Binoculars Range Calculator

Binocular rangefinders convert the values of the reticle into distances. If a binocular or spotting scope has scales on its reticle, one can measure how many scale units an object takes up and from that calculate the distance to the object. By the same principle, observers at sea can use their altitude above the waterline to read off the range to a target below the horizon.

The purpose of this calculation tool:

This tool estimates the range to a target in two ways. The size-based ranging method requires entering the actual height or width of the target and the number of crosshair units that span the target to calculate the range. The horizon method requires entering the height from water level to eye level, as well as the number of milliradians (mil) below the horizon the target is located. This method is suitable for marine binoculars with vertical scales. You can choose whether to enter crosshair values in milliradian (mil) or MOA (Minute of Angle). A correction may be applied if using optical devices with a secondary focal plane, where the scale is accurate only at certain magnifications.

Application:

Select a method and set the reticle units to match your optic. Enter the number of milliradians (mil) or MOA (Minute of Angle) that span the target. For size-based range estimation enter the actual height or width of the target, for the horizon method enter the elevation from water to eye level. Check the calculated distance in the results area and switch units to display the range in meters, yards, kilometers, or nautical miles.

Information about milliradian (mil).

A milliradian (or "mil") is one-thousandth of a radian. Since a "mil" corresponds to a meter at a distance of one thousand meters, this gives rise to the classic range estimation formula.

D is the distance, H is the actual size of the target, both in meters. "Mils" is the value read on the crosshair. Assuming a person 1.8 meters tall takes up 5 "mils" on the crosshair, then this formula would be used to calculate the distance:

1000 is just a value to convert the number of "mils" expressed in radians into an integer. So this formula is an approximation for small angles where the distance is the result of dividing the size by the angle.

Distance estimation with MOA:

Some optical devices display values in "MOA" (Minutes of Angle). One MOA is one sixtieth of a degree and is approximately 0.2909 "mils". Therefore, this calculator first converts the read values to radians before performing the division. In the yard-pound system it is customary to express the same relationship as follows, where the size of the target is given in inches and the distance in yards:

If a target of 40 inches diameter covers a spread circle of 4 MOA (Minute Of Angle), then the distance is approximately equal to the result of multiplying 40 by 95.5 and dividing by 4, which equals about 955 yards. If units are consistent both methods will give the same distance.

Horizon method

Marine binoculars are usually fitted with vertical scales to measure distance at sea. Align the top mark on the horizon and then count how many scale units there are down to your target below the waterline. The same ratio in mils still applies if eye height above the water is used instead of size of target.

A bridge 10 meters above the water allows you to sight a target that is 20 mils below the horizon. The distance would be approximately 500 meters. This method works especially well for measuring distances to animals or ships in the background of water, as it assumes that the target is at sea level.

Correction for second focal plane

On optical instruments with a secondary focal plane the reticle maintains the same apparent size but as the image of the target is magnified or reduced the scales are only accurate at certain magnifications. If reading a target at a different magnification you must first proportionally adjust the readout value.

If a crosshair that is correctly calibrated at 10x magnification is read at 5x magnification, the effective reading will double and the estimated distance will halve. As the crosshair remains accurate in the first focal plane at all magnifications no corrections are required.

Why a lower reading means higher risk:

Because the distance and angle vary in opposite directions, a smaller measurement is more susceptible to error. A difference of just one or two milliradians can cause the result to be hundreds of meters off, while ten milliradians will have little effect on the same margin of error. If possible, stabilize your optical equipment, read the largest dimension of the target, and count carefully. The following table shows the distance for various measurements in milliradians when the size of the target is one meter.

Areas of application:

When it is necessary to determine distance without a laser and through optical devices, ranging with crosshairs is used. Marine biologists on research vessels use binoculars with crosshairs to measure the distance of whales. Sailors and coastal observers estimate the distance of buoys or headlands. Hunters and shooters use telescopic sights with mil-dot or MOA scales to determine the range of game animals or steel targets. This is a useful skill in the outdoors, as it requires only a scale and known size, and is worth mastering even though modern rangefinders are available.

This calculation tool is for general educational purposes and on-site estimations only. As the range finder depends upon accurate measurements with a crosshair and known target size, results should be considered estimates. In critical situations verify values with a laser rangefinder or nautical charts.