Radians to Seconds of Arc Converter

Enter the angle in radians below to get the value converted to seconds of arc. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

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Result in Seconds of Arc:

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1 rad = 206,264.806247 arcsec

Do you want to convert seconds of arc to radians?

How to Convert Radians to Seconds of Arc

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To convert a measurement in radians to a measurement in seconds of arc, multiply the angle by the following conversion ratio: 206,264.806247 seconds of arc/radian.

Since one radian is equal to 206,264.806247 seconds of arc, you can use this simple formula to convert:

seconds of arc = radians × 206,264.806247

The angle in seconds of arc is equal to the angle in radians multiplied by 206,264.806247.

For example, here's how to convert 5 radians to seconds of arc using the formula above.
seconds of arc = (5 rad × 206,264.806247) = 1,031,324.031235"

How Many Seconds of Arc Are in a Radian?

There are 206,264.806247 seconds of arc in a radian, which is why we use this value in the formula above.

1 rad = 206,264.806247"

Radians and seconds of arc are both units used to measure angle. Keep reading to learn more about each unit of measure.

What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π degrees, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.

Radians are often expressed using their definition. The formula to find an angle in radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

Learn more about radians.

What Is a Second of Arc?

The second of arc is a unit of angle equal to 1/60th of one minute of arc or 1/3,600 of one degree.

A second of arc is sometimes also referred to as an arc second or arcsecond. Seconds of arc can be abbreviated as arcsec, and are also sometimes abbreviated as asec. For example, 1 second of arc can be written as 1 arcsec or 1 asec.

The second of arc is most commonly expressed using a double prime (″), though a double quote is often used as well. For example, 1 second of arc is most often written as 1″.

Learn more about seconds of arc.

Radian to Second of Arc Conversion Table

Table showing various radian measurements converted to seconds of arc.
Radians Seconds Of Arc
0.00001 rad 2.0626"
0.00002 rad 4.1253"
0.00003 rad 6.1879"
0.00004 rad 8.2506"
0.00005 rad 10.31"
0.00006 rad 12.38"
0.00007 rad 14.44"
0.00008 rad 16.5"
0.00009 rad 18.56"
0.000001 rad 0.206265"
0.00001 rad 2.0626"
0.0001 rad 20.63"
0.001 rad 206.26"
0.01 rad 2,063"
0.1 rad 20,626"
1 rad 206,265"

References

  1. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf

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