Hunting Scope Magnified Field of View (MFOV): How Does Yours Measure Up?

By Scott Fletcher

“Calculating numbers is easy. How or if to apply them requires graduation from the School of Hard Knocks”.  -  Scott Fletcher

The article about hunting scope selection considerations introduced the notion that a hunting scope’s FOV capability is as important as its magnification. Quite simply, target acquisition time (TAT) can be reduced if a scope’s FOV is wide enough to accommodate reference vegetation features or animals within the sight picture of “the” animal, particularly at the magnification the hunter believes is required to precisely identify the aim point, such as the heart. For example, if the magnification multiplier of 4 presented in the article is used to acquire the heart as the target, and the animal is laser-ranged at 200 yards, the resultant scope magnification of 8 should have a magnified field of view (MFOV) that produces a sight picture wide enough to reasonably accommodate peripheral reference objects so that “the” animal can be quickly identified.

This article first presents a method to calculate any scope’s FOV at magnifications intermediate of the scope’s maximum and minimum FOVs. Simple example problems show how this equation is used. The scope’s FOV values are required to enable a determination of the field of view presented by the scope when viewing an object at any distance at any selected magnification. This sight picture is defined as magnified field of view, MFOV. A simple equation and example problems are presented to demonstrate how MFOV is calculated.

MFOV is “just another number” unless some degree of field relevance can be attached to it. As presented and explained with example problems in this article, MFOV can be used in conjunction with the length of the animal being hunted to evaluate if the scope’s MFOV is reasonably wide enough to likely minimize target acquisition time (TAT) based on the defined hunting problem. This article presents guidance for evaluating MFOV in that context. Such evaluations could indicate a modification to the assumed/planned hunting strategy is warranted, or that the scope being considered is a marginal/poor choice for the intended application.

Calculate a scope’s field of view at any of its magnifications.

Manufacturers furnish a scope’s maximum and minimum FOVs in their published specifications. The scope’s maximum FOV occurs at its minimum magnification; the scope’s minimum FOV occurs at its maximum magnification. The FOVs at magnifications intermediate of the scope’s maximum and minimum must first be calculated in order to calculate any MFOVs. The FOVs intermediate of their specified maximum and minimum can be calculated using the equation found here. 

As an example, consider a scope with a specified magnification range of 3 to 18 power. The manufacturer-specified maximum FOV (FOV max) is 38.3 feet (11.7 m) at its minimum magnification (M min) of 3 power. The manufacturer-specified minimum FOV (FOV min) is 6.4 feet (2.0 m) at its maximum magnification (M max) of 18 power.

What would be the FOV at a magnification (M calc) of 9 power?

Substituting these numbers into the furnished equation yields:

FOV = [38.3] – [(9 - 3) x (VRF)]    where:

              VRF = [(38.3 - 6.4)] / [(18) – (3)] = [31.9] / [15] = 2.13

FOV = [38.3] – [(6) x (2.13)] = 38.3 – 12.8

FOV = 25.5 feet (7.8 m)

In this example, the sight-picture width at 9 power would be 25.5 feet (7.8 m).

What would be the FOV at a magnification (M calc) of 12 power?

Substituting these numbers into the furnished equation yields:

FOV = [38.3] – [(12 - 3) x (VRF)]    where:

              VRF = [(38.3 - 6.4)] / [(18) – (3)] = [31.9] / [15] = 2.13

FOV = [38.3] – [(9) x (2.13)] = 38.3 – 19.2

FOV = 19.1 feet (5.8 m)

In this example, the sight-picture width at 12 power would be 19.1 feet (5.8 m).

For this article to be meaningful and applied, I recommend that the manufacturer-specified FOV max and FOV min for a personal scope be identified, and the FOV’s for each scope power intermediate of its maximum and minimum power be calculated. For example, if the scope magnification ranges from 3 to 9 power, calculate its FOVs for 4, 5, 6, 7, and 8 power, as these values will be instrumental in evaluating the scope in the context of the subsequently presented example problems.

Calculate a scope’s field of view at any of its magnifications and at any distance.

