Convert Degrees (°) to Seconds (")
1 degree equals 3600 seconds.
Degree to Second Converter
What Is a Degree?
The degree (°) is a non-SI unit of plane angle defined as exactly 1/360 of a full rotation. It is accepted for use with the SI due to its importance in navigation, surveying, engineering, and astronomy.
In the DMS (Degrees-Minutes-Seconds) system, each degree is subdivided into 60 arcminutes, and each arcminute into 60 arcseconds — giving 3,600 arcseconds per degree. This sexagesimal hierarchy originates from Babylonian astronomy.
Key equivalences: 1° = π/180 rad = 60′ = 3,600″.
What Is an Arcsecond?
The arcsecond (″), also called second of arc, is exactly 1/3,600 of a degree (1/60 of an arcminute). Its exact relationship to the radian is 1″ = π/648,000 rad.
At this scale, angular measurement enters the realm of high-precision science — one arcsecond of latitude on Earth's surface corresponds to approximately 30.87 meters. Arcseconds are the standard unit for stellar parallax, telescope resolution limits, and precise geodetic coordinates.
Key equivalences: 3,600″ = 1°; 60″ = 1′; 1,296,000″ = 360°.
Degrees to Arcseconds Formula
The conversion factor is exact:
arcseconds = degrees × 3,600
This is a definition: 1° = 60 arcminutes × 60 arcseconds = 3,600 arcseconds exactly.
Worked Example
Convert 0.5° to arcseconds:
- Multiply: 0.5 × 3,600 = 1,800″
One arcsecond of latitude ≈ 30.87 m on Earth's surface, so 0.5° spans about 55.6 km — roughly the distance from London to Canterbury.
Quick Estimation
For mental math, multiply degrees by 3,600. For small decimal degrees, multiply by 36 and add two zeros. Example: 0.01° × 3,600 = 36″. Each 0.001° = 3.6″.
Common Conversions at a Glance
| Degrees | Arcseconds |
|---|---|
| 0.001° | 3.6″ |
| 0.01° | 36″ |
| 0.1° | 360″ |
| 0.5° | 1,800″ |
| 1° | 3,600″ |
| 15° | 54,000″ |
| 90° | 324,000″ |
Which Is Bigger: Degree or Arcsecond?
A degree is exactly 3,600 times larger than an arcsecond. A degree covers about the width of your little finger at arm's length. An arcsecond is far too small to perceive with the naked eye — it corresponds to about 31 meters on Earth's surface, or roughly the angular size of a dime seen from 4 kilometers away.
When You Need This Conversion
- Astronomy and astrometry: Stellar parallax is measured in arcseconds. Proxima Centauri has a parallax of 0.7687″. The parsec is defined as the distance where 1 AU subtends 1 arcsecond.
- Satellite geodesy: GPS coordinates to 5 decimal places (≈ 1 m precision) correspond to about 0.03″. High-precision surveys require sub-arcsecond accuracy.
- Telescope specifications: Hubble resolves 0.05″, ground-based telescopes are limited to ~1″ by atmospheric seeing. Adaptive optics improve this to ~0.05″.
- Precision manufacturing: Optical instruments, semiconductor lithography, and laser alignment specify angular tolerances in arcseconds.
Frequently Asked Questions
How many arcseconds are in one degree?
Exactly 3,600 arcseconds (60′ × 60″). To convert: degrees × 3,600 = arcseconds. Example: 0.5° = 1,800″.
What is a parsec and how does it relate to arcseconds?
A parsec (parallax arcsecond) is the distance at which 1 AU subtends exactly 1 arcsecond. It equals about 3.26 light-years or 3.086 × 10¹³ km. The name combines "parallax" and "arcsecond."
How far is one arcsecond on Earth's surface?
One arcsecond of latitude ≈ 30.87 meters (about 101 feet). Longitude arcseconds vary — about 30.87 m at the equator, shrinking to zero at the poles.
What angular resolution can telescopes achieve?
Hubble: 0.05″. Ground-based with adaptive optics: ~0.05″. Standard ground-based: ~1″ (atmospheric limit). Radio VLBI: milliarcsecond resolution by combining telescopes across continents.
How do arcseconds relate to GPS accuracy?
Standard GPS accuracy (~3 m) corresponds to about 0.1 arcseconds of latitude. Differential GPS (~1 cm) achieves ~0.0003″. Expressing GPS precision in arcseconds helps compare with astronomical and geodetic standards.
Common Degree to Second Conversions
| Degree | Second | Actions |
|---|---|---|
| 1 degree | 3600 seconds | |
| 5 degrees | 18000 seconds | |
| 10 degrees | 36000 seconds | |
| 30 degrees | 108000 seconds |
| Degree | Second | Actions |
|---|---|---|
| 60 degrees | 216000 seconds | |
| 90 degrees | 324000 seconds | |
| 120 degrees | 432000 seconds |
Degrees to seconds Conversion Table
Reference table with common degrees to seconds conversions. All values calculated with high precision.
Degrees to Seconds Table
1 to 100000
Seconds to Degrees Table
10000 to 1 × 109
Looking for the reverse? Convert Second to Degree
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