Tim
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.
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
MRAD Calculator
MRAD Calculator – A simple calculator to calculate MRAD (Milliradian) at distance.
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
MIL(NATO) Calculator
MIL Calculator – A simple calculator to calculate MIL (NATO) at any distance.
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)
What is a milliradian?
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.
How many mil is a milliradian?
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
What is 0.1 MRAD at 100m?
0.1 MRAD = 10mm (1cm) at 100m.
How many MRADS are in a MOA?
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.