All manufacturers reference both the maximum and minimum FOVs to either 100 yards (91 m) or 100 meters (109 yds), meaning that the specified fields of view and those fields of view intermediate of the maximum and minimum are only applicable to objects positioned at these distances. If a manufacturer has used 100 yards (91 m) as the referenced distance, an object being viewed at a distance greater than 100 yards (91 m) would have a FOV that is greater than the number specified. If the object being viewed is at a distance less than 100 yards (91 m), the FOV would be less than the number specified.

Fields of view (sight-picture widths) at any distance and at any magnification can be easily calculated if the FOVs for each of the scope’s magnifications has been determined as in the previous examples. I am defining a scope’s field of view (sight-picture width) at any magnification and at any distance as its magnified field of view, MFOV. The equation to calculate MFOV is shown here.

In the previously worked examples, the manufacturer had specified that the FOVs were referenced to 100 yards (91 m). That means all MFOV calculations must be performed using yards, then converted to meters (if desired).

Suppose you determined with a laser range-finder that a North American pronghorn was facing broadside at a distance of 300 yards. What would be the MFOV at 9 power using the 3-18 scope? 

Substituting numbers into the furnished equation yields:

MFOV = (FOV) x (SD / 100)

             = (25.5) x (300 / 100) = 25.5 x 3

             = 76.5 feet (23.3 m)

What would be the MFOV at 12 power using the 3-18 scope?

MFOV = (FOV) x (SD / 100)

             = (19.1) x (300 / 100) = 19.1 x 3

             = 57.3 feet (17.5 m)

Notice two things: first, the increase in target distance beyond the referenced 100 yards increased the sight-picture width by a considerable amount. Second, the increase in scope power reduced it.

If you were hunting from a blind near a water “tank” and the pronghorn was only 50 yards away, what would be the MFOV if it were viewed at 9 power?

MFOV = (FOV) x (SD / 100)

             = (25.5) x (50 / 100) = 25.5 x .5

             = 12.8 feet (3.9 m)

What would be the MFOV if you viewed the pronghorn at 12 power?

MFOV = (FOV) x (SD / 100)

             = (19.1) x (50 / 100) = 19.1 x .5

             = 9.6 feet (2.9 m)

Note that a decrease in target distance to less than 100 yards decreased MFOV by a considerable amount. As with the 300-yard example, increasing the scope’s magnification again decreased MFOV.

How much MFOV is reasonably “enough” so that TAT is likely not adversely affected?

These two examples demonstrate that any increase in a scope’s magnification decreases its field of view, no matter what the distance. Any benefit gained from this magnification increase must be evaluated based on any potential detrimental impact on TAT that the reduced MFOV may create.

In an ideal world, a lower-bound TAT occurs when a scope power compatible with the desired aim point produces a MFOV in which the animal is instantaneously identified without panning the scope or adjusting its magnification. The next-best scenario is that the scope only needs to be panned slightly, without adjusting the magnification. Beyond those desirable initial target acquisition steps, TAT time increases exponentially with the number of magnification adjustments that are made to first acquire the animal, then sufficiently magnify the intended aim point.

I believe a reasonable judgement of how much MFOV is “enough” comes from evaluating both herd characteristics and the length-wise dimension of the animals being hunted. Most big-game animal herds are not oval-shaped pods associated with agricultural animals. Although Photo 1 is of a cape buffalo herd, its oval shape is not typical of the majority of big-game herds. A typical herd configuration is linear, such as with the blue wildebeest herd in Photo 2. Even bachelor herds are primarily linear, such as in Photo 3.  Photo 2 and Photo 3 identify animals that can reasonably described as nose-to-rump.

Herds can be linearly strung out, such as with the zebras in Photo 4. Photo 4 also depicts what a PH could identify as reference animals in order for the hunter to find “the” target animal. The PH could describe the actual animal selected as “the second zebra up the hill from the stacked two facing in opposite directions”. Note that all the animals “look the same”, and such a reference is required to target “the” animal.

Photo 5 is another example of a herd that is linearly strung out. All the kudus have horns that negate a quick target acquisition. The PH must once again reference “the” bull, likely based on the two clustered on the right.

