Degrees to Seconds (Arcseconds) Converter
Enter an angle in decimal degrees and this converter gives you the total number of arcseconds, the full degrees-minutes-seconds (DMS) breakdown, and the reverse arcseconds-to-degrees result. Useful for astronomy, surveying, navigation, and geographic coordinates. Switch to reverse mode to convert arcseconds back to degrees.
How degrees and arcseconds relate
An angle in degrees can be divided into finer units using a sexagesimal (base-60) system. One degree is split into 60 arcminutes, and each arcminute is split into 60 arcseconds. That means one full degree contains exactly 3,600 arcseconds (60 x 60 = 3,600). So to convert any angle from decimal degrees to arcseconds, you multiply by 3,600. For example, 45 degrees equals 45 x 3,600 = 162,000 arcseconds. To go the other way, divide arcseconds by 3,600 to recover decimal degrees.
Degrees-minutes-seconds (DMS) notation
When an angle is not a whole number of degrees, you can write it in DMS notation: degrees-minutes-seconds, written as 47 degrees 30 minutes 0 seconds, or 47° 30' 0". To convert a decimal-degree angle to DMS, take the whole-number part as the degrees, multiply the decimal remainder by 60 and take the whole number as arcminutes, then multiply that remainder by 60 again for arcseconds. For 47.5 degrees: 47 degrees, 0.5 x 60 = 30 arcminutes, 0 arcseconds, giving 47° 30' 0". This calculator performs that three-step breakdown automatically and displays the DMS string alongside the total arcseconds.
Where arcseconds are used
Arcseconds appear wherever very small angular differences matter. In astronomy, stellar parallax (the tiny shift in a star's apparent position as Earth orbits the Sun) is measured in arcseconds: a parallax of one arcsecond defines one parsec, equal to about 3.26 light-years. In navigation and surveying, geographic coordinates are often expressed to arcsecond precision because one arcsecond of latitude corresponds to roughly 30.9 metres on the Earth's surface. Optical telescopes and cameras quote angular resolution in arcseconds, and GPS receivers report position accuracy at sub-arcsecond precision.
Arcseconds versus time seconds
The word "seconds" can refer to either arcseconds (a unit of angle) or time seconds (a unit of time), and the two are unrelated in value but share an origin: both use the ancient Babylonian base-60 counting system. When astronomers discuss right ascension (the celestial equivalent of longitude), they often measure it in hours, minutes, and time-seconds rather than degrees, arcminutes, and arcseconds. One hour of right ascension equals 15 degrees, so one time-second of right ascension equals 15 arcseconds. This converter deals only with angular arcseconds, not time.
Common angle conversions
| Decimal degrees | Arcseconds | Arcminutes | Radians | DMS |
|---|---|---|---|---|
| 1 | 3,600 | 60 | 0.017453 | 1° 0' 0" |
| 5 | 18,000 | 300 | 0.087266 | 5° 0' 0" |
| 15 | 54,000 | 900 | 0.261799 | 15° 0' 0" |
| 30 | 108,000 | 1,800 | 0.523599 | 30° 0' 0" |
| 45 | 162,000 | 2,700 | 0.785398 | 45° 0' 0" |
| 60 | 216,000 | 3,600 | 1.047198 | 60° 0' 0" |
| 90 | 324,000 | 5,400 | 1.570796 | 90° 0' 0" |
| 120 | 432,000 | 7,200 | 2.094395 | 120° 0' 0" |
| 180 | 648,000 | 10,800 | 3.141593 | 180° 0' 0" |
| 270 | 972,000 | 16,200 | 4.712389 | 270° 0' 0" |
| 360 | 1,296,000 | 21,600 | 6.283185 | 360° 0' 0" |
Arcseconds, arcminutes, radians and DMS equivalents for benchmark angles.
Frequently asked questions
How many arcseconds are in one degree?
Exactly 3,600 arcseconds. One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds: 60 x 60 = 3,600. Multiply any angle in decimal degrees by 3,600 to get the total arcseconds.
What is the formula to convert degrees to arcseconds?
Arcseconds = degrees x 3,600. For the reverse, degrees = arcseconds / 3,600. For example, 2.5 degrees equals 2.5 x 3,600 = 9,000 arcseconds. And 5,400 arcseconds divided by 3,600 gives 1.5 degrees.
What is DMS notation?
DMS stands for degrees-minutes-seconds. It breaks a decimal angle into three integer-style components: the whole number of degrees, the remaining arcminutes (0 to 59), and the remaining arcseconds (0 to 59.999...). For example, 1.505 degrees is 1° 30' 18" in DMS notation: 1 degree, 30 arcminutes (0.505 x 60 = 30.3, whole = 30), and 18 arcseconds (0.3 x 60 = 18).
Why do we use a base-60 system for angles?
The sexagesimal (base-60) system was developed by ancient Babylonian mathematicians around 2000 BCE and was later adopted by Greek astronomers including Ptolemy. 60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which makes fractions much simpler to express as whole numbers. That convenience kept the system in use for navigation and astronomy for millennia, and it remains standard in GPS coordinates, telescope pointing, and geographic information systems today.
How precise is one arcsecond on Earth?
One arcsecond of latitude corresponds to approximately 30.9 metres on the Earth's surface (the exact value varies slightly because the Earth is not a perfect sphere). One arcsecond of longitude varies from about 30.9 metres at the equator to 0 metres at the poles, because lines of longitude converge. Consumer GPS devices typically achieve accuracy of a few metres, which is a few tenths of an arcsecond.
How are arcseconds used in astronomy?
In astronomy, arcseconds measure angular separation, angular diameter, and parallax. The angular diameter of the full Moon is about 1,800 arcseconds (half a degree). The Hubble Space Telescope can resolve features smaller than 0.05 arcseconds. Stellar parallax is measured in arcseconds: a star with a parallax of exactly 1 arcsecond is defined to be at a distance of one parsec (3.26 light-years). The closest star to the Sun, Proxima Centauri, has a parallax of 0.7687 arcseconds.