Arcsecond (″) - Unit Information & Conversion
🔄 Quick Convert Arcsecond
What is a Arcsecond?
Arcsecond (arcsec or second of arc) is 1/3600 of a degree, measuring tiny angles in astronomy and precision optics. Symbol: ″. 1° = 3600 arcseconds. Used for stellar parallax, telescope resolution, and GPS precision.
History of the Arcsecond
Derived from Babylonian sexagesimal system. Critical for astronomical measurements since telescope invention (1600s). Modern usage includes satellite positioning and high-precision surveying.
Quick Answer
What is an Arcsecond? An arcsecond is 1/3600 of a degree, used for measuring extremely small angles. A penny viewed from 4 km away appears about 1 arcsecond wide. 1 arcsecond = 1/60 arcminute = 1/3600 degree ≈ 0.000278°. Use our angle converter for instant conversions.
Key Facts: Arcsecond
| Property | Value |
|---|---|
| Symbol | ″ |
| Quantity | Angle |
| System | Metric/SI Derived |
| Derived from | Radian |
| Category | Angle |
| Standard Body | NIST / ISO |
Definition
1 arcsecond = 1/60 arcminute = 1/3600 degree ≈ 0.000278° ≈ 0.00000485 radians
Symbol: ″ (double prime) or arcsec
Key conversions:
- 60 arcseconds = 1 arcminute
- 3600 arcseconds = 1 degree
- 1 arcsecond ≈ 4.848 × 10⁻⁶ radians
Common Uses
Astronomy: Measuring star positions, planetary motion, stellar parallax, and telescope resolution. Surveying: High-precision land measurements and geodetic surveys. GPS Systems: Coordinate precision (1 arcsecond ≈ 30 meters at equator). Optics: Telescope and microscope angular resolution specifications.
Real-World Examples
Astronomical Measurements and Precision
How tiny angles matter in astronomy:
| Object/Measurement | Angular Size | Arcseconds | Notes |
|---|---|---|---|
| Sun diameter | 0.53° | 1,910" | Perfect match for Moon (eclipse) |
| Full Moon | 0.52° | 1,870" | Matches Sun in sky |
| Jupiter | 0.1° (at opposition) | 360" | Largest planet in night sky |
| Saturn | 0.08° | 288" | With rings |
| Mars | 0.025° | 90" | At closest approach |
| Venus | 0.01° | 36" | At brightest phase |
| Sirius A | ~0.005" | 0.005" | Brightest star, point-like |
| Hubble resolves | ~0.05" | 0.05" | Space telescope limit |
| Earth from Moon | ~0.5° | 1,800" | How big Earth appears from Moon |
Stellar Parallax: Distance Measurement
How astronomers measure star distances using arcseconds:
| Star | Parallax (arcseconds) | Distance (parsecs) | Distance (light-years) | Notes |
|---|---|---|---|---|
| Proxima Centauri | 0.768" | 1.30 pc | 4.24 ly | Closest star |
| Alpha Centauri A | 0.742" | 1.35 pc | 4.37 ly | Brightest nearby |
| Sirius | 0.379" | 2.64 pc | 8.6 ly | Brightest star |
| Arcturus | 0.089" | 11.2 pc | 36.7 ly | Northern sky |
| Deneb | 0.002" | 500 pc | 1,600 ly | Very distant |
Key insight: Smaller parallax = farther away; 1 parsec = parallax of 1 arcsecond
Telescope and Instrument Resolution
Angular resolution capabilities:
| Instrument | Resolution | Arcseconds | Capability |
|---|---|---|---|
| Human eye | 1 arcminute | 60" | Can distinguish |
| Binoculars (10x) | ~10" | 10" | Better than eye |
| Small telescope | ~1" | 1" | Resolves close doubles |
| Hubble Space Telescope | ~0.05" | 0.05" | Exceptional space-based |
| James Webb Space Telescope | ~0.1" | 0.1" | Infrared excellence |
| Interferometer arrays | ~0.001" | 0.001" | Radio astronomy |
| Very Large Array (VLA) | ~0.0001" | 0.0001" | Ultra-high resolution |
Rule: Smaller wavelength and larger aperture = better angular resolution
GPS Precision by Coordinate Accuracy
How arcsecond precision translates to real-world location accuracy:
| Precision | In Degrees | In Arcseconds | Distance (equator) | Use Case |
|---|---|---|---|---|
| ±1 degree | ±1° | ±3,600" | ±111 km | Regional |
| ±1 arcminute | ±0.0167° | ±60" | ±1.85 km | Rough GPS |
| ±1 arcsecond | ±0.000278° | ±1" | ±30.9 m | Standard GPS |
| ±0.1 arcsecond | ±0.0000278° | ±0.1" | ±3.1 m | High-precision GPS |
| ±0.01 arcsecond | ±0.00000278° | ±0.01" | ±31 cm | RTK-GPS, surveying |
Angular Comparisons: What Looks Like 1 Arcsecond?
Visual references for understanding tiny angles:
| Object | Distance | Appearance |
|---|---|---|
| Penny (19mm) | 4 km (2.5 miles) | 1 arcsecond |
| Human hair (70µm) | 1 meter (3.3 feet) | ~20 arcseconds |
| Letter on eye chart | 20 feet (6 meters) | 1 arcminute (60 arcseconds) |
| Moon crater Tycho | From Earth | ~80 arcseconds diameter |
| ISS (spacecraft) | Overhead | ~60 arcseconds |
| Satellite | Typical orbit | <1 arcsecond (point of light) |
Arcsecond Conversion Formulas
To Degree:
To Radian:
To Gradian:
To Arcminute:
To Turn:
To Revolution:
To Quadrant:
To Gon:
To Mil:
Frequently Asked Questions
Formula: Degrees = Arcseconds ÷ 3600 Examples:
- 3600 arcseconds = 1°
- 1800 arcseconds = 0.5°
- 60 arcseconds = 1 arcminute = 0.0167°
- 1 arcsecond ≈ 0.000278° Arcseconds to Degrees converter →
Convert Arcsecond
Need to convert Arcsecond to other angle units? Use our conversion tool.