Photo 6 shows an easily identifiable impala ram within a primarily linear herd. If this was a management hunt, however, the PH would have identified “the” ewe, again using a reference, likely either the ram or the bush.

The animals identified in the previous photos all have a published, identifiable length. Table 1 presents such data for selected animals. If a zebra is about 1.5 times longer than an impala, three zebras standing nose-to-rump will occupy the same MFOV width as almost five impala standing nose-to-rump. Consequently, any judgement of a reasonable MFOV width should also consider the length of the animal being viewed.

This judgement can be made easier based on selecting a reasonable ratio of the animal’s nose-to-rump length to the MFOV width afforded by the scope at the selected magnification. Personal experience indicates a lower-bound MFOV width at least 5 times greater than the length of the animal contributes to a reduction in TAT. The value of 5 is determined by dividing a scope’s MFOV by the animal’s length.  This MFOV width to animal length is a ratio, defined as R, found in equation form here. Values of R progressively greater than 5 are judged to potentially decrease TAT; values of R progressively less than 5 are judged to exponentially increase it.

How are all these equations used to determine R?

In word form, the sequential steps to determine R are as follows:

1) Calculate FOV’s for all the scope magnifications on the scope being considered using the equation found here.

2) Select a magnification multiplier considered appropriate for the defined hunting problem. A discussion of selection issues is presented in this article on page 5.

3) Calculate the required magnification for the shot distance being considered using the equation presented in this article on page 5.

4) Calculate the MFOV using the equation found here for the shot distance being considered using the scope’s FOV identified in Step 2) at the required magnification identified in Step 3).

5) Calculate R using the equation found here using the calculated MFOV in Step 4) and the rump-to-tail length of the selected animal.

The previous example problems for the 3-18 power scope identified a FOV and MFOV at both 9 and 12 power. The following example demonstrates the sequence of how these calculations can be used for determining R. The animal referenced is a North American pronghorn antelope. Table 1 shows an average length of 4.6 feet (1.4 m). As stated, the animal is laser-ranged at 300 yards (273 m).

A lung shot is desired, and the corresponding magnification multiplier is 3. The resultant scope power is [(3) x (300)] /100 = 9, as identified in Step 3).

As calculated in the previous examples, the scope’s FOV at 9 power is 25.5 feet (7.8 m), with the resulting scope’s MFOV at 300 yards (273 m) calculated as 76.5 feet (23.3 m). The resulting R is 76.5 / 4.6 = 16.6, considerably more than 5. For this animal in this hunting scenario, the scope’s MFOV is more than ample.

What if a heart shot is desired? The corresponding magnification multiplier is 4, and the resulting scope power is [(4) x (300)] /100 = 12. As previously calculated, the scope’s FOV at 12 power is 19.1 feet (5.8 m), and the calculated MFOV at 300 yards (273 m) is 57.3 feet (17.5 m). The resulting R is 57.3 / 4.6 = 12.5, considerably more than 5. Again, for this animal in this hunting scenario, the scope’s MFOV is more than ample.

How are all these equations used to evaluate a scope’s MFOV in actual hunting situations?

The previous example is reasonably simple because the animal, the shot distance, the scope, and the magnification multiplier were all stipulated. What if the shot distances could range from 50 to 400 yards (46 to 364 m) and the animal could be either a mule deer or an elk? What if the scope on the selected rifle was judged to have inadequate magnification for the 400-yard shot and there were only several alternative scopes to choose from, each with a different magnification range? What if the hunted animals were on a “hunt of a lifetime” and any shot opportunity not taken could never be replaced?

The previous questions represent real-world issues associated with a potential hunt. Judgements made to resolve such issues are a matter of personal choice that are influenced by risks a hunter is willing to take and the cost and effort associated with any risk mitigation. There are no “right” or “wrong” judgements, only personal ones where any adverse outcomes must be “owned”.

Evaluating a scope’s MFOV should be done in the context of a defined hunting problem with the embedded personal preferences of each hunter. The following examples present hunting problems where the resultant scope evaluations could be reasonably applied to other defined hunting problems. The intent is to “let the numbers speak for themselves”; what they “say” must be individually interpreted by each hunter.

