Ballistic Visualizer

Version 1.3.0 · 2026-11-06

Documentation

1. What the tool is and what it does

The Ballistic Visualizer is a tool for seeing which combinations of cartridge caliber and projectile are suitable for hunting a given game animal, while staying within several limits on projectile performance.

You enter values describing the game being hunted, the firearm, the projectile type, and the atmospheric conditions. The tool then computes the range of possible projectile weights, calibers and recommended muzzle velocities, and displays them as a 3-dimensional solid on a 3D graph. Any point inside the solid is a combination that satisfies every limit below. All calculation and drawing happen in your browser; nothing is sent to a server.

The six limitations

Minimum sectional density. The projectile must have sufficient sectional density for the chosen game weight. This ensures the projectile can penetrate sufficiently, assuming the bullet construction is also appropriate for the chosen game. See section 3 for details on how this value is computed.
Minimum stability factor. Given the barrel twist rate, the projectile must be able to be stabilized in flight, and therefore must have a stability factor of at least 1.5 using the Miller twist rule formula.
Minimum energy. The projectile must have sufficient energy to ethically harvest the game, assuming the bullet construction is suitable to deliver this energy to the target. See section 3 for details on how this value is computed.
Maximum projectile RPM. The projectile type (jacketed, bonded, or copper monolithic) determines the maximum spin rate (RPM) the projectile can withstand in flight. Given the barrel twist rate, this RPM limit caps the maximum velocity.
Minimum velocity for expansion. The projectile must be traveling fast enough to expand.
Maximum recoil. The combination of firearm weight, projectile weight, powder charge and muzzle brake efficiency determines the recoil the firearm produces. The choice of caliber and projectile is limited by the recoil energy limit you set. See section 3 for details on how recoil is computed.

In addition, the solid is bounded by the edges of the graph: projectile weight 15–450 gr, caliber 0.170–0.500 in, and velocity 0–3500 fps.

The solid shows only combinations that satisfy the six limits above. It does not judge whether a particular bullet’s construction is suitable for a given animal, or whether a cartridge is legal for a given hunt. Those remain your responsibility; see section 4.

2. How to use the tool

Reading the graph

X axis (red): projectile weight, in grains (15–450).
Y axis (green): caliber, in inches (0.170–0.500).
Z axis (blue, vertical): projectile velocity, in feet per second (0–3500).

The translucent solid is the set of acceptable combinations. If your inputs allow no combination at all, no solid is drawn and the readout in the lower left says “No feasible region for these inputs.” Otherwise that readout lists the solid’s extents on each axis, how much of the graph box it fills, and how many triangles were drawn.

Navigating the graph

Action	Mouse	Touch screen
Rotate	Left-drag	One-finger drag
Pan (move the graph in the window)	Right-drag	Two-finger drag
Zoom	Mouse wheel	Pinch

The View section of the controls also has Zoom in, Zoom out, Pan left/right/up/down, and Reset view buttons. Reset view returns to the starting angle and position.

Input controls

The Inputs section of the controls box (upper right) holds the values that shape the solid. The solid is recomputed as you move each control.

Control	Units	Range	Default	What it is
Game animal	pull-down menu	38 animals, or User Weight	Whitetail Deer	The game animal being hunted. Choosing an animal (together with a size) fills in the game weight. See “Selecting the game animal and size” below.
Game size	pull-down menu	Small, Average, Large, or User Weight	Average	The size of the animal within its species.
Game weight	lb	3 – 2200	230 (Whitetail Deer, Average)	Weight of the animal being hunted. Sets the minimum sectional density and minimum energy required. It is filled in by the animal and size menus, or you can drag the slider or type a weight.
Twist rate	in per turn	3 – 16	8	Inches of barrel travel per full rotation of the projectile (for example, 8 means 1:8). Affects stability and the maximum velocity allowed by the RPM limit.
Powder charge	grains	3 – 125	43	Weight of the powder charge. Contributes to recoil.
Muzzle brake	% efficiency	0 – 100	75	Efficiency of the muzzle brake. A higher value reduces recoil. Use 0 for no brake.
Recoil limit	ft-lbs	5 – 60	22	Maximum recoil energy you will accept.
Firearm weight	oz	10 – 320	136	Weight of the firearm as it will be shot. A heavier firearm recoils less.
Projectile type	pull-down menu	3 choices	Jacketed Copper-Lead	Construction of the projectile. See the table below.
Ambient temp	°F	−40 – 120	80	Air temperature. Affects the stability factor.
Altitude	feet above sea level	0 – 14000	200	Elevation of the hunt. Affects the stability factor through air pressure.

