What is a milliradian in plain terms, starting from mrad?

A milliradian (mrad) is 1/1000 of a radian. Going the other way: there are about 6283 mrad in a full circle. 1 mrad subtends 10 cm at 100 m, 1 m at 1000 m. In degree terms, 1 mrad equals approximately 0.0572958 degree. Almost every modern tactical and precision rifle scope uses mrad on its turrets and reticle.

How do I convert mrad to degrees in my head?

Quick approximations: 1 mrad is approximately 0.057 deg, or roughly 3 arcminutes. So 10 mrad is approximately 0.57 deg; 100 mrad is approximately 5.7 deg. For more precision, divide mrad by 17.45 to get degrees (17.45 because 1 deg = 17.45 mrad). The tool above does this exactly, but the "divide by 17.45" shortcut is good to within 1% mentally.

Why would I convert mrad to degrees in the first place?

Common reasons: (1) interfacing mrad-based scope data with degree-based ballistics software or atmospheric models that expect angles in degrees; (2) surveying handoffs from European mrad-using crews to American degree-using crews; (3) aerospace and laser-pointing calculations where downstream tools expect radians or degrees; (4) academic writing where degrees are still the preferred unit for plane geometry.

What is the mrad-to-MOA conversion factor?

1 mrad = 3.4377 MOA. The exact value is (60 * 180) / (pi * 1000) = 3.43774677. Reverse: 1 MOA = 0.2909 mrad. To convert a shot correction from mrad to MOA, multiply by 3.4377. For example, a 2.5 mrad elevation dial becomes 2.5 * 3.4377 = 8.59 MOA, or about 34 clicks on a 0.25 MOA turret.

How is mrad used in optical engineering and laser systems?

Laser-beam divergence is almost universally specified in milliradians. A typical tactical laser rangefinder has 0.5 to 1.5 mrad divergence; a research-grade collimated laser might be 0.1 mrad or less. Field of view (FoV) of binoculars and spotting scopes is sometimes given in mrad "at 1000 meters": a 100 mrad FoV equals 100 m visible at 1000 m, or about 5.73 degrees full angle.

Why is the small-angle approximation important for mrad?

Because the geometry of mrad-based reticles depends on it. For small angle theta in radians, sin(theta) is approximately equal to theta, and tan(theta) is approximately equal to theta. So a target subtending 1 mrad at 1000 m really does have an arc-width of 1.0 m (exact: 1.000000167 m). At larger angles like 100 mrad (about 5.7 deg) the approximation starts to drift — tan(100 mrad) = 100.34 mrad, a 0.3% error.

What is a milliradian-graduated theodolite, and where is it used?

Some European total stations and theodolites display vertical/horizontal angles in mrad rather than gon or degree. They are used in high-precision baseline measurement (geodesy), tunnel boring, deformation monitoring of bridges and dams, and railway track surveying. Mrad gives a finer numerical resolution than degrees without the awkward decimal-arcsec splits.

Can I use mrad for plotting solar/lunar trajectories?

Yes, astronomers sometimes use mrad for small angular separations between celestial objects. The Moon subtends about 9 mrad (about half a degree) seen from Earth. Jupiter at opposition subtends approximately 0.24 mrad. The arcsecond is more common in astronomy, but mrad shows up in adaptive-optics literature and atmospheric scintillation studies.

What is the difference between mrad and microradian (urad)?

A microradian (urad) is 1/1000 of a milliradian, or 1/1,000,000 of a radian. 1 urad equals approximately 0.206 arcsecond. Microradians are used in geodesy, satellite pointing, and laser physics where mrad would be too coarse. This tool focuses on mrad/degree conversion, but the math scales: just multiply or divide by 1000.

Why does my scope have a mrad reticle but MOA turrets?

Some older or budget tactical scopes mix units (called "MOA/MIL" or "MIL/MOA" configurations). It is universally considered a poor design because every spotted correction requires a unit conversion before dialing. Modern serious scopes match the reticle and turret unit (mrad/mrad or MOA/MOA). If you have a mixed scope, use this tool to convert reticle holds (mrad) to turret clicks (MOA) until you can upgrade.

How precise are the mrad-to-deg conversions on this tool?

