# MOA Calculator – Minute of Angle

URL: https://speedycalculator.com/calculators/physics/moa/
Last updated: 2026-10-30

> The MOA calculator converts the size of a group or an adjustment at a given distance into minutes of angle (MOA) and milliradians (MIL), and gives the size per 100 yards and per 100 metres.

## Inputs

- Distance (yd, m, ft, km)
- Spread (group size or correction) (in, mm, cm, ft, m)

## Results

- Angle in MOA
- Angle in MIL (mrad)
- Size at 100 yards
- Size at 100 metres
- Clicks at ¼ MOA

## Formula

```
MOA = arctan(size / distance) in arcminutes,  MIL = size / distance × 1000
1 MOA ≈ 1.047 in at 100 yd ≈ 2.91 cm at 100 m
```

## Explanation

Minute of angle (1/60 of a degree) is the angular unit used by shooters, scope makers and surveyors. A rifle that groups within 1 MOA puts its shots inside about one inch at 100 yards. Many scopes adjust in ¼-MOA or 0.1-MIL clicks.

### How to use the MOA Calculator – Minute of Angle

- **Distance**
- **Spread (group size or correction)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the target distance and the spread (group size or correction you need). The calculator returns the angle in MOA and milliradians and the equivalent size at the standard distances.

### Inputs explained

FieldWhat to enterDistanceUnits: yd, m, ft, kmSpread (group size or correction)Units: in, mm, cm, ft, m

### What each result means

- **Angle in MOA** = deg(atan([Spread (group size or correction)]÷[Distance]))×60
- **Angle in MIL (mrad)** = atan([Spread (group size or correction)]÷[Distance])×1000
- **Size at 100 yards** = tan(atan([Spread (group size or correction)]÷[Distance]))×91.44
- **Size at 100 metres** = [Spread (group size or correction)]÷[Distance]×100
- **Clicks at ¼ MOA** = [Angle in MOA]×4

### Example values

How the main result changes when **Distance** changes and everything else stays at the example values above:

Distance (yd)Angle in MOA (MOA)501.9099751.27321000.95491250.76391500.63662000.4775

## Worked example

Inputs — Distance: 100 yd; Spread (group size or correction): 1 in.

Results — **Angle in MOA = 0.9549 MOA**; Angle in MIL (mrad) = 0.2778 mil; Size at 100 yards = 1 in; Size at 100 metres = 2.7778 cm; Clicks at ¼ MOA = 3.8.

## Key terms

- **Minute of angle**: 1/60 of a degree.

## FAQ

**How big is 1 MOA at 100 yards?**
About 1.047 inches.

**What is a MIL?**
A milliradian: 1/1000 of the distance – 10 cm at 100 m.

**How many MOA in a MIL?**
About 3.438.

**What is "shooter's MOA"?**
A rounded 1 inch at 100 yards, slightly smaller than a true MOA.


## Sources

- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)