Arcsecond to Radian Converter
Convert arcsecond to radian instantly. 1 arcsecond = 5e-06 radian.
Arcsecond to Radian Table
| Arcsecond | Radian |
|---|---|
| 1 " | 5e-06 rad |
| 5 " | 2.4e-05 rad |
| 10 " | 4.8e-05 rad |
| 30 " | 0.000145 rad |
| 45 " | 0.000218 rad |
| 90 " | 0.000436 rad |
| 180 " | 0.000873 rad |
| 360 " | 0.001745 rad |
Related Conversions
Quick Answer
Formula: Radian = Arcsecond × 4.8481e-6
Multiply any arcsecond value by 4.8481e-6 to get radian.
Reverse: Arcsecond = Radian × 2.063e+05
Worked Examples
Arcsecond to Radian Conversion Table
Common arcsecond values — factor: 1 ″ = 4.8481e-6 rad
| Arcsecond (″) | Radian (rad) | Context |
|---|---|---|
| 1 ″ | 4.848e-06 rad | 1″ — star parallax |
| 5 ″ | 2.424e-05 rad | 5″ |
| 10 ″ | 4.848e-05 rad | 10″ |
| 30 ″ | 0.0001454 rad | 0.5′ |
| 60 ″ | 0.0002909 rad | 1′ |
| 300 ″ | 0.001454 rad | 5′ |
| 600 ″ | 0.002909 rad | 10′ |
| 1800 ″ | 0.008727 rad | 30′ |
| 3600 ″ | 0.01745 rad | 1° |
| 1.08e+04 ″ | 0.05236 rad | 3° |
| 2.16e+04 ″ | 0.1047 rad | 6° |
| 4.32e+04 ″ | 0.2094 rad | 12° |
| 8.64e+04 ″ | 0.4189 rad | 24° |
| 3.24e+05 ″ | 1.571 rad | 90° right angle |
| 1.296e+06 ″ | 6.283 rad | 360° |
Mental Math Tricks
1 ″ = 4.8481e-6 rad. Memorize for instant estimates.
Right angle: 90° = 1.571 rad.
Multiply result by 2.063e+05 to recover the original ″ value.
Who Uses This Conversion?
Measures stellar parallax in arcseconds to determine distances to nearby stars.
Designs positioning systems where 1 arcsecond of latitude ≈ 30 meters on Earth.
Specifies pointing accuracy and tracking error in arcseconds for precision instruments.
Measures Earth's polar precession (50 arcsec/year) and tidal deformation.
Achieves sub-arcsecond resolution with VLBI radio telescope arrays.
Maintains spacecraft pointing accuracy measured in arcseconds.
Related Conversions
Frequently Asked Questions
About Arcsecond and Radian
Arcsecond (″)
The arcsecond (″) is 1/3600 of a degree or 1/60 of an arcminute. It is the standard unit for precise astronomical measurements, astrometry, and geodesy.
Stellar parallax — the apparent shift of nearby stars due to Earth's orbital motion — is measured in arcseconds. The parsec (parallax arcsecond) is defined as the distance at which 1 AU subtends 1 arcsecond. GPS systems achieve precision of a few centimeters, corresponding to fractions of an arcsecond.
Interesting fact: The closest star (Proxima Centauri) has a parallax of just 0.7687 arcseconds. The Hubble Space Telescope can resolve features as small as 0.05 arcseconds. Earth's polar precession moves at about 50 arcseconds per year.
Radian (rad)
The radian is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. It was formally adopted by the SI system in 1995, though it had been used in mathematics since the 18th century.
Radians simplify calculus and physics: derivatives of trigonometric functions, wave equations, and angular velocity formulas are all cleaner in radians. One full circle = 2π radians ≈ 6.2832 rad.
Interesting fact: The name 'radian' was coined by physicist James Thomson in 1873. At exactly 1 radian, the arc length equals the radius — the elegant geometric relationship that makes radians so mathematically natural.
About Arcsecond to Radian Conversion
Converting arcsecond to radian is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 1.571 rad. A full circle (360°) = 6.283 rad. Reverse: 1 rad = 2.063e+05 ″. Exact factor: 1 ″ = 4.8481e-6 rad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.