?
- 4.8481 × 10^-6. 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 arcseconds?
- Divide by 4.8481 × 10^-6, or multiply by 206264.81 — they are the same operation.
Other angle conversions
Radians to arcseconds — the same conversion the other way.