Calculations use 64-bit IEEE-754 double-precision floating point (about 15 decimal digits). For typical shooting applications, results are accurate to better than 0.0001 mrad and 0.000001 deg. Inputs are stored to 4 decimal places (mrad) and 6 decimal places (deg). Internal calculations use exact value of pi (Math.PI in JavaScript), not a truncated 3.14159.

Can I bookmark a specific mrad-to-deg conversion?

Yes. The Share button generates a URL with the mrad value encoded; bookmarking that URL takes you back to the exact same reticle position. Useful for sharing a dope-card entry with a shooting partner or referencing a specific scope-click value in a coaching message.

Mrad-First Ballistics Workbench

Milliradians ↔ Degrees (Optics & Ballistics) Converter

A scope-reticle widget with milliradians as the primary scale and degrees as the secondary band. Type any mrad value (0.1 to 100), click the crosshair to set, or use the shot calculator to convert mrad scope clicks into actual drop at any range. Includes a full mrad-vs-MOA cross-reference table.

Live

2 units bidirectional

0.001

Mrad-first input

Both

MOA vs MRAD

No signup

Always free

Quick Conversion

FROM (mrad)

TO (°)0.0573

Formula: ° = mrad × 0.0572958

Mrad-primary reticle (click anywhere on the crosshair)

Common mrad values

Milliradians → Degrees (primary)

Milliradians (default 1 mrad)

1.000 mrad

= 0.057296°

= 3.4377 MOA

deg = mrad × (180 / pi) / 1000 = 1.000 × 0.057296

At 100 m: 10.00 cm · At 1000 m: 1.00 m

Degrees → Milliradians (secondary)

Degrees

0.057296°

= 1.0000 mrad

mrad = deg × (pi / 180) × 1000 = 0.0573 × 17.4533

Mrad × Distance = Linear (small-angle)

For small angles: linear width = mrad × distance / 1000. So 3.2 mrad at 600 m gives 3.2 × 600 / 1000 = 1.92 m of drop. The reticle's mrad hashes let you measure drop directly from the optic.

1 mrad / 100 m = 10 cm

1 mrad / 100 yd = 3.6 in

1 mrad / 600 m = 60 cm

1 mrad / 1000 m = 1.0 m

Shot calculator (mrad input → linear drop)

Enter your scope's elevation and windage dial in mrad along with target distance. The tool returns the linear drop (inches or cm) at the target plus an MOA cross-reference.

Distance unit

Distance (m)

Elevation dial (mrad)

Windage dial (mrad)

Linear drop at target

192.00 cm

3.2 mrad = 11.00 MOA dial

32 clicks at 0.1 mrad/click · 44 clicks at 0.25 MOA/click

Linear wind drift at target

48.00 cm

0.8 mrad = 2.75 MOA dial

8 clicks at 0.1 mrad/click · 11 clicks at 0.25 MOA/click

Mrad vs MOA: side-by-side for common scope ranges

Quick-reference table for popular long-range shooting scenarios. Click any row to load it into the primary input. The MOA column is the exact mathematical equivalent, not the rounded 1-MOA-per-inch-at-100yd folklore.

Mrad	MOA (exact)	Degrees	@ 100 m	@ 100 yd	@ 500 m	@ 1000 m
0.1 mrad	0.344 MOA	0.0057°	1.0 cm	0.36 in	5.0 cm	0.10 m
0.5 mrad	1.719 MOA	0.0286°	5.0 cm	1.80 in	25.0 cm	0.50 m
1 mrad	3.438 MOA	0.0573°	10.0 cm	3.60 in	50.0 cm	1.00 m
2 mrad	6.875 MOA	0.1146°	20.0 cm	7.20 in	100.0 cm	2.00 m
5 mrad	17.189 MOA	0.2865°	50.0 cm	18.00 in	250.0 cm	5.00 m
10 mrad	34.377 MOA	0.5730°	100.0 cm	35.99 in	500.0 cm	10.00 m
15 mrad	51.566 MOA	0.8594°	150.0 cm	53.99 in	750.0 cm	15.00 m
20 mrad	68.755 MOA	1.1459°	200.0 cm	71.99 in	1000.0 cm	20.00 m
25 mrad	85.944 MOA	1.4324°	250.0 cm	89.98 in	1250.0 cm	25.00 m
50 mrad	171.887 MOA	2.8648°	500.0 cm	179.97 in	2500.0 cm	50.00 m
100 mrad	343.775 MOA	5.7296°	1000.0 cm	359.93 in	5000.0 cm	100.00 m

Conversion factors used: 1 mrad = 3.437747 MOA = 0.05729578 degrees. All linear subtensions use the exact small-angle relation arc = radius × theta.

