How this instrument works
The degree is Babylonian inheritance. Cutting any circle into 360 parts passed into Greek astronomy, and Ptolemy's Almagest subdivided each part sexagesimally: pars minuta prima, which English shortened to minute, then pars minuta secunda, which became second. Those names are a record of arithmetic — first small part, second small part — and they explain why an angle and an hour are chopped up identically. A full turn holds 1,296,000 arcseconds.
Seconds of arc are working currency wherever an angle is tiny and consequential. Stellar parallax named the parsec: distance at which one astronomical unit subtends exactly one arcsecond, near 3.26 light-years. Atmospheric seeing at good mountain sites smears starlight across roughly one arcsecond, which is why Hubble's 0.05 arcsecond resolution mattered so much. Land surveyors specify total stations by angular accuracy — 1″ instruments cost multiples of 5″ ones — and target shooters keep using minute of angle, 60 arcseconds, spreading to about 1.047 inches at 100 yards.
Multiplication by 3600 is pure counting: 60 × 60, an integer with no measurement standing behind it and no uncertainty to propagate. Contrast that with radians, where one degree equals π/180, a transcendental ratio you can only truncate. Every digit typed into a degree field survives into seconds of arc intact, so any rounding you notice belongs to display precision alone.
- Type your angle into Degrees (deg); it opens loaded with 1 as reference.
- Read Arcseconds (arcsec) directly beneath — six decimal places, recomputed while you type.
- Holding a degrees-minutes-seconds reading? Fold it down first: add minutes ÷ 60 and seconds ÷ 3600 onto whole degrees, then enter that decimal.
- Reversing direction is division by 3600. Because that factor carries no error, a round trip returns exactly what you started with.
- Negative entries are refused by design — type magnitude here and carry sign or hemisphere separately.
Worked example — framing one degree of sky
Say you are planning a wide-field exposure of Pleiades and want a frame spanning one degree. Leave Degrees (deg) sitting at 1; Arcseconds (arcsec) answers 3600.0. That figure is definitional, so it holds whether your target is a star cluster, a survey traverse, or a slice of latitude.
Now bring in optics. Your camera resolves 1.2 arcseconds per pixel, so 3600 ÷ 1.2 = 3000 pixels must span that frame — a 2048-pixel sensor reaches only 0.68 degrees. Halve your target to 0.5 degrees, which is 1800 arcseconds and near enough to a full Moon's apparent width, and 1500 pixels suffice.
Questions
Is one degree exactly 3600 arcseconds?
Yes, exactly — this is a counting relationship, not a measured one. Sixty arcminutes make a degree and sixty arcseconds make an arcminute, both by definition, so 60 × 60 = 3600 with zero uncertainty attached. BIPM lists degree, arcminute and arcsecond together as non-SI units accepted for use alongside SI, with those subdivisions fixed. Nothing here rounds; only your screen does.
How does an arcsecond differ from a second of time?
They are separate quantities that happen to share a word and symbol history. Earth turns 360 degrees in roughly 24 hours, so 15 degrees pass per hour and one second of clock time sweeps 15 arcseconds at the celestial equator. Right ascension compounds this by being tabulated in hours, minutes and seconds of time rather than degrees, so a catalogue entry reading 2 seconds means 30 arcseconds along the equator — and less at high declination, scaled by cos δ.
How much ground does one arcsecond cover on Earth?
About 30.9 metres along a meridian. A degree of latitude runs close to 111 kilometres, and dividing by 3600 leaves roughly 30.87 metres per arcsecond — which is exactly why global elevation datasets such as SRTM ship as 1-arcsecond tiles and get described as 30-metre data. Longitude shrinks with latitude: multiply by cos(latitude), leaving about 23.5 metres per arcsecond in Madrid and near zero at either pole.
What trips people up converting decimal degrees?
Reading decimal fractions as minutes. Latitude 40.5° is 40° 30′, never 40° 50′, because that .5 is half of sixty rather than fifty. Safest route is multiplying straight through to arcseconds: 40.5 × 3600 = 145,800 arcseconds, then divide by 3600 for whole degrees, take the remainder over 60 for arcminutes, and whatever survives is arcseconds. Watch symbols too — prime and double prime mark arcminutes and arcseconds, and swapping in typewriter quotes breaks many coordinate parsers.
How do arcseconds relate to radians and to minute of angle?
One arcsecond equals π/648000 radians, roughly 4.8481368 × 10⁻⁶ rad, since 648000 arcseconds span half a turn. That tiny value gives a handy shortcut: an object one arcsecond across at distance d has physical size about d/206265. Minute of angle, favoured on rifle ranges, is simply 60 arcseconds, and a scope clicking in quarter-MOA steps moves 15 arcseconds per click.
Why report angles in arcseconds instead of decimal degrees?
Because small numbers beat long strings of leading zeros. A seeing disc of 0.00028 degrees communicates almost nothing, while 1 arcsecond tells any observer immediately what conditions were. Astrometry pushes further into milliarcseconds and microarcseconds, where Gaia measures parallaxes; surveying instrument datasheets, telescope pointing budgets and adaptive-optics specifications all follow suit. Decimal degrees still rule machine-readable coordinate files, which is precisely where this conversion earns its keep.