The Rifle Cartridge Killing Power Formula

By Chuck Hawks

I don't have much faith in killing power formulas in general. Most such formulas are obviously designed to reinforce someone's pre-conceived notions. As a result, these "killing power," "stopping power," "knock out" (or whatever they may be called) formulas typically disregard factors that are detrimental to their case.

I was curious to see what the results would look like if I included the most obvious, easily quantifiable, factors in a simple killing power formula. These factors are velocity, energy, bullet weight, sectional density (SD), and bullet cross-sectional area (frontal area). Upon reflection I realized that since velocity is already the most important factor in calculating kinetic energy, it would not be necessary to incorporate it separately.

That left the factors of energy, bullet weight, SD, and cross-sectional area. Then I received an e-mail from Ole Swang, who is a mathematician, and he pointed out that sectional density and frontal area equal bullet weight. Thus by including bullet weight separately I was, essentially, squaring its value. So I eliminated bullet weight. (But remember that, like velocity, it is actually present in the remaining factors.) That left the numbers for energy, SD, and frontal area to work with.



I am no mathematician; I am hopeless at algebra, and I can barely run a calculator. So whatever I attempted in the way of calculations would have to be simple. The KISS principle at work.

After playing around with those numbers on my hand calculator, I found that if I took energy at 100 yards and multiplied it by bullet sectional density (a fractional number) and bullet cross-sectional area (also a fractional number), the result was a manageable two or three digit number, which I then rounded off to one decimal place. Ergo, the killing power number.

Why, you may ask, did I choose energy at 100 yards instead of at the muzzle, or 200 yards, or someplace else? The answer is that I figured that most CXP2 to CXP4 game is probably killed between 50 and 150 yards. 100 yards is right in the middle of that spread, and energy at 100 yards is included in most ballistics tables, so it's an easy number to use. For our metric readers, 100 meters is only slightly longer than 100 yards, so for all practical purposes the same killing power results will apply at 100 meters as well as 100 yards. If you want to compare the killing power of cartridges at some other distance, just plug-in the energy figures for that distance and work the equation.

Here is the formula:
Energy at 100 yards (in foot pounds) x Sectional Density (taken from reloading manuals) x Bullet Frontal Area (in square inches) = Killing Power figure at 100 yards.

I am convinced that the most important factor in killing power, by far, is bullet placement. The second most important factor is probably bullet terminal performance (the area of the wound channel created by the bullet). The third most important factor is probably the physical and mental state of the game animal in question at the moment it is shot. As most experienced hunters have observed, even a well hit animal can run a long way on a full charge of adrenaline. This formula takes into account none of those factors. Unfortunately, those key factors are not quantifiable, at least by me.

So for the basis of this exercise in futility I am assuming that the hunter knows how to shoot, where to put the bullet, and that the bullet is appropriate for the game and conditions. Honestly, if you don't know where to aim, or can't hit your target, or have chosen an inappropriate bullet for your intended purpose, the killing power of your rifle becomes a moot point. As someone commented about gun fighting, "you can't miss fast enough to win."

I will say that after I had initially calculated the results for a number of common rifle cartridges using the formula above, I was encouraged. The results seemed reasonable in light of my personal research and experience.

I do, for example, think that the standard .24 and .25 caliber cartridges (.243 Win., 6mm Rem., .250 Sav., and .257 Rob.) are just about the minimum practical deer cartridges, that they are far superior to any .22 caliber cartridge for the purpose, and that there is not a great deal to choose between them. Further, I would argue that the .30-30 is an effective 100 yard deer cartridge and that the 7mm-08 represents an increase in killing power over the .30-30. For shooting the largest hoofed game, I would rate the .338 Win. Mag. superior in killing power to the .325 WSM, and I would have to say that the .375 H&H is even deadlier than the .338 Mag.

I think that most experienced and unbiased big game hunters would agree with those statements and, fortunately, the killing power numbers calculated by the formula above tend to verify those assertions. I therefore believe that, although undoubtedly not perfect, these killing power numbers generally seem to have a positive correlation with reality. That alone makes them more useful than most!

Remember that these numbers are the result of an attempt to apply a simple formula to an extremely complex problem--irregularities are bound to result. In any case, these are just numbers derived by an arbitrary formula. Unlike the creators of "pounds-feet," "impulse energy," "hydro-static shock" and other pseudo scientific terms, I want it to be clearly understood that these numbers do not represent any scientific quantity or unit of measurement. Use them as an indicator as seems appropriate, but do not attempt to make them into some sort of killing power dogma.

The list that follows is intended to suggest the relative killing power of various big game hunting cartridges and loads at 100 yards (or meters, if you prefer) when those cartridges are used appropriately. (Cartridge, bullet weight in grains, muzzle velocity in feet per second - killing power number at 100 yards.)

