Arcsecond to Milliradian Converter
Convert arcsecond to milliradian instantly. 1 arcsecond = 0.004848 milliradian.
Arcsecond to Milliradian Table
| Arcsecond | Milliradian |
|---|---|
| 1 " | 0.004848 mrad |
| 5 " | 0.024241 mrad |
| 10 " | 0.048481 mrad |
| 30 " | 0.145444 mrad |
| 45 " | 0.218166 mrad |
| 90 " | 0.436332 mrad |
| 180 " | 0.872665 mrad |
| 360 " | 1.745329 mrad |
Related Conversions
Quick Answer
Formula: Milliradian = Arcsecond × 0.004848
Multiply any arcsecond value by 0.004848 to get milliradian.
Reverse: Arcsecond = Milliradian × 206.3
Worked Examples
Arcsecond to Milliradian Conversion Table
Common arcsecond values — factor: 1 ″ = 0.004848 mrad
| Arcsecond (″) | Milliradian (mrad) | Context |
|---|---|---|
| 1 ″ | 0.004848 mrad | 1″ — star parallax |
| 5 ″ | 0.02424 mrad | 5″ |
| 10 ″ | 0.04848 mrad | 10″ |
| 30 ″ | 0.1454 mrad | 0.5′ |
| 60 ″ | 0.2909 mrad | 1′ |
| 300 ″ | 1.454 mrad | 5′ |
| 600 ″ | 2.909 mrad | 10′ |
| 1800 ″ | 8.727 mrad | 30′ |
| 3600 ″ | 17.45 mrad | 1° |
| 1.08e+04 ″ | 52.36 mrad | 3° |
| 2.16e+04 ″ | 104.7 mrad | 6° |
| 4.32e+04 ″ | 209.4 mrad | 12° |
| 8.64e+04 ″ | 418.9 mrad | 24° |
| 3.24e+05 ″ | 1571 mrad | 90° right angle |
| 1.296e+06 ″ | 6283 mrad | 360° |
Mental Math Tricks
1 ″ = 0.004848 mrad. Memorize for instant estimates.
Right angle: 90° = 1571 mrad.
Multiply result by 206.3 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 Milliradian
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.
Milliradian (mrad)
The milliradian (mrad) is 1/1000 of a radian, approximately 0.0573°. It was adopted by military organizations in the early 20th century for artillery range calculations and is now standard in precision shooting and optics.
The milliradian has a practical property: at 1,000 meters distance, 1 mrad corresponds to approximately 1 meter of lateral displacement. This 'mil-dot' relationship makes range estimation and scope adjustment intuitive for military and hunting applications.
Interesting fact: NATO and many militaries use a slightly rounded version — the NATO mil — where a full circle is defined as 6,400 mils (instead of the mathematically exact 6,283.19 mrad). This makes angular calculations easier in the field.
About Arcsecond to Milliradian Conversion
Converting arcsecond to milliradian 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°) = 1571 mrad. A full circle (360°) = 6283 mrad. Reverse: 1 mrad = 206.3 ″. Exact factor: 1 ″ = 0.004848 mrad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.