Milliradian to Arcsecond Converter

Convert milliradian to arcsecond instantly. 1 milliradian = 206.264806 arcsecond.

1 Milliradian =
Arcsecond
From
To

Milliradian to Arcsecond Table

MilliradianArcsecond
1 mrad206.264806 "
5 mrad1031.324031 "
10 mrad2062.648062 "
30 mrad6187.944186 "
45 mrad9281.916279 "
90 mrad18563.832558 "
180 mrad37127.665116 "
360 mrad74255.330232 "

Quick Answer

Formula: Arcsecond = Milliradian × 206.3

Multiply any milliradian value by 206.3 to get arcsecond.

Reverse: Milliradian = Arcsecond × 0.004848

Worked Examples

1 mrad
1 mrad × 206.3 = 206.3 ″
Single unit reference.
45 mrad
45 mrad × 206.3 = 9282 ″
45° — half a right angle.
90 mrad
90 mrad × 206.3 = 1.856e+04 ″
90° — one right angle.
180 mrad
180 mrad × 206.3 = 3.713e+04 ″
180° — a straight line / half circle.

Milliradian to Arcsecond Conversion Table

Common milliradian values — factor: 1 mrad = 206.3 ″

Milliradian (mrad)Arcsecond (″)Context
0.1 mrad20.63 ″~0.006°
0.5 mrad103.1 ″~0.029°
1 mrad206.3 ″~0.057° / 1m at 1km
5 mrad1031 ″~0.286°
10 mrad2063 ″~0.573°
50 mrad1.031e+04 ″~2.86°
100 mrad2.063e+04 ″~5.73°
500 mrad1.031e+05 ″~28.6°
1000 mrad2.063e+05 ″~57.3°
1571 mrad3.24e+05 ″90°
2000 mrad4.125e+05 ″~115°
3142 mrad6.48e+05 ″180°
5000 mrad1.031e+06 ″~286°
6283 mrad1.296e+06 ″360°
1e+04 mrad2.063e+06 ″~573°

Mental Math Tricks

Exact factor

1 mrad = 206.3 ″. Memorize for instant estimates.

Key anchors

Right angle: 90° = 3.24e+05 ″.

Reverse

Multiply result by 0.004848 to recover the original mrad value.

Who Uses This Conversion?

Sniper / Precision Shooter

Uses milliradians for scope adjustments — 1 mrad = 10 cm at 100 m.

Artillery Officer

Calculates fire missions using milliradians for angular measurements and corrections.

Optical Engineer

Specifies laser beam divergence and lens field of view in milliradians.

Radar Engineer

Measures antenna beamwidth and angular resolution in milliradians.

Robotics Engineer

Specifies servo and stepper motor angular precision in milliradians.

Ballistics Analyst

Computes angular corrections and dispersion in milliradians for weapon systems.

Frequently Asked Questions

About Milliradian and Arcsecond

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.

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.

About Milliradian to Arcsecond Conversion

Converting milliradian to arcsecond 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°) = 3.24e+05 ″. A full circle (360°) = 1.296e+06 ″. Reverse: 1 ″ = 0.004848 mrad. Exact factor: 1 mrad = 206.3 ″.

All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.