.223 Remington (60 grain at 3000 fps) - 6.3

.223 WSSM (64 grain at 3600 fps) - 10.1

.243 Winchester (87 grain at 3100 fps) - 15.2
.243 Winchester (95 grain at 3100 fps) - 18.3
.243 Winchester (100 grain at 2960 fps) - 18.1

6mm Remington (100 grain at 3100 fps) - 20.0

.243 WSSM (100 grain at 3100 fps) - 20.0

6x62 Freres (100 grain at 3200 fps) - 20.2

.240 Weatherby Magnum (100 grain at 3200 fps) - 20.2
.240 Weatherby Magnum (100 grain at 3406 fps) - 24.5
.25 Remington (117 grain at 2300 fps) - 13.3

.25-35 Winchester (117 grain at 2300 fps) - 13.3

.250 Savage (87 grain at 3000 fps) - 13.8
.250 Savage (100 grain at 2820 fps) - 15.1

.257 Roberts (100 grain at 2900 fps) - 17.4
.257 Roberts +P (115 grain at 2800 fps) - 22.3
.257 Roberts +P (120 grain at 2700 fps) - 22.0

.25 WSSM (115 grain at 3060 fps) - 26.7

.25-06 Remington (115 grain at 3060 fps) - 26.7

.25-06 Remington (120 grain at 2990 fps) - 26.5

.257 Weatherby Magnum (115 grain at 3200 fps) - 29.4
.257 Weatherby Magnum (120 grain at 3100 fps) - 29.3
.257 Weatherby Magnum (120 grain at 3305 fps) - 33.4

6.5x55 SE (120 grain at 2890 fps) - 28.0
6.5x55 SE (140 grain at 2700 fps) - 30.7
6.5x55 SE (160 grain at 2500 fps) - 30.9

.260 Remington (140 grain at 2750 fps) - 31.6
.260 Remington (160 grain at 2500 fps) - 30.9

6.5x57 (140 grain at 2700 fps) - 30.7

6.5mm-284 (140 grain at 2900 fps) - 35.6

6.5mm-06 (140 grain at 2900 fps) - 35.6

6.5mm Remington Magnum (120 grain at 3210 fps) - 30.2
6.5mm Remington Magnum (140 grain at 2900 fps) - 35.6

6.5x68 S (140 grain at 2900 fps) - 35.6

.264 Winchester Magnum (140 grain at 3030 fps) - 37.8

.270 Winchester (130 grain at 3150 fps) - 35.0
.270 Winchester (140 grain at 2950 fps) - 37.0
.270 Winchester (150 grain at 2850 fps) - 37.4

.270 WSM (140 grain at 3125 fps) - 40.1

.270 Weatherby Magnum (150 grain at 3245 fps) - 51.4

7x57 Mauser (139 grain at 2800 fps) - 31.7

7mm-08 Remington (140 grain at 2860 fps) - 33.6

.280 Remington (140 grain at 3000 fps) - 37.1

7mm Remington SAUM (150 grain at 3110 fps) - 44.8

7mm WSM (150 grain at 3110 fps) - 44.8

7mm Remington Magnum (139 grain at 3100 fps) - 39.1
7mm Remington Magnum (150 grain at 3110 fps) - 44.8
7mm Remington Magnum (175 grain at 2860 fps) - 53.3

7mm Weatherby Magnum (154 grain at 3260 fps) - 55.3
7mm Weatherby Magnum (175 grain at 3070 fps) - 62.4

7mm STW (140 grain at 3325 fps) - 44.5

7mm Remington Ultra Mag (154 grain at 3260 fps) - 55.3

.30 Carbine (110 grain at 1990 fps) - 7.4

.30-30 Winchester (150 grain at 2390 fps) - 22.8
.30-30 Winchester (170 grain at 2200 fps) - 25.4

.300 Savage (150 grain at 2630 fps) - 30.0

.307 Winchester (170 grain at 2500 fps) - 30.7

.308 Winchester (150 grain at 2820 fps) - 34.7
.308 Winchester (180 grain at 2620 fps) - 46.2

.30-06 Springfield (150 grain at 2920 fps) - 37.3
.30-06 Springfield (180 grain at 2700 fps) - 49.2
.30-06 Springfield (220 grain at 2410 fps) - 54.6

.300 Remington SAUM (150 grain at 3200 fps) - 47.2
.300 Remington SAUM (180 grain at 2960 fps) - 59.5

.300 WSM (150 grain at 3200 fps) - 47.2
.300 WSM (180 grain at 2960 fps) - 59.5

.308 Norma Magnum (180 grain at 2960 fps) - 59.5

.300 H&H Magnum (180 grain at 2960 fps) - 59.5

.300 Winchester Magnum (150 grain at 3200 fps) - 47.2
.300 Winchester Magnum (180 grain at 2960 fps) - 59.5

.300 Weatherby Magnum (180 grain at 3240 fps) - 72.8
.300 Weatherby Magnum (220 grain at 2845 fps) - 77.9

.300 Remington Ultra Mag (180 grain at 3240 fps) - 72.8

7.62x39 Soviet (123 grain at 2365 fps) - 15.7

.303 British (150 grain at 2685 fps) - 33.2
.303 British (180 grain at 2460 fps) - 40.1

