arcseconds to radians | Exact Decimal + Formula
1 Arcsecond = 0.000005 Radian
One radian equals about 206.3 thousand arcseconds (exactly 206264.8062 arcsec). Real-world use: astronomical measurements of star positions and telescope resolution. This page expresses those values in radians, which is used for calculus, physics, and programming trigonometry functions. Type a value above for an instant answer; the exact formula and the reference table are below.
About Arcsecond and Radian
Arcsecond (arcsec)
An arcsecond is 1/3,600 of a degree.
Where it's used: Astronomical measurements of star positions and telescope resolution.
Radian (rad)
A radian is the angle subtended by an arc equal to the circle's radius; a full circle is 2π radians.
Where it's used: Calculus, physics, and programming trigonometry functions.
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Formula
rad = arcsec × 4.848137e-6
To convert Arcsecond to Radian, use the formula displayed above.
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Arcsecond to Radian: Quick Reference Table
| Arcsecond | Radian (Decimal) | Fraction |
|---|---|---|
| 0.001 arcsec | 4.8481e-9 rad | - |
| 0.01 arcsec | 4.8481e-8 rad | - |
| 0.1 arcsec | 4.8481e-7 rad | - |
| 0.5 arcsec | 0.000002 rad | - |
| 1 arcsec | 0.000005 rad | - |
| 2 arcsec | 0.00001 rad | - |
| 5 arcsec | 0.000024 rad | - |
| 10 arcsec | 0.000048 rad | - |
| 25 arcsec | 0.000121 rad | - |
| 50 arcsec | 0.000242 rad | - |
| 100 arcsec | 0.000485 rad | - |
| 250 arcsec | 0.001212 rad | - |
| 500 arcsec | 0.002424 rad | - |
| 1000 arcsec | 0.004848 rad | - |
arcsec to rad Formula and Examples
Direct Formula
rad = arcsec × 4.848137e-6 Inverse Formula
arcsec = rad × 206264.806247 Mental Math Shortcut
Divide the value by roughly 206264.8 to quickly estimate the converted result.
Common Arcsecond to Radian Calculations
- 5 arcsec = 0.000024 rad
- 10 arcsec = 0.000048 rad
- 50 arcsec = 0.000242 rad
- 100 arcsec = 0.000485 rad
- 500 arcsec = 0.002424 rad
Precision & Practical Use
For example, 10 arcsec = 0.000048 rad — roughly fractional unit measurement.
Results are computed to up to 9 decimal places. Round to the precision of your measuring instrument — for most angle applications, 2–3 significant figures are plenty.
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How to Convert Arcsecond to Radian
How many radians are in one arcsecond?
One Arcsecond (arcsec) equals 0.000005 Radian (rad). To convert arcseconds to radians, multiply the arcsecond value by 0.000005.
How do I convert Arcsecond to Radian?
Multiply your arcsecond value by 0.000005 to get the result in Radian: rad = arcsec × 0.000005. For example, 5 arcsec = 0.000024 rad.
What is the formula for converting arcsec to rad?
The conversion formula is rad = arcsec × 0.000005. Use the calculator above for any value, and see the reference table below for common inputs from 0.001 to 1000.
Is there a quick mental estimate for arcsec to rad?
Divide the value by roughly 206264.8 to quickly estimate the converted result.
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