Convert Radians to Seconds Of Arc

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

Results in Seconds Of Arc:
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1 rad = 206,264.806247 arcsec

How to Convert Radians to Seconds Of Arc

Protractors are often used to measure angle

To convert a radian measurement to a second of arc measurement, multiply the angle by the conversion ratio. One radian is equal to 206,264.806247 seconds of arc, so use this simple formula to convert:

seconds of arc = radians × 206,264.806247

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

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

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


A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc. 1 radian is equal to 180/π, 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 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.

Seconds 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″.

Radian Measurements and Equivalent Second Of Arc Conversions

Common radian values converted to the equivalent second of arc value
Radians Seconds Of Arc
1 rad 206,265"
2 rad 412,530"
3 rad 618,794"
4 rad 825,059"
5 rad 1,031,324"
6 rad 1,237,589"
7 rad 1,443,854"
8 rad 1,650,118"
9 rad 1,856,383"
10 rad 2,062,648"
11 rad 2,268,913"
12 rad 2,475,178"
13 rad 2,681,442"
14 rad 2,887,707"
15 rad 3,093,972"
16 rad 3,300,237"
17 rad 3,506,502"
18 rad 3,712,767"
19 rad 3,919,031"
20 rad 4,125,296"
21 rad 4,331,561"
22 rad 4,537,826"
23 rad 4,744,091"
24 rad 4,950,355"
25 rad 5,156,620"
26 rad 5,362,885"
27 rad 5,569,150"
28 rad 5,775,415"
29 rad 5,981,679"
30 rad 6,187,944"
31 rad 6,394,209"
32 rad 6,600,474"
33 rad 6,806,739"
34 rad 7,013,003"
35 rad 7,219,268"
36 rad 7,425,533"
37 rad 7,631,798"
38 rad 7,838,063"
39 rad 8,044,327"
40 rad 8,250,592"

More Radian Angle Conversions

Convert to Milliradians
1 rad is equal to 1,000 milliradians
Convert to Degrees
1 rad is equal to 57.29578 degrees
Convert to Minutes Of Arc
1 rad is equal to 3,437.75 minutes of arc
Convert to Gradians
1 rad is equal to 63.661977 gradians
Convert to Revolutions
1 rad is equal to 0.159155 revolutions
Convert to Circles
1 rad is equal to 0.159155 circles
Convert to Mils (NATO)
1 rad is equal to 1,018.59 mils (NATO)

Unit of Measurement Conversion Made Easy!

There are thousands of units of measure in use across the globe, and converting from one to another can be very difficult since each conversion requires a different formula to derive the result. Our unit of measurement conversion tools are meant to be dead easy. We break the mold of the typical dry and complicated experience. In addition to converting from one measurement to another, we provide the formula so you can see how the conversion is done, use it on you’re own calculator if you need to!

Convert units of length, weight, volume, and area between imperial and metric measures

Understanding the Metric System

The metric system makes it relatively easy to convert from one metric unit to another metric unit. The metric system uses a base unit, think meters or grams, and a prefix such as kilo or milli. The prefixes differ from the base units by differing powers of 10. So to convert within the metric system it’s usually a matter of multiplying or dividing by one of the powers of 10.

Here is a list of some of the common metric prefixes:

  • “kilo” – 1,000x larger
  • “hecto” – 100x larger
  • “deca” – 10x larger
  • “deci” – 10x smaller
  • “centi” – 100x smaller
  • “milli” – 1,000x smaller

There is a helpful mnemonic for remembering the prefixes: “King Henry Died Until Drinking Chocolate Milk.”
The u in Until refers to the base unit.