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Arc seconds to degrees: exact 3600 factor, DMS context, conversion chart, and precision surveying tips
Conversion formula
Verification: factors follow standard unit definitions; round for display only.
Quick reference chart
| Arc Second | Degree |
|---|---|
| 1 | 0.000278 |
| 2 | 0.000556 |
| 3 | 0.000833 |
| 4 | 0.001111 |
| 5 | 0.001389 |
| 6 | 0.001667 |
Educational explanation
Arc seconds to degrees
Convert arcsec (") to ° when a star catalog, boundary call, or total-station readout lists arc seconds but your GIS layer, rotation matrix, or spreadsheet expects decimal degrees.
An arc second (arcsec, ") is one-three-thousand-six-hundredth of a degree—sixty arc seconds make one arc minute, and sixty arc minutes make one degree. The relationship is exact: 3,600 arcsec = 1°.
° = arcsec ÷ 3600 · equivalently ° = arcsec × 0.000277778
This site's angle catalog stores Degree = 1 and Arc Second = 0.0002777778 in the shared unit graph. Divide arc seconds by 3,600 for high-precision coordinates; round only when publishing a final report.
Step-by-step conversions (worked examples)
3,600 arcsec (definition anchor):
- 3,600 ÷ 3600 = 1°
7,200 arcsec (two degrees in arc-second form):
- 7,200 ÷ 3600 = 2°
- Sanity check: 7,200″ = 120′ = 2°
1.5 arcsec (fine telescope pointing tweak):
- 1.5 ÷ 3600 = 0.000416667°
- At the equator, one arc second of longitude spans roughly 30 m—small angles still matter in surveying.
Arc seconds to degrees conversion chart
| Arc seconds (") | Degrees (°) | Typical context |
|---|---|---|
| 1″ | 0.000277778 | Finest common sexagesimal step |
| 30″ | 0.00833333 | Half arc minute |
| 60″ | 0.0166667 | One arc minute (1′) |
| 3,600″ | 1 | One degree — definition anchor |
| 162,000″ | 45 | 45° expressed entirely in arc seconds |
| 1,296,000″ | 360 | Full circle in arc-second form |
Where arcsec → degrees comes up
- Geodesy & cadastral law: Metes-and-bounds descriptions sometimes specify bearings to the arc second while GIS storage uses decimal degrees.
- Astronomy: Planet-disk diameters, double-star separations, and adaptive optics corrections are routinely quoted in arc seconds.
- GNSS adjustment reports: Standard errors may be listed in arc seconds even when vertex coordinates are stored as decimal degrees.
- Photogrammetry: Exterior orientation residuals in arc seconds must be folded into decimal-degree rotation matrices for bundle adjustment.
Degrees to arc seconds
Convert ° to arcsec when a map API, CAD rotation, or spreadsheet lists decimal degrees but your instrument panel, legal description, or star chart expects arc seconds.
Invert the forward relationship: multiply degrees by 3,600, or divide by 0.000277778.
arcsec = ° × 3600 · catalog: arcsec = ° × 3600
Step-by-step conversion (worked example)
Convert 0.001° (one milli-degree, common GIS tolerance):
- 0.001 × 3600 = 3.6 arcsec
- Catalog check: 3.6 arcsec
Convert 45° to arc seconds:
- 45 × 3600 = 162,000 arcsec
Degrees to arc seconds conversion chart
| Degrees (°) | Arc seconds (") | Typical context |
|---|---|---|
| 0.000278° | 1″ | One arc second as decimal degrees |
| 0.001° | 3.6 | Sub-arcsec GIS noise floor (order of magnitude) |
| 0.25° | 900 | 15′ expressed as arcsec (900″) |
| 1° | 3600 | Definition anchor |
| 45° | 162000 | Common survey angle |
Use the calculator above—or flip units with degree to arc second.
DMS chain, arc minutes, mistakes, and related tools
Arc seconds are the finest customary step in DMS notation. Chain conversions through 60 and 3600 exactly, and separate angle units from time units.
Sexagesimal chain at a glance
| Step | Factor | Example |
|---|---|---|
| ° → ′ | × 60 | 1° = 60′ |
| ′ → " | × 60 | 1′ = 60″ |
| ° → " | × 3600 | 1° = 3600″ |
| " → ° | ÷ 3600 | 3600″ = 1° |
Building decimal degrees from DMS
DD = degrees + arcmin/60 + arcsec/3600. Example: 40° 26′ 46″ → 40 + 26/60 + 46/3600 ≈ 40.446111°.
Common mistakes to avoid
- Confusing arc seconds with time seconds—check for the double-prime symbol (") or the word “arcsec.”
- Using 3,600 for arcmin—that factor is °↔arcsec; °↔arcmin uses 60.
- Insufficient precision in DD—one arc second is about 0.000278°; store enough decimal places for surveying work.
- Mixing radians—confirm the source unit before applying 3600.
Related angle converters
Degree to arc second, Arc minute to degree, Degree to arc minute, and radians to degrees.
Frequently asked questions
How do you convert arc seconds to degrees?
Divide arc seconds by 3600, or multiply by 0.000277778. Example: 7200 arcsec ÷ 3600 = 2°.
How many arc seconds are in one degree?
Exactly 3,600 arc seconds per degree (60 arc minutes × 60 arc seconds per minute).
How many degrees is 3600 arc seconds?
3600 arcsec = 1° exactly—this is the definition anchor for the sexagesimal system.
What is 1 arc second in decimal degrees?
1″ = 0.000277778° (1 ÷ 3600). At the equator that is roughly 30 m of ground distance for longitude.
How do you convert degrees to arc seconds?
Multiply degrees by 3600. Example: 0.001° × 3600 = 3.6 arcsec. Catalog factor: × 3600.
Is arc second to degree exact?
Yes—it follows the geometric definition (3600 arc seconds per degree). Only rounding for display introduces small differences.
Are arc seconds the same as time seconds?
No. Arc seconds measure angles; time seconds measure duration. The word 'minute' is also shared—always check for the double-prime (″) symbol or 'arcsec' wording.
How do I convert DMS to decimal degrees using arc seconds?
Add arcsec/3600 to arcmin/60 plus whole degrees: DD = D + M/60 + S/3600. Example: 38° 12′ 30″ → 38.208333°.
Why do star catalogs use arc seconds?
Celestial separations and disk sizes are tiny compared to a degree. Arc seconds keep numbers readable (e.g., 0.5″ separation) instead of long decimals like 0.000139°.
What is 45 degrees in arc seconds?
45° × 3600 = 162,000 arcsec.
Can I round-trip arcsec and degrees?
Yes. Convert 1.5 arcsec → degrees → arcsec and you should recover 1.5 within floating-point limits. Early rounding in DD storage is the usual source of drift.
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