Suggested metrics for defining any hunting problem are presented in eBook Chapter 9. Metrics essential for these example problems are:

-         Hunting method

-         Shot distance

-         Vegetation

-         Terrain

-         Shooting position

-         Aim point target size

-         Animal

Hunting Example Problem #1

The hunt will be primarily for trophy animals in Africa. Animals on the bag list include an impala, a kudu, and a blue wildebeest. The outfitter has indicated there will be management hunt opportunities for impala ewes, kudu cows, and blue wildebeest cows. The vegetation and terrain are as depicted in Photo 7.

The desired hunting method for the trophy animals is spot and stalk/walk and stalk. The outfitter expects shot distances to range from about 90 to 220 yards (82 – 200 m). The outfitter has volunteered that the average shot distance is on the order of 150 yards (137 m). The primary shooting position will be from sticks. The outfitter has indicated that the PH will require shots to be placed on the shoulder of the trophy animals, primarily from the broadside shooting angle. Because shots will be placed on the shoulder, the presumptive target is the heart or plumbing directly above the heart, and the heart’s average diameter is assumed to be 5 inches (13 cm).

Management hunts will be either spot and stalk or ambush from a blind situated adjacent to a water source. Photo 8 depicts what the shooting conditions could resemble when viewed from the blind, and Photo 9 depicts the blind when viewed from the water source. The water source could range from about 75 to no greater than 150 yards (68 – 137 m) from the blind. As identified in the photos, the shooting position will be seated using a bipod. You have assumed that the primary aim point on the animals will be the lungs to reduce the potential volume of bloodshot meat on the shoulder. You have further assumed that the average diameter of the lungs for all animals is 10 inches (25 cm).

Two scopes are available:  a 1.7-10 power with a fixed focus and specifications identified in Table 2, and a 3-18 power with an adjustable focus and specifications identified in Table 3. How each scope’s magnification, focus, eye relief, and reticle illumination can potentially affect TAT are discussed here. Magnified fields of view, MFOV, and the MFOV to animal-length ratios, R, are presented in Table 4.

In terms of “R”, can either of these scopes be considered acceptable for this stipulated hunt definition? If both are considered acceptable, is one “better” than the other? How well would your selected scope likely perform in this example problem?

Table 4 presents compiled data for both scopes at shot distances slightly less and slightly more than those identified by the outfitter. R values for a lung shot and a heart shot are presented for an impala, a kudu, and a blue wildebeest at these expanded shot distances.

Evaluating the R values for a heart shot on a blue wildebeest is the most conservative way of evaluating the data because a blue wildebeest is the longest animal that will be hunted, and the higher magnification required for a heart shot reduces the MFOV. This combination of short MFOV and long animal length produces the smallest R values. The R values vs shot distances for a heart shot on a blue wildebeest are presented in Bar Graph 1.

The 1.7-10 power scope is designated as Scope 1, and the 3-18 power scope is designated as Scope 2. This bar graph indicates Scope 1 has an R value greater than 5 for shot distances from 50 to 200 yards (46 – 182 m).  Scope 1 is clearly superior to Scope 2 for shot distances between 50 and 150 yards, as its R values range from about 36 to 93 % greater than Scope 2’s. At 200 yards (182 m), both scopes have identical R values substantially greater than 5.

Bar Graph 1 indicates Scope 2 is clearly superior to Scope 1 for shot distances greater than 200 yards (182 m). Scope 1’s sole, marginal value of 4.4 occurs at 250 yards (228 m). At that distance, Scope 2’s R value is about 85 % greater than Scope 1’s. However, Scope 2’s R value of 2.7 at 50 yards (46 m) is about 46 % less than the R value of 5 that is considered to be a reasonable lower bound.

Objectively, both scopes can be considered satisfactory when only R values are considered. A marginal R value for Scope 1 only occurs at a conservatively selected shot distance of 250 yards (228 m) for the largest animal that will be hunted. The odds of such a circumstance occurring on the hunt are probably low. If the 220-yard (200 m) maximum shot distance identified by the outfitter occurs, a scope power of only 9 would be required for a heart shot. At this scope power and yardage, Scope 1’s calculated R value for the blue wildebeest is 6.2.