The projectile type sets three values used by the calculations:

Projectile type	Density term	Maximum RPM	Minimum velocity for expansion
Jacketed Copper-Lead	0.409	300,000	1800 fps
Bonded Copper-Lead	0.409	325,000	1800 fps
Copper Monolithic	0.323	400,000	2200 fps

Selecting the game animal and size

The first three controls in the Inputs section set the game weight, and there are two ways to use them:

Pick an animal. Choose a North American game animal in the Game animal menu and a Game size of Small, Average or Large. The Game weight slider is filled in with the weight for that animal and size from the table below. The tool starts with Whitetail Deer at Average size (230 lb).
Enter your own weight. Drag the Game weight slider, or type a weight in pounds into its number box, just as before. Once you do, both menus change to User Weight, showing that the weight no longer comes from the table.

You can return to the table at any time by choosing an animal or a size again. If you choose an animal while the size shows User Weight, the size is set to Average (or to the last size you chose). If you choose a size while the animal shows User Weight, the last animal you chose is used. Choosing User Weight in either menu keeps the current weight and sets both menus to User Weight.

The game weight can range from 3 lb up to 2200 lb (Large Bison). Weights above 1250 lb are not well referenced; see section 4.

Game animal	Small (lb)	Average (lb)	Large (lb)
Alaska Brown Bear	180	740	1300
Alaska Yukon Moose	800	1200	1600
American Badger	10	22	33
American Elk	375	738	1100
Barren-Ground Caribou	150	240	330
Beaver	24	45	66
Bighorn Sheep	160	255	350
Bison	790	1495	2200
Black Bear	130	395	660
Canadian Moose	600	1095	1590
Central Canada Barren-Ground Caribou	250	350	450
Columbian Blacktail Deer	150	175	200
Coues Deer	60	80	100
Cougar	64	142	220
Coyote	18	31	44
Dall Sheep	130	215	300
Desert Bighorn Sheep	115	198	280
Grizzly Bear	180	940	1700
Groundhog	5	10	14
Mountain Caribou	400	500	600
Mule Deer	120	235	350
Muskox	400	650	900
Polar Bear	330	440	550
Pronghorn Antelope	75	108	140
Quebec/Labrador Caribou	200	300	400
Rabbit	3	5	6
Raccoon	11	19	26
Red Fox / Gray Fox	5	18	31
Rocky Mountain Goat	180	283	385
Roosevelt Elk	700	950	1200
Shiras Moose	600	900	1200
Sitka Blacktail Deer	80	140	200
Stone Sheep	150	185	220
Tule Elk	370	460	550
Whitetail Deer	150	230	310
Wild Boar	75	163	250
Wolverine	18	29	40
Woodland Caribou	300	350	400

The legend and surface colors

The legend in the upper left, under the title, explains what each colored surface of the solid represents. It lists only the surfaces that actually form part of the solid’s boundary for the current inputs. Where a surface has a fixed numeric limit, the limit is shown in parentheses: the sectional density, the energy in ft-lbs, the recoil limit in ft-lbs, and the velocity limits in fps. The values update as you change the inputs. Surfaces named for the edge of the graph (for example “Weight ≤ 450 gr” or “Velocity ≥ 0 fps”) show where the solid is cut off by the range of the axes.

Tip: temporarily set Solid opacity to 1.00. With the solid fully opaque, the colors of the individual surfaces are much easier to see, and you can match them to the legend. Set it back to a lower value to see inside the solid again.

Display settings

The Display section changes how the solid and graph are drawn. It does not change the calculation.

Setting	Range / default	Effect
Solid opacity	0 – 1, default 0.35	How see-through the solid is. At low values you can see the marker point, plane and graph behind and inside the solid. At 1.00 the solid is fully opaque.
Color by surface	on / off, default on	On: each boundary surface has its own color, matching the legend. Off: the whole solid is a single color and the legend is hidden.
Solid color	color picker	The single color used when Color by surface is off.
Show edges	on / off, default on	Draws thin white lines where two surfaces meet, making the outline of the solid easier to read.
Grid resolution	32 – 128, default 64	How finely the curved surfaces are sampled. Higher values give smoother surfaces but slower updates. Edges where surfaces meet stay sharp at any setting. The change applies when you release the slider.
Show mesh	on / off, default off	Overlays the triangle mesh used to draw the solid.
Show grid	on / off, default on	Shows faint grid lines on the floor and two back walls of the graph.
Show axes / labels	on / off, default on	Shows the graph box, axes, tick values and axis titles.

