radians to arcseconds | Exact Decimal + Formula
1 Radian = 206264.806247 Arcsecond
One radian equals about 206.3 thousand arcseconds (exactly 206264.8062 arcsec). Real-world use: calculus, physics, and programming trigonometry functions. This page expresses those values in arcseconds, which is used for astronomical measurements of star positions and telescope resolution. Type a value above for an instant answer; the exact formula and the reference table are below.
About Radian and Arcsecond
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.
Arcsecond (arcsec)
An arcsecond is 1/3,600 of a degree.
Where it's used: Astronomical measurements of star positions and telescope resolution.
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Formula
arcsec = rad × 206264.806247096
To convert Radian to Arcsecond, use the formula displayed above.
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Radian to Arcsecond: Quick Reference Table
| Radian | Arcsecond (Decimal) | Fraction |
|---|---|---|
| 0.001 rad | 206.264806 arcsec | - |
| 0.01 rad | 2062.648062 arcsec | - |
| 0.1 rad | 20626.480625 arcsec | - |
| 0.5 rad | 103132.403124 arcsec | - |
| 1 rad | 206264.806247 arcsec | - |
| 2 rad | 412529.612494 arcsec | - |
| 5 rad | 1031324.031235 arcsec | - |
| 10 rad | 2062648.062471 arcsec | - |
| 25 rad | 5156620.156177 arcsec | - |
| 50 rad | 10313240.312355 arcsec | - |
| 100 rad | 20626480.62471 arcsec | - |
| 250 rad | 51566201.561774 arcsec | - |
| 500 rad | 103132403.123548 arcsec | - |
| 1000 rad | 206264806.247096 arcsec | - |
rad to arcsec Formula and Examples
Direct Formula
arcsec = rad × 206264.806247096 Inverse Formula
rad = arcsec × 0.000005 Mental Math Shortcut
Multiply the value by roughly 206264.8 to calculate the equivalent amount in your head.
Common Radian to Arcsecond Calculations
- 5 rad = 1031324.031235 arcsec
- 10 rad = 2062648.062471 arcsec
- 50 rad = 10313240.312355 arcsec
- 100 rad = 20626480.62471 arcsec
- 500 rad = 103132403.123548 arcsec
Precision & Practical Use
For example, 10 rad = 2062648.062471 arcsec — roughly multiple unit increments.
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 Radian to Arcsecond
How many arcseconds are in one radian?
One Radian (rad) equals 206264.806247 Arcsecond (arcsec). To convert radians to arcseconds, multiply the radian value by 206264.806247.
How do I convert Radian to Arcsecond?
Multiply your radian value by 206264.806247 to get the result in Arcsecond: arcsec = rad × 206264.806247. For example, 5 rad = 1031324.031235 arcsec.
What is the formula for converting rad to arcsec?
The conversion formula is arcsec = rad × 206264.806247. 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 rad to arcsec?
Multiply the value by roughly 206264.8 to calculate the equivalent amount in your head.
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