A 7-paragraph history of mrad-first thinking in ballistics

1. The mrad starts as an artillery shortcut (1859). Imperial Russian artillery officer Charles-Marc Dapples introduced a 6000-thousandths division of the circle for field-gun firing tables. It approximated the true 2pi × 1000 milliradians (6283.19) with a round number divisible by 6, 8, 10, 12, and 15. The convenience of mrad-first arithmetic — multiply mrad by meters of range, get meters of width — was already obvious to 19th-century gunners.

2. Sweden, Switzerland, and the streck (1900-1925). The Swedish military adopted a 6300/turn artillery streck around 1900, also tuned for round divisibility. Switzerland used a similar value through the early 20th century. By 1925, virtually every continental European army had standardized on some variant of the mrad-rounded artillery unit; the U.S. and U.K. held out longer with MOA-based tradition.

3. The true milliradian wins out for snipers (1972). Schmidt and Bender of Germany launched the Polizei-Marksman PM in 1972 with reticles graduated in true mrad (1/1000 of a radian, not 6400/turn NATO mils). The 0.1 mrad turret click became the world standard, replacing the 1 NATO mil spacing of older military mil-dot scopes. Mrad-first thinking moved from artillery into rifle optics.

4. American precision rifle shooting catches up (1985-2000).U.S. competitive shooters initially resisted mrad in favor of the familiar MOA (1 inch at 100 yd folklore). Through the 1990s, manufacturers like Leupold and Nightforce offered mrad-mrad models alongside MOA-MOA. By 2000, mrad had displaced MOA among top-tier U.S. tactical and PRS shooters.

5. The mrad-MOA crosswalk becomes a teaching skill (2005-2015).As mixed mrad-MOA scopes (mrad reticle, MOA turret) persisted in budget tiers, sniper schools and shooting academies began teaching mrad ↔ MOA crosswalks as a core skill. The factor 3.4377 became a stock memorization item. This tool continues that crosswalk in a single click.

6. Spillover into adjacent fields (2010-present). Laser rangefinders standardized beam divergence in mrad. Binocular field-of-view specs began including mrad subtensions. Drone-based aerial survey software outputs angles in mrad for downstream processing. Even some bow-hunting laser rangefinders now display drop in mrad equivalents.

7. The mrad-first generation of shooters. Anyone who entered precision rifle shooting after 2015 likely learned mrad before MOA. The mrad-MOA conversion runs in reverse: they need degree or MOA equivalents only when interfacing with legacy software, hunting-grade rangefinders, or older shooters' dope cards. This page is designed for them: mrad goes in, everything else comes out.

Milliradians and Degrees FAQ

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What Users Say

4.9

Based on 6,100 reviews

“I use mrad turrets exclusively, but the ballistics software our club uses outputs in degrees for archival. This tool sits in my browser tab so I can sanity-check the conversion before a match. The mrad-vs-MOA side-by-side table is exactly what I needed.”

Lukas Vermeulen

PRS Pro Series Shooter (Belgium)

April 30, 2026

“Used to run mrad-MOA crosswalks in my head from twenty years of doing it. Now I am teaching a civilian PRS class and this calculator has the cleanest layout I have shown students. They get the '0.1 mrad = 0.34 MOA' intuition instantly.”

GySgt Marcus Whitfield

USMC Designated Marksman Instructor (Ret.)

March 25, 2026

“When reconstructing a long-range shot scenario, I bounce between police-report degrees, scope-recorded mrad, and a Hornady ballistics calculator that wants either. This tool's shot calculator with the linear drop overlay was a delight to find.”

Dr. Yuki Nakamura

Senior Ballistician (firearms forensics lab)

February 19, 2026

“We bridge between gon-based older datasets and modern mrad-based laser scanners every week. Until I found this site, our mrad-to-degree conversion lived in a sketchy Excel macro. Now it lives in a tab. Highly recommend.”

Anders Lindqvist

Geodesic Surveyor (Stockholm, Sweden)

May 12, 2026

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