.32 Winchester Special (170 at 2250 fps) - 25.4

8x57 JS Mauser (195 grain at 2550 fps) - 52.0

.325 WSM (180 grain at 3060 fps) - 65.3
.325 WSM (200 grain at 2950 fps) - 75.6
.325 WSM (220 grain at 2840 fps) - 81.7

8mm Remington Magnum (200 grain at 2900 fps) - 68.5

.338x57 O'Connor (200 grain at 2400 fps) - 39.7

.338-06 A Square (200 grain at 2750 fps) - 64.9

.338 Winchester Magnum (200 grain at 2960 fps) - 70.3
.338 Winchester Magnum (225 grain at 2800 fps) - 87.4
.338 Winchester Magnum (250 grain at 2650 fps) - 94.8

.340 Weatherby Magnum (250 grain at 2963 fps) - 117.4

.357 Magnum (Rifle) (158 grain at 1830 fps) - 12.7
.357 Magnum (Rifle) (180 grain at 1550 fps) - 9.5

.35 Remington (150 grain at 2300 fps) - 19.8
.35 Remington (200 grain at 2080 fps) - 28.7

.356 Winchester (200 grain at 2460 fps) - 44.6

.358 Winchester (200 grain at 2490 fps) - 47.0

.35 Whelen (200 at 2675 fps) - 56.4
.35 Whelen (250 at 2400 fps) - 75.3

.350 Remington Magnum (200 grain at 2700 fps) - 56.9
.350 Remington Magnum (200 grain at 2770 fps) - 60.9
.350 Remington Magnum (225 grain at 2550 fps) - 69.9
.350 Remington Magnum (225 grain at 2600 fps) - 72.8
.350 Remington Magnum (225 grain at 2640 fps) - 75.1
.350 Remington Magnum (250 grain at 2400 fps) - 76.7
.350 Remington Magnum (250 grain at 2500 fps) - 80.7

9.3x62 (270 grain at 2500 fps) - 92.8

9.3x74R (270 grain at 2300 fps) - 77.5

.375 Winchester (220 grain at 2200 fps) - 40.9

.375 H&H Magnum (270 grain at 2690 fps) - 106.2
.375 H&H Magnum (300 grain at 2530 fps) - 113.0

.376 Steyr (270 grain at 2600 fps) - 102.0

.378 Weatherby Magnum (300 grain at 2925 fps) - 150.5

.38-55 Winchester (220 grain at 1600 fps) - 21.2

.405 Winchester (300 grain at 2200 fps) - 70.7

.416 Remington Magnum (400 grain at 2400 fps) - 188.4

.416 Rigby (400 grain at 2400 fps) - 188.4

.44 Remington Magnum (Rifle) (240 grain at 1760 fps) - 26.4
.44 Remington Magnum (Rifle) (275 grain at 1580 fps) - 31.2

.444 Marlin (240 grain at 2350 fps) - 46.9
.444 Marlin (265 grain at 2325 fps) - 63.4
.444 Marlin (300 grain at 2200 fps) - 74.9

.45-70 Government (300 grain at 1810 fps) - 50.1
.45-70 Government (350 grain at 2100 fps) - 88.9
.45-70 Government (405 grain at 1330 fps) - 55.0

.450 Marlin (350 grain at 2100 fps) - 88.9

.458 Winchester Magnum (350 grain at 2100 fps) - 88.9
.458 Winchester Magnum (500 grain at 2090 fps) - 217.3

.458 Lott (500 grain at 2300 fps) - 228.5

.460 Weatherby Magnum (500 grain at 2600 fps) - 332.3

Post Script:
A couple of months after writing this article I chanced on a reference in the July/August 2005 issue of Rifle Shooter magazine to John Wooter's "lethality-factor index formula," of which I was not previously aware. The "L" formula apparently multiplies kinetic energy (in ft. lbs.) x sectional density x bullet diameter (in inches). Thus it incorporates two of the three factors I adopted for my Rifle Cartridge Killing Power Formula, and makes a nod in the direction of the third. (Apparently great minds think alike!)

I did a Google search and was able to discover that Mr. Wooters published his formula in the Jan 1996 issue of Peterson's Hunting magazine. I was not able to discover if the "L" formula was intended to be applied to handgun or rifle cartridges, or both, and I have not been able to locate a copy of the original article.

The difference between the two formulas seems to be that Wooters' chose to include bullet diameter as his third criteria, which has the advantage of being obvious, while I chose to use cross-sectional area, which must be computed (or taken from the list on the Tables, Charts and Lists Page). Both are attempts to take into account the size of the bullet.

Bullet diameter indicates the bullet's frontal area, while cross-sectional area is the bullet's frontal area. So in that sense I suspect that my formula is a bit more precise. But, if I had known about John Wooters earlier work I probably would have just used it as the basis of the table above and not bothered to develop my own killing power formula. I imagine that the comparative results would be quite similar (although perhaps not identical). But I did not.

Chuck Hawks, June 2005

Source: http://www.familyfriendsfirearms.com/forum/archive/index.php/t-42802.html&s=1980db8c4353b2add3da8fadb240e345&

Further reading:  http://forums.gunboards.com/showthread.php?21969-Killing-power-by-Chuck-Hawks