The marker point

The marker point lets you mark a candidate projectile on the graph and see whether it is inside the computed envelope. It appears as a yellow sphere, set with the Marker point / plane controls:

Control	Units	Range	Default
Weight	grains	15 – 450	130
Caliber	inches	0.170 – 0.500	0.264
Velocity	fps	0 – 3500	2860

Show point turns the marker on or off.
Drop lines draws lines from the point down to the floor of the graph and along the floor to the weight and caliber axes, so you can read its position.
If the point is inside the solid, the combination satisfies all six limits. If it is outside, rotate the graph to see which surface it falls beyond. Lowering Solid opacity helps you see the point through the solid.

The plane

Turning on Show plane draws a flat plane through the marker point, perpendicular to the axis chosen in Plane normal axis (at point): Projectile Weight, Caliber or Velocity. The plane sits at the marker’s value on that axis. For example, with the plane set to Caliber and the marker caliber at 0.264, the plane is at caliber 0.264.

The part of the plane that lies inside the solid is highlighted in a brighter color, with a white outline where it meets the solid’s boundary surfaces. This is the cross-section of the envelope at that plane.

The plane is especially useful when set to Caliber. The highlighted area then shows, for that single caliber, every combination of projectile weight and velocity that is acceptable: read the weight range along the X axis and the velocity range along the Z axis. Change the marker’s caliber to step through other calibers. Since the marker point always lies on the plane, the point is inside the envelope exactly when it sits within the highlighted area.

Setting inputs from the web address

Inputs can be set by adding parameters to the page’s web address. Any parameter you leave out keeps its default. Numbers outside a control’s range are limited to that range, and unreadable values are ignored. Example:

BallisticVisualizer.html?w=400&t=9&pt=c&pw=180&cal=0.308&vel=2700&plane=caliber

Parameter	Sets	Values
`ga`	Game animal	An animal name from the table above, such as `Whitetail Deer`. Capitalization, spaces and punctuation are ignored, so `whitetaildeer` and `whitetail-deer` also work.
`gs`	Game size	`small`, `average` or `large` (or `s`, `a`, `l`). If only one of `ga` and `gs` is given, the other defaults to Whitetail Deer or Average.
`w`	Game weight	3–2200 lb. If `w` is given it overrides `ga` and `gs`, and both menus show User Weight.
`t`	Twist rate	3–16 in per turn
`p`	Powder charge	3–125 gr
`b`	Muzzle brake	0–100 (percent)
`rl`	Recoil limit	5–60 ft-lbs
`f`	Firearm weight	10–320 oz
`pt`	Projectile type	`j` = Jacketed Copper-Lead, `b` = Bonded Copper-Lead, `c` = Copper Monolithic
`temp`	Ambient temperature	−40–120 °F
`alt`	Altitude	0–14000 ft
`pw`	Marker weight	15–450 gr
`cal`	Marker caliber	0.170–0.500 in
`vel`	Marker velocity	0–3500 fps
`marker`	Show the marker point	`1` or `0`
`plane`	Show the plane, and its normal axis	`weight`, `caliber`, `velocity`, or `none`
`gui`	Controls box	`0` hides it

3. How the sectional density, energy and recoil limits are computed

Minimum sectional density

The minimum sectional density is computed from recommended sectional densities for different game weights, published by Chuck Hawks at https://www.chuckhawks.com/sd_vs_game_weight.htm.

The sectional densities in that source were plotted in Excel against game weight, and an equation was curve-fit to them. That equation is:

S = 0.0684 * w^0.2095

where w is the game weight in pounds and S is the minimum sectional density. For example, a 250 lb animal gives S ≈ 0.217.

A projectile’s own sectional density is its weight in pounds (grains divided by 7000) divided by the square of its caliber in inches. A weight and caliber combination meets this limit when its sectional density is at least S. Because heavier, narrower projectiles have higher sectional density, this limit appears as a surface that excludes light, wide projectiles from the solid.

Minimum energy

The minimum energy is computed from data published on the Burris Optics website, listing ethical loads by game species:

Burris Optics: https://burrisoptics.zendesk.com/hc/en-us/articles/36813352161431-Ethical-Loads-by-Game-Species

As with sectional density, the data was plotted in Excel against game weight, and an equation was curve-fit to it. That equation is:

E = -0.0006 * w^2 + 2.8846 * w + 397.23

where w is the game weight in pounds and E is the minimum energy in foot-pounds (ft-lbs). For example, a 250 lb animal gives E ≈ 1081 ft-lbs.