 A marginal R value of 2.7 for Scope 2 only occurs at the conservatively selected short (50 yd/46 m) shot distance, again with the longest animal on the hunt. As with the long-shot scenario with Scope 1, the probability of this short-shot scenario with Scope 2 is probably low.

If the 90-yard (82 m) minimum shot distance identified by the outfitter occurs with Scope 2, a scope power of 4 would be required for a heart shot. At this scope power and yardage, Scope 2’s calculated R value for the blue wildebeest is 4.6, about 70 % greater than its R value of 2.7 at 50 yards (46 m).

If Scope 2 was used for a 50-yard (46 m) shot from a blind, the concealed location and shooting position would likely allow sufficient time to identify “the” animal and take the shot regardless of a marginal R value. However, if any shot distance less than 100 yards (91 m) occurred while shooting from the sticks, TAT could be significantly affected because of increased difficulty in initially identifying the selected animal.

Hunters must judge how frequent either a short-distance or long-distance shot could occur in the context of potentially not being able to find the animal or expeditiously take the shot. In the case of this example problem, this judgement could potentially be the basis for selecting the scope for this hunt.

Hunting Example Problem #2

The hunt will be primarily for trophy animals in Africa. Animals on the bag list include a springbok, a blesbok, and a zebra. The outfitter has indicated there will be management hunt opportunities for springbok ewes and blesbok cows. The vegetation and terrain are as depicted in Photo 10.

The desired hunting method for both the trophy and management animals is spot and stalk/walk and stalk. Shot distances are expected to range from about 150 to 350 yards (137 – 319 m). The outfitter has volunteered that the average shot distance is on the order of 225 yards (205 m) for zebra, and 300 yards (273 m) for both the springbok and the blesbok. The primary shooting position will be from sticks. The outfitter has indicated that the PH will require shots to be placed on the shoulder for the trophy animals, primarily from the broadside shooting angle. Because shots will be placed on the shoulder, the presumptive target is the heart or plumbing directly above the heart, and the heart’s average diameter is assumed to be 5 inches (13 cm).  For the management hunts, you have assumed that the primary aim point on the animals will be the lungs to reduce the potential volume of bloodshot meat on the shoulder. You have further assumed that the average diameter of the lungs for all animals is 10 inches (25 cm).

Two scopes are available:  the previously identified 3-18 power with an adjustable focus and specifications identified in Table 3, and a 6.5-20 power with an adjustable focus and specifications identified in Table 5. As with Example Problem #1, how each scope’s magnification, focus, eye relief, and reticle illumination could potentially affect TAT are discussed here. Magnified fields of view, MFOV, and the MFOV to animal-length ratios, R, are presented in Table 6.

In terms of “R”, can either of these scopes be considered acceptable for this stipulated hunt definition? If both are considered acceptable, is one “better” than the other? How well would your selected scope likely perform in this example problem?

Table 6 presents compiled data for both scopes at shot distances slightly less and slightly more than those identified by the outfitter. R values for a lung shot and a heart shot are presented for a springbok, a blesbok, and a zebra at these expanded shot distances. As with Example Problem # 1, evaluating the R values of the zebra is the most conservative way of evaluating the data, as this animal is the longest and thus has the lowest R values. The R values vs shot distances for a heart shot on a zebra are presented in Bar Graph 2.

The 3-18 power scope is again designated as Scope 2. The 6.5-20 power scope is designated as Scope 3. This graph indicates Scope 2 has an R value greater than 5 for all shot distances when only heart shots on zebras are considered. This graph also indicates that Scope 3 had no R value greater than 5 for any shot distance when only heart shots on zebras are considered, even though its magnification capabilities are similar to those of Scope 2. If the shot distance is from 150 to 350 yards (137 - 319 m), Scope 3 has R values ranging from about 8 to 40 % less than the R value of 5 that is considered to be a reasonable lower bound. For an average shot of 225 yards (205 m) on a zebra, Scope 3 has an R value of 4.0, 51 % lower than Scope 2’s value of 8.1.

