Arcseconds to Degrees Converter
Unit ConversionConvert arcseconds to degrees by dividing by 3,600. Free converter with a DMS breakdown, a conversion table, and worked examples.
Degrees
Equivalent angle in decimal degrees
As Degrees, Minutes, Seconds
1° 0′ 0″
The same angle written in DMS notation, for example 5,025″ as 1° 23′ 45″.
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SponsoredTo convert arcseconds to degrees, divide by 3,600 (degrees = arcseconds ÷ 3,600). One degree contains 60 arcminutes of 60 arcseconds each, so the conversion is exact, and the calculator also shows the result in degrees, minutes, and seconds.
An arcsecond, also called a second of arc, abbreviated arcsec or asec and written with the double prime symbol ″, is a very small angle used in astronomy, geodesy, surveying, and precision optics. Converting it to decimal degrees is necessary whenever software, a spreadsheet, or a formula expects degrees.
Quick answer: 3,600″ = 1°, 1,800″ = 0.5°, 60″ = 1′ ≈ 0.016667°, and 1″ ≈ 0.000278°.
This page covers arcseconds to degrees only. The related converters below handle the reverse direction, arcminutes, and full DMS coordinates.
How to Convert Arcseconds to Degrees
The formula is: degrees = arcseconds ÷ 3,600. Large values carry over into whole degrees and minutes in the DMS result, so 5,025″ appears as 1.395833° and as 1° 23′ 45″.
Worked example: 900″ ÷ 3,600 = 0.25°.
Keep at least 6 decimal places in the result. Rounded to 4 places, 1″ shows as 0.0003° instead of 0.000278°, an error of about 8% that grows when many small values are added together.
Once the value is in decimal degrees, it can go straight into tools that work in degrees, such as the Trigonometric Functions Calculator, and the Central Angle Calculator returns its results in degrees and radians.
What Is an Arcsecond?
An arcsecond (second of arc) is 1/60 of an arcminute and 1/3,600 of a degree. Like the arcminute, it comes from the base 60 (sexagesimal) system of Babylonian astronomy.
Arcseconds, Milliarcseconds, and Radians
Astronomy often goes smaller still, to milliarcseconds (mas, 1/1,000 of an arcsecond) and microarcseconds. In radians, one arcsecond is exactly π/648,000 rad, about 0.00000485 rad, which is the factor used when an arcsecond value feeds a physics formula.
Arcseconds to Degrees Table
Common arcsecond values in decimal degrees and DMS notation:
| Arcseconds | Degrees | DMS |
|---|---|---|
| 1″ | 0.000278° | 0° 0′ 1″ |
| 10″ | 0.002778° | 0° 0′ 10″ |
| 30″ | 0.008333° | 0° 0′ 30″ |
| 60″ | 0.016667° | 0° 1′ 0″ |
| 100″ | 0.027778° | 0° 1′ 40″ |
| 600″ | 0.166667° | 0° 10′ 0″ |
| 900″ | 0.25° | 0° 15′ 0″ |
| 1,000″ | 0.277778° | 0° 16′ 40″ |
| 3,600″ | 1° | 1° 0′ 0″ |
| 5,025″ | 1.395833° | 1° 23′ 45″ |
| 36,000″ | 10° | 10° 0′ 0″ |
Where Arcseconds to Degrees Conversion Is Used
Star catalogs give positions down to arcseconds, while plotting tools and many formulas expect degrees. Surveyors and GIS users meet the same conversion when a coordinate is recorded with seconds. For angle work that wraps past 360°, the Coterminal Angle Calculator brings any result back into the 0° to 360° range.
For arc length at a given radius, the Perimeter of a Sector Calculator takes the angle in degrees, and the Scientific Calculator keeps the extra decimal places that arcsecond work needs.
Frequently Asked Questions
How do you convert arcseconds to degrees?
Divide the arcseconds by 3,600. For example, 1,800″ ÷ 3,600 = 0.5°.
How many degrees is 1 arcsecond?
1 arcsecond is 1/3,600 of a degree, about 0.000278°.
How many arcseconds are in a full circle?
1,296,000: 360 degrees times 3,600 arcseconds per degree.
Can the result be negative?
Yes. A negative angle is valid and means the opposite direction, so -3,600″ converts to -1°. In DMS form the minus sign belongs to the whole angle: -5,025″ is -1° 23′ 45″.
Can I convert degrees back to arcseconds?
Yes. Use the Degrees to Arcseconds Converter, which multiplies by 3,600 instead.
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