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The Seconds of Arc to Degrees Converter converts extremely fine angular measurements from arc seconds to degrees, arc minutes, and radians. An arc second is 1/3600 of a degree (or 1/60 of an arc minute), making it the standard unit for expressing very small angles in astronomy, geodesy, satellite positioning, and high-precision optics.
In astronomy, arc seconds are indispensable. The parsec (parallax second) — a fundamental unit of cosmic distance — is defined as the distance at which one astronomical unit subtends an angle of 1 arc second. Stellar positions, proper motions, and angular separations of binary stars are all measured in arc seconds. The Hubble Space Telescope achieves a resolution of about 0.05 arc seconds, while ground-based telescopes are limited to about 0.5-1 arc second by atmospheric turbulence (seeing).
In geodesy and surveying, arc seconds specify precise positions on Earth's surface. One arc second of latitude equals approximately 30.87 meters (about 101 feet). GPS coordinates are commonly expressed to 5-6 decimal places of a degree, equivalent to sub-arc-second precision. Modern GNSS systems achieve accuracy of 0.01-0.1 arc seconds.
Our converter outputs decimal degrees for calculation, arc minutes for navigation and DMS notation, and radians for scientific and computational applications. The high-precision output (10 decimal places for radians) accommodates the extreme precision required in astrometric and geodetic work.
The formula: degrees = arc seconds / 3600, because 1° = 60' = 3600". For arc minutes: arcmin = arcsec / 60. For radians: radians = (arcsec / 3600) × pi/180, or equivalently radians = arcsec × pi/648000.
One arc second at Earth's surface ≈ 30.87 meters along a meridian. The smallest angle resolvable by the human eye ≈ 60 arc seconds (1 arc minute). Space telescopes resolve down to milliarcseconds. For reference: 3600" = 1°, 1" = 0.000278°.
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3600" = 1°
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Hubble resolves ~0.05"
1 arc second = 1/3600 of a degree = 0.000277778 degrees. It is a very small angle.
At the equator, 1 arc second of latitude ≈ 30.87 meters (101.3 feet). This varies slightly with latitude due to Earth's oblate shape.
A parsec is the distance at which 1 AU (Earth-Sun distance) subtends 1 arc second. 1 parsec ≈ 3.26 light-years = 3.086 × 10^13 km.
360° × 3600"/° = 1,296,000 arc seconds in a full circle.
Exoplanet direct imaging requires milliarcsecond (0.001") resolution. Current interferometers and space telescopes like JWST approach this limit.
Earth's atmosphere typically limits ground telescopes to 0.5-2 arc second resolution. Adaptive optics can improve this to 0.03-0.1 arc seconds.
Standard GPS: ~3 meters ≈ 0.1". RTK GPS: ~2 cm ≈ 0.001". Survey-grade GNSS: ~1 cm ≈ 0.0003".
Geographic coordinates in DMS format use arc seconds for the finest precision. Example: 51° 28' 38" N, 0° 0' 0" W (Greenwich Observatory).
A milliarcsecond (mas) is 1/1000 of an arc second. The ESA Gaia mission measures stellar positions to ~0.02 mas (20 microarcseconds).
Multiply by pi/648000, or equivalently divide by 206264.806. 1" ≈ 4.848 × 10^-6 radians.
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