The significant disparity in R values between these two scopes can be attributed to their internal design. Scope 2 is a hunting scope purposely designed with generous FOVs at both its maximum and minimum magnifications. Scope 3 is a long-range target scope where FOV is not a primary design priority. As identified in Bar Graph 2, the R values calculated for Scope 3 indicate that this long-range target scope cannot be reasonably considered as acceptable for a trophy hunt in this hunting example problem, particularly when Scope 2 is available.

Using the maximum length of the animal on a trophy hunt is, admittedly, a conservative way to evaluate these scopes. Some could consider such conservatism overly restrictive. Fair enough. Do the data in Table 6 suggest a reasonable application for Scope 3?

The data suggest that a reasonable application of Scope 3 could be on a springbok or a blesbok management hunt in the terrain, vegetation, and distances cited for this example problem. As shown in Bar Graph 3, R values for a lung shot on springboks are essentially at 5 or greater for shot distances ranging from 150 to 400 yards (137 – 364 m). For blesboks, R values greater than 5 occur at shot distances from 250 to 400 yards (228 – 364 m). For an average shot distance of 300 yards (273 m) , a lung shot on a springbok results in an R value of 8.7, and a lung shot on a blesbok results in an R value of 6.1, both above the lower-bound value of 5.

Hunting Example Problem Takeaways

Both example problems demonstrate the merit of critically evaluating a scope’s FOV and its resulting MFOV in the context of a defined hunting problem. Key data in that definition include hunting method, shot distance, vegetation, terrain, shooting position, aim-point target size, and specific animals. The resultant calculation of R can be a reasonable basis for selecting a scope compatible with the defined hunting problem.

In Example Problem #1, the presumably inferior magnification of the 1.7-10 power scope is offset by its generous FOV and the resulting MFOV and R values calculated in the context of the defined hunting problem. Its magnification range is “enough” for the stipulated target size at the typical shot distances expected. If the shot distances for the defined hunting problem had been greater or the majority of the shots taken would be between 200 to 250 yards (182 – 228 m), the 3-18 power scope would likely be preferred. However, if the maximum-length animal had been a kudu, the resulting R value at 250 yards (228 m) for the 1.7-10 power scope would have been 5.1. As a consequence, there would have been virtually no hunt circumstances of concern that could not be easily accommodated by the 1.7-10 power scope.

In Example Problem #2, both scopes had reasonably similar magnifications. Because of the expected shot distances, the 6.5-20 power scope was presumably the “obvious” choice strictly based on its greater magnification. However, evaluation of its MFOV and attendant R values in the context of the defined hunting problem indicated a likely serious deficiency in it field performance, particularly when trophy hunting zebras.

Example Problem #2 also better demonstrates the importance of how the hunting problem definition affects the evaluation of a candidate scope. The original definition was for a trophy hunt that included a zebra. The target selection of the heart and the zebra as the maximum-length animal effectively eliminated the 6.5-20 power scope from consideration. As described, a management hunt for springboks and blesboks would have resulted in the 6.5-20 power scope being at least considered. If it was the only scope available, the analysis indicated likely acceptable performance in this defined management hunt application.

Homework Problem

The hunt will be a management hunt for blue wildebeest, both cows and bulls. Photo 11 identifies the terrain and vegetation. Note that the vegetation is a combination of conditions identified in Photo 7 and Photo 10. The primary hunting method will be spot and stalk, but some ambush hunting at water sources from field-fabricated blinds will occur. Shot distances could range from 50 to 400 yards (46 – 364 m).

Would your personal scope be a satisfactory choice for use in this hunting problem? Why or why not?

If your personal scope is not a satisfactory choice, would any of the scopes identified in this article be satisfactory? Why or why not?

Is there any scope from any manufacturer that is “better” than either your personal scope or any of the three identified in this article? Why or why not?

Select a scope for use on this defined hunt.  What are its limitations within the defined hunt circumstances that could result in an unsatisfactory outcome? In what ways could these limiting circumstances be mitigated during the hunt?

I wish you all success and good hunting.