Rangefinding Formulas

Whether you’re hunting, target shooting, or just curious about the mathematics behind optics, being able to estimate distance to a target is incredibly useful. With nothing more than a rifle scope and some basic measurements, you can calculate range with surprising accuracy.

The principle is elegantly simple: if you know the actual size of an object and can measure how large it appears through your scope’s reticle, basic trigonometry will give you the distance. The formulas differ slightly depending on whether you’re using a first focal plane (FFP) or second focal plane (SFP) scope.

MIL and Its Relationship to Millimeters

MIL refers to milliradian (mrad), which is an angular measurement used in optics and ballistics. The key to understanding rangefinding is grasping the relationship between this angular measurement and linear distance.

The fundamental relationship:

• 1 milliradian subtends exactly 1 millimeter at 1 meter distance
• At 100 meters, 1 mrad = 100mm (10cm)
• At 1000 meters, 1 mrad = 1000mm (1 meter)

This linear relationship is what makes the rangefinding formula work. When you observe a target through your scope’s reticle and measure how many mils it spans, you’re measuring the angular size. Combined with knowledge of the target’s actual physical size, you can calculate the distance using basic trigonometry.

For example, if you know a deer is approximately 950mm tall and you observe it spanning 2 mils in your scope, the distance would be: $\text{Distance} = \frac{950\text{mm}}{2\text{mils}} = 475\text{meters}$

First Focal Plane

$\text{Distance (meters)} = \frac{\text{Actual size (mm)}}{\text{Observed size (mils)}}$

Second Focal Plane

$\text{Distance (meters)} = \frac{\text{Actual size (mm)} \times \text{Calibration magnification}}{\text{Observed size (mils)} \times \text{Current magnification}}$

Second focal plane scopes have reticles that change apparent size as you adjust magnification. This means the mil markings are only accurate at one specific magnification level (typically maximum magnification). The formula accounts for this by introducing a calibration magnification constant (the magnification where reticle markings are true to reality) and the current magnification variable.

Important note: If you’re using an SFP scope at maximum magnification, you can typically just use the simpler FFP formula since the reticle markings may be calibrated to be accurate at that setting.

Applying The Formula

If you are hunting animals you may want to set up a table similar to below:

Disclaimer: The measurements below are approximate averages and should not be relied upon for critical applications. Animal sizes vary significantly based on species, age, sex, and geographic location. Always verify measurements and practice safe shooting protocols. The author assumes no liability for the accuracy of these estimates or their use in field applications.

Animal	Average Height (mm)
Deer	950
Wild Boar	950
Fox	400
Cat	250
Goat	830
Dog	600
Kangaroo	2000
Camel	2000