Arcseconds to Radians (″ → rad)
Formula
1 ″ = 0.00000484813681109536 radConversion Table
| ″ | rad |
|---|---|
| 0 | 0 |
| 1.0000 | 0.0000048481 |
| 2.0000 | 0.0000096963 |
| 3.0000 | 0.000014544 |
| 4.0000 | 0.000019393 |
| 5.0000 | 0.000024241 |
| 6.0000 | 0.000029089 |
| 7.0000 | 0.000033937 |
| 8.0000 | 0.000038785 |
| 9.0000 | 0.000043633 |
| 10.000 | 0.000048481 |
| 11.000 | 0.000053330 |
| 12.000 | 0.000058178 |
| 13.000 | 0.000063026 |
| 14.000 | 0.000067874 |
| 15.000 | 0.000072722 |
| 16.000 | 0.000077570 |
| 17.000 | 0.000082418 |
| 18.000 | 0.000087266 |
| 19.000 | 0.000092115 |
| ″ | rad |
|---|---|
| 20.000 | 0.000096963 |
| 21.000 | 0.00010181 |
| 22.000 | 0.00010666 |
| 23.000 | 0.00011151 |
| 24.000 | 0.00011636 |
| 25.000 | 0.00012120 |
| 26.000 | 0.00012605 |
| 27.000 | 0.00013090 |
| 28.000 | 0.00013575 |
| 29.000 | 0.00014060 |
| 30.000 | 0.00014544 |
| 31.000 | 0.00015029 |
| 32.000 | 0.00015514 |
| 33.000 | 0.00015999 |
| 34.000 | 0.00016484 |
| 35.000 | 0.00016968 |
| 36.000 | 0.00017453 |
| 37.000 | 0.00017938 |
| 38.000 | 0.00018423 |
| 39.000 | 0.00018908 |
| ″ | rad |
|---|---|
| 40.000 | 0.00019393 |
| 41.000 | 0.00019877 |
| 42.000 | 0.00020362 |
| 43.000 | 0.00020847 |
| 44.000 | 0.00021332 |
| 45.000 | 0.00021817 |
| 46.000 | 0.00022301 |
| 47.000 | 0.00022786 |
| 48.000 | 0.00023271 |
| 49.000 | 0.00023756 |
| 50.000 | 0.00024241 |
| 51.000 | 0.00024725 |
| 52.000 | 0.00025210 |
| 53.000 | 0.00025695 |
| 54.000 | 0.00026180 |
| 55.000 | 0.00026665 |
| 56.000 | 0.00027150 |
| 57.000 | 0.00027634 |
| 58.000 | 0.00028119 |
| 59.000 | 0.00028604 |
| ″ | rad |
|---|---|
| 60.000 | 0.00029089 |
| 61.000 | 0.00029574 |
| 62.000 | 0.00030058 |
| 63.000 | 0.00030543 |
| 64.000 | 0.00031028 |
| 65.000 | 0.00031513 |
| 66.000 | 0.00031998 |
| 67.000 | 0.00032483 |
| 68.000 | 0.00032967 |
| 69.000 | 0.00033452 |
| 70.000 | 0.00033937 |
| 71.000 | 0.00034422 |
| 72.000 | 0.00034907 |
| 73.000 | 0.00035391 |
| 74.000 | 0.00035876 |
| 75.000 | 0.00036361 |
| 76.000 | 0.00036846 |
| 77.000 | 0.00037331 |
| 78.000 | 0.00037815 |
| 79.000 | 0.00038300 |
Arcseconds to Radians Conversion
Converting Arcseconds (″) to Radians (rad) is a common angle conversion. 1 ″ equals 0.000005 rad. For example, 100 ″ is equal to 0.000485 rad.
Quick Mental Math: Arcseconds to Radians
Use 648,000 arcseconds as pi radians, so 324,000 arcseconds is about 1.57 radians.
Why is converting Arcseconds to Radians tricky?
arcseconds to radians hides a pi-based factor, so treating the step as a clean base-10 shift gives the wrong size.
Quick Reference Values
1 ″ = 0.000005 rad. 5 ″ = 0.000024 rad. 10 ″ = 0.000048 rad. 25 ″ = 0.000121 rad. 50 ″ = 0.000242 rad. 100 ″ = 0.000485 rad.
What is Arcseconds?
Arcseconds (″) is a unit of angle. An arcsecond is 1/60 of an arcminute or 1/3600 of one degree. This unit represents 1/1,296,000 of a full circle and is used for very precise angular measurements in astronomy and optics [iso-80000]. One arcsecond equals exactly 1/60 of an arcminute. Divisions of degrees into arcseconds originated from the sexagesimal system used by ancient astronomers and were standardized by international bodies for use in precise angular measurements [iso-80000]. Arcseconds are critical in astronomical observations for locating stars and planets with precision. Surveying and satellite navigation systems also rely on arcseconds globally [nist-si-guide].
What is Radians?
Radians (rad) is a unit of angle. A radian is the SI unit of plane angle defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One radian equals approximately 57.2958 degrees or exactly 1 rad = radius/arc length ratio. It is a dimensionless unit used extensively in mathematics, physics, and engineering [bipm-si-brochure]. The radian concept was formalized in the 19th century, with mathematicians like Roger Cotes contributing to its development. The radian was adopted as the standard angular unit in the SI system to provide a natural measure of angles based on circle geometry [bipm-si-brochure]. Radians are the standard unit of angular measurement in science, engineering, and technology worldwide. They are used in trigonometry, rotational dynamics, and signal processing, with formal adoption by the BIPM and ISO 80000 standards [bipm-si-brochure, iso-80000].
Common Misspellings
People often search for this conversion using these alternate spellings: arc second, arc sec, arcsec, arseconds, radianes, radias, radans, radiens. All of these refer to the Arcseconds to Radians conversion.