- June 7, 2022

## Milliradian (MIL or MRAD)

#### TABLE OF CONTENTS

There are plenty of little quirks, vagaries and misunderstandings that you come across in this game. This definitely falls into that category. It is generally thought that MRAD and MIL are the same animal. They are not! Unlikely to bother anyone at small ranges. However, open up the distance and ………… well, decide for yourself. Read on.

## Milliradians or MRAD

A Milliradian or (MRAD) is a unit of angle measurement. Milliradians, like Minutes of Angle (MOA), are a way of adjusting a firearms sights for elevation and windage.

- A radian is a mathematical method of precise calculations involving a circle.
- There are 2π Radians making up a full circle.
- Mathematically this means there are roughly 6283.18 milliradians to a full circle.
- A milliradian is 1/1000 of a radian.
- One degree = 17.45393 milliradians.
- One milliradian = 0.057296 degrees.

### How to Calculate MRAD

#### Milliradians (MRAD)

Calculating MRAD uses a circular trigonometric calculation using two known factors:

R = Circle Radius = Range to the target.

C = Circle Circumference = Elevation (or windage) we want to adjust for.

To find a third unknown factor, the Angle = MRAD we want to adjust.

The equation is C = 2πR

##### Calculating MRAD

Range (R) of 100 meters. To convert to mm multiply by 1,000.

R = 100m x 1,000 = 100,000.

π = 3.141592654

C = 2 π R

C = 2 x 3.141592654 x 100,000 = 628318.5308mm

That’s a full circle so we divide C by 6283

C = 628318.5308mm / 6283 = 100.002949mm

So 1 MRAD at 100m = 100.002949 (100mm)

Therefore one MRAD ≈ 1 meter (1000mm) at 1,000 meters.

100mm at 100m for a one MRAD adjustment on a scope is not fine enough so most scopes are calibrated with adjustments of 0.1 MRAD per click (one increment of a turret adjustment).

Therefore 1 click = 0.1 MRAD which gives a 10mm (1cm) at 100m.

This makes it easy for a shooter to calculate.

For example a scope with:

Elevation adjustments (clicks) 0.1 MRAD

Range 200 meters

1 MRAD at 200m = 200mm

Adjustment required 20mm up

Required clicks = 2 MRAD

200mm multiplied by 0.1

= 20 x 0.1 = 20

= 20 clicks up

##### Table MRAD (Meters)

MRAD (mm) | Range (meters) |
---|---|

100 | 100 |

200 | 200 |

300 | 300 |

400 | 400 |

500 | 500 |

600 | 600 |

700 | 700 |

800 | 800 |

900 | 900 |

1000 | 1000 |

## MILS (NATO)

### How to Calculate MILS

#### MILS (NATO)

A MIL refers to a slightly different value than a true milliradian. Most European and US forces (now NATO) in World War one, did away with degrees and minutes on their artillery sights. They adopted milliradians. However, instead using 6,283 milliradians to a full circle they opted to round it up to **6400** and called the new measurement a **MIL**.

- One degree = 17.7777 mils.
- One mil = 0.05625 degrees.

##### Calculating Mils

What we are doing is using a circular trigonometric calculation using two known factors:

- R = Circle Radius = Range to the target.
- C = Circle Circumference = Elevation (or windage) we want to adjust for.

To find a third unknown factor, the Angle = MILS we want to adjust.

The equation is **C = 2πR**

Breaking it down.

Consider a target at a Range (R) of 100 meters.

We want to use mm so 1m = 1000mm therefore R = 100m x 1000 = 100,000.

C = 2 π R

C = 2 x 3.141592654 x 100,000 = 628318.5308mm

That’s a full circle so we divide C by 6400 (NATO, rounded up in WWI, for MRAD 6283)

C = 628318.5308mm / 6400 = 98.17477mm

So 1 MIL at 100m = 98.17477 (100mm)

So for simplicity’s sake one MIL ≈ 1 meter (1000mm) at 1,000 meters.

100mm at 100m for a one MIL adjustment on a scope is not fine enough so most scopes are calibrated with adjustments of 0.1 MIL per click (one increment of a turret adjustment).

Therefore 1 click = 0.1 MIL which gives a 10mm (1cm) at 100m.

This makes it easy for a shooter to calculate.

For example a scope with:

Elevation adjustments (clicks) 0.1 MIL

Range 200 meters

1 MIL at 200m = 200mm

Adjustment required 20mm up

Required clicks = 2 MIL

200mm multiplied by 0.1

= 20 x 0.1 = 20

= 20 clicks up

##### Table MIL (Meters)

MIL (mm) | Range (meters) |
---|---|

98 | 100 |

196 | 200 |

295 | 300 |

393 | 400 |

491 | 500 |

589 | 600 |

687 | 700 |

785 | 800 |

884 | 900 |

982 | 1000 |