Seconds of Arc to Radians Converter

Enter the angle in seconds of arc below to get the value converted to radians.

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Result in Radians:

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1 arcsec = 4.8481E-6 rad
Hint: use a scientific notation calculator to convert E notation to decimal

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How to Convert Seconds of Arc to Radians

To convert a measurement in seconds of arc to a measurement in radians, multiply the angle by the following conversion ratio: 4.8481E-6 radians/second of arc.

Since one second of arc is equal to 4.8481E-6 radians, you can use this simple formula to convert:

radians = seconds of arc × 4.8481E-6

The angle in radians is equal to the angle in seconds of arc multiplied by 4.8481E-6.

For example, here's how to convert 500,000 seconds of arc to radians using the formula above.
radians = (500,000" × 4.8481E-6) = 2.424068 rad

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

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.

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.

Second of Arc to Radian Conversion Table

Table showing various second of arc measurements converted to radians.
Seconds Of Arc Radians
1" 0.0000048481 rad
2" 0.0000096963 rad
3" 0.000014544 rad
4" 0.000019393 rad
5" 0.000024241 rad
6" 0.000029089 rad
7" 0.000033937 rad
8" 0.000038785 rad
9" 0.000043633 rad
10" 0.000048481 rad
100" 0.000485 rad
1,000" 0.004848 rad
10,000" 0.048481 rad
100,000" 0.484814 rad
1,000,000" 4.8481 rad

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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