MILLIRADIAN MIL OR MRAD
Scopes

MILLIRADIAN MIL OR MRAD

Milliradian MIL or MRAD are units of angle measurement. Milliradian like Minute of Angle (MOA) is a way of adjusting a firearms sights for elevation and windage.

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.
2π Radians in a full circle
1 Milliradian
MRAD per 1 degree diagram
MRAD per 1 degree diagram

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)

MRAD Elevation Calc

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.

Scope turret with 0.1 MRAD adjustment

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

MRAD Calculator

MRAD Calculator – A simple calculator to calculate MRAD (Milliradian) at distance.

MRAD Scale to 1000m
MRAD Scale to 1000m
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.
MRAD / MILS
Calculating Mils

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

  1. R = Circle Radius = Range to the target.
  2. 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

MIL Elevation Description

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.

MIL Turret

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

MIL(NATO) Calculator

MIL Calculator – A simple calculator to calculate MIL (NATO) at any distance.

MIL Scale
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

FAQ (Frequently Asked Questions)

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.

One milliradian is equal to 1/1000 of a radian, which is the standard unit of angle measurement in mathematics.

Milliradians are used in hunting to measure the amount of adjustment necessary to make small changes in aim when using a scope. For example, a scope with 1/10 milliradian click adjustments would allow the shooter to adjust their aim by 1/10 of a milliradian with each click of the elevation or windage adjustment knob.

1 MRAD = 1.018591 MIL

1 MIL =  0.981748 Milliradians (MRAD)

In a full circle there are:

  • 6283.18 Milliradians (MRAD)
  • 6400 MILS

1 MIL =  6283.18 / 6400 = 0.981748 Milliradians (MRAD)

1 MRAD = 6400 / 6283.18 = 1.018591MIL

0.1 MRAD = 10mm (1cm) at 100m.

1 MOA =  3.4377 Milliradians (MRAD)

1 MRAD = 0.290888 MOA

In a full circle there are:

  • 6283.18 Milliradians (MRAD)
  • 21600 MOA

1 MOA =  21600 / 6283.18 = 3.4377 Milliradians (MRAD)

1 MRAD = 6283.18 / 21600 = 0.290888 MOA

Minute of Angle (MOA) or Minute of Arc is a unit of angle measurement and is used extensively with shooters that are used to an imperial measurement system.

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