Calculate Minute of Angle (1 MOA = 1.047 in at 100 yds), scope turret click adjustments (1/4 MOA, 1/8 MOA, 0.1 MRAD), target subtension, shot group dispersion, and MIL conversions with the free MOA Calculator.
10 Clicks (1/4 MOA) • 0.69 MIL / MRAD • 1 MOA @ 100 yds = 1.047 in (26.6 mm)
1/4 MOA turret
7 clicks @ 0.1 MRAD
1.000" / 100 yds
6.35 cm
2.66 cm
91.4 meters
In optics, marksmanship, and ballistics engineering, Minute of Angle (abbreviated as MOA, or minute of arc) is an angular unit of geometric measurement representing exactly \(1/60\text{th}\) of a single degree (\(1/21,600\text{th}\) of a complete \(360^\circ\) circle). Because firearm bullets travel along expanding angular cones from the rifle barrel's bore, MOA provides a universal, distance-independent scale for precision:
A circle consists of \(360\) degrees, with each degree subdivided into \(60\) minutes of arc. Thus, \(1\text{ MOA} = \frac{1^\circ}{60} = 0.016667^\circ = 0.0002908882\text{ radians}\).
Because MOA is an angle, its linear spread expands proportionally with target distance: exactly \(1.047\text{ inches at } 100\text{ yards}\), \(2.094\text{ inches at } 200\text{ yards}\), and \(10.472\text{ inches at } 1,000\text{ yards}\).
Precision rifle scopes feature calibrated click turrets (\(1/4\text{ MOA}\) or \(1/8\text{ MOA}\) per click) allowing shooters to dial precise elevation and windage corrections without guesswork.
Summary of the foundational equations used in optics, zeroing, and long-range shooting:
| Optical Metric | Mathematical Formula | Standard Units & Values |
|---|---|---|
| True MOA (TMOA) at Distance | $$\text{TMOA} = \frac{\text{Offset (in)}}{\left(\frac{D_{\text{yds}}}{100}\right) \times 1.0471975}$$ | \(1\text{ TMOA} = 1.0472\text{ in @ } 100\text{ yds}\) |
| Shooter's MOA (SMOA / IPHY) | $$\text{SMOA} = \frac{\text{Offset (in)}}{\left(\frac{D_{\text{yds}}}{100}\right) \times 1.0000}$$ | \(1\text{ SMOA} = 1.0000\text{ in @ } 100\text{ yds}\) |
| Scope Turret Click Adjustment | $$\text{Clicks} = \frac{\text{Angle (MOA)}}{\text{Click Value (e.g. 0.25)}}$$ | \(4\text{ clicks/MOA on } 1/4\text{ MOA}\) |
| Metric MOA Subtension (mm/m) | $$\text{Subtension (mm)} = D_{\text{m}} \times \text{MOA} \times 0.290888$$ | \(1\text{ MOA} = 29.09\text{ mm @ } 100\text{ m}\) |
| Milliradian (MIL / MRAD) Conversion | $$1\text{ MIL} = \left(\frac{180 \times 60}{\pi \times 1000}\right)\text{ MOA} = \mathbf{3.4377\text{ MOA}}$$ | \(1\text{ MIL} = 3.60\text{ in @ } 100\text{ yds} = 10\text{ cm @ } 100\text{ m}\) |
| Reticle Target Range Estimator | $$D_{\text{yds}} = \frac{\text{Target Size (in)} \times 95.5}{\text{Reticle Size (MOA)}}$$ | Distance in yards |
Enter your target distance (e.g., \(100\text{ yds}\)) and point-of-impact error (e.g., \(2.5\text{ inches low}\)) or shot group size.
Select your turret click value (\(1/4\text{ MOA}\), \(1/8\text{ MOA}\), \(1/2\text{ MOA}\), or \(0.1\text{ MRAD}\)).
Toggle between True MOA (\(1.047\text{ in}\)) for exact long-range ballistics or Shooter's MOA (\(1.000\text{ in}\)) for standard quick zeroing.
Inspect exact turret click adjustments, MIL equivalent angles, and step-by-step mathematical trigonometric derivations.
Why confusing True MOA with Shooter's MOA causes significant misses past \(600\text{ yards}\):
The true geometric standard: \(\tan(1/60^\circ) \times 3600\text{ in} = \mathbf{1.0472\text{ in}}\). Standard for tactical and precision optics like Nightforce, Leupold, and Vortex.
A simplified American convention (Inches Per Hundred Yards). While harmless at \(100\text{ yds}\), this \(4.719\%\) error compounds into a \(16.5\text{-inch}\) miss on a \(1,000\text{-yard}\) bullet drop adjustment of \(35\text{ MOA}\).
Understanding turret mechanical click detents and linear shift per click:
Scope turrets use internal screw detents to tilt erector tube lenses by precise angular increments:
Compute zeroing clicks, convert known MOA to linear target subtension, or estimate unknown target range.
Toggles seamlessly between exact True MOA (\(1.047\text{ in}\)) and Shooter's MOA (\(1.000\text{ in}\)).
Supports \(1/4\text{ MOA}\), \(1/8\text{ MOA}\), \(1/2\text{ MOA}\), \(1\text{ MOA}\), and \(0.1\text{ MRAD / MIL}\) clicks.
Converts automatically between MOA, Milliradians (MRAD), inches, centimeters, and millimeters.
Renders clear trigonometric proofs and scope dial calculations with live substitutions.
Executes instantly on your smartphone at the shooting range with zero server lag and total data privacy.
Instead of trial-and-error shooting, measure point of impact once, input the offset, and dial exact turret clicks to zero in 2 shots.
Eliminates the \(4.7\%\) error when converting ballistic drop charts between True MOA and IPHY at \(600\text{ to }1,000\text{ yards}\).
Comparison of the two dominant optical reticle systems:
Based on imperial units (\(\sim 1\text{ inch at } 100\text{ yards}\)). Finer turret click resolution (\(1/4\text{ MOA} = 0.262\text{ in}\) vs. \(0.1\text{ MIL} = 0.360\text{ in}\) at \(100\text{ yds}\)), ideal for benchrest and precision hunting.
Based on the base-10 metric decimal system (\(1\text{ MIL} = 10\text{ cm at } 100\text{ m} = 1\text{ m at } 1,000\text{ m}\)). Universally favored in military, law enforcement, and Precision Rifle Series (PRS) matches for fast range estimation.
How reticle optical placement affects MOA subtensions at varying magnification:
In a First Focal Plane (FFP) scope, the reticle grows and shrinks with magnification zoom, ensuring that 1 MOA remains exactly 1 MOA at all magnification powers. In a Second Focal Plane (SFP) scope, the reticle stays the same size; thus, MOA hashmarks are only true at one calibrated power (typically maximum magnification).
How snipers and precision marksmen calculate unknown target distances without laser rangefinders:
When the physical dimensions of a target are known (such as an 18-inch IPSC steel silhouette or 30-inch deer chest height), measuring how many MOA hashmarks it covers in the reticle reveals its exact range:
How to accurately measure center-to-center shot dispersion on target paper:
Measure outer edge-to-edge bullet hole distance with calipers and subtract exact bullet diameter: \(\text{Group Size} = D_{\text{outer}} - d_{\text{bullet}}\).
A rifle qualifies as "Sub-MOA" when a 5-shot or 10-shot group spans less than \(1.047\text{ inches at } 100\text{ yards}\) or \(5.236\text{ inches at } 500\text{ yards}\).
Accounting for optic tilt and steep uphill/downhill firing angles:
A mere \(3^\circ\) cant of the rifle scope can throw a 1,000-yard bullet impact over \(15\text{ inches}\) off-target laterally. When shooting at steep uphill or downhill incline angle \(\theta\), gravity acts only on horizontal flight, requiring the Rifleman's Rule:
How distance between front and rear iron sights governs mechanical shift per MOA:
Unlike optical scopes with fixed internal prisms, iron sight click values depend directly on the firearm's sight radius (\(R_{\text{sight}}\), the linear distance between front sight post and rear aperture):
On an AR-15 carbine with a \(14.5\text{-inch}\) sight radius, moving the front post by \(0.0042\text{ inches}\) shifts the point of impact by \(1\text{ MOA}\), whereas a \(20\text{-inch}\) rifle requires \(0.0058\text{ inches}\) per MOA.
Converting crosswind speed and clock direction into angular MOA hold-offs:
Winds blowing directly from 3 o'clock or 9 o'clock exert maximum aerodynamic force on the bullet body, requiring full MOA windage compensation: \(\text{Hold (MOA)} = \frac{\text{Range/100} \times V_{\text{wind}}}{C_{\text{ballistic}}}\).
Quartering winds from 1, 2, 4, 5, 7, 8, 10, or 11 o'clock impart a trigonometric vector component of \(\sin(45^\circ) \approx 70.7\%\), requiring roughly \(70\%\) of full MOA value.
Why temperature gradients shift group zero by \(0.5\text{ to }2.0\text{ MOA}\):
A clean, lubricated cold barrel exhibits different bore friction than a warm, fouled barrel, creating a predictable Cold Bore POI Shift (typically \(0.5\text{ to }1.5\text{ MOA}\) high or low). Under rapid fire strings, uneven thermal expansion along the barrel steel induces vertical or diagonal group stringing, which precision marksmen monitor using angular MOA dispersion tracking.
Comprehensive answers to common questions about Minute of Angle calculations, scope turret clicks, target subtension, and MIL conversions.