A projectile’s energy is calculated from its weight and velocity, and a combination meets this limit when that energy is at least E. Heavier projectiles need less velocity to reach the required energy, so this limit appears as a surface that excludes slow, light projectiles from the solid.

Both equations are curve fits to published recommendations. They are an approximation of those sources, not a replacement for them, and the fits are only as good as the underlying data. See section 4 about game weights above 1250 lb.

Recoil

The recoil felt by the shooter is computed using the physics rule that the total momentum of everything that leaves the firearm must equal the total momentum of the firearm itself, with the movement in the opposite direction.

There are three sources of momentum leaving the firearm:

The projectile leaving the barrel.
The powder. The powder burns into a gas, and that gas also leaves the barrel.
The jet effect. The gas is pressurized while it is in the barrel. As it leaves and depressurizes, it adds further momentum, called the “jet effect.”

The sum of all three sources is the total momentum that the firearm must reflect in the opposite direction. Once the total momentum is known, the firearm weight is used to compute the firearm’s rearward velocity, and from that velocity, the recoil energy. The tool uses these steps, with x the projectile weight (grains), z the velocity (fps), p the powder charge (grains), b the muzzle brake efficiency (as a fraction, 0 to 1) and f the firearm weight (oz):

Quantity	Equation
Projectile momentum	`m1 = (x / 7000) * z`
Powder momentum	`m2 = (p / 14000) * z`
Jet effect momentum	`m3 = 1.7 * (p / 7000) * z * (1 - b)^(1 / sqrt(e))`
Firearm rearward velocity (ft/s)	`R1 = (m1 + m2 + m3) / (f / 16)`
Recoil energy (ft-lbs)	`R2 = R1^2 * (f / 16) / (2 * 32.17405)`

Momentum is expressed here as weight times velocity (with grains converted to pounds by dividing by 7000, and ounces to pounds by dividing by 16), so the gravitational constant cancels when dividing by the firearm weight. A combination of projectile weight and velocity is acceptable when its recoil energy R2 does not exceed the recoil limit you set.

Reference: the equations used for the recoil calculation are from https://robrobinette.com/Gun_Recoil_Calculator.html.

How much recoil is too much? For most shooters, recoil above 15 ft-lbs of energy starts to get uncomfortable after several shots. Recoil above 22 ft-lbs causes most shooters to develop a flinch after several shots. The default recoil limit is 22 ft-lbs.

The jet effect and muzzle brakes. The jet effect is the majority contributor to recoil in high-velocity rifles. Muzzle brakes work by redirecting the depressurizing gases sideways, which eliminates the majority of the recoil from the jet effect. Muzzle brakes can reduce total recoil by up to 50%. Typical efficiencies for most rifle caliber muzzle brakes are from 75–80%, which is why the default muzzle brake setting is 75%. In the equation above, the brake efficiency b reduces only the jet effect term.

4. Limitations and caveats

Projectile construction is not taken into account. The projectile must be of a type that is suitable for the animal being hunted. Projectiles that are too fragile (like bullets intended for varmints) will channel their energy into destruction of the bullet if used on game that is larger than varmints. This can also happen with bullets intended for light-to-medium game like white-tail deer when they are used on much larger game. Projectiles that are designed to stay together for deep penetration, intended for very large game, will fail to expand and fail to transfer energy when used on lighter game. It is the hunter’s responsibility to select an appropriately constructed projectile for the game being hunted.
Legality is not taken into account. The legality of a particular projectile or particular cartridge is not considered by this tool. Some regulations require lead-free projectiles, straight-walled cartridges, or minimum caliber sizes. It is the hunter’s responsibility to obey all local regulations.
Game weights above 1250 lb do not have good references. The sectional density and minimum energy equations were fit to references that cover game weights up to about 1250 lb. The game weight control accepts weights up to 2200 lb so that the largest animals in the table can be selected, but above 1250 lb the application’s recommendations may be inaccurate. This affects the Large size of Alaska Brown Bear, Alaska Yukon Moose, Canadian Moose and Grizzly Bear, and the Average and Large sizes of Bison.
The stability factor is a rough estimate. The tool makes a rough estimate of the stability factor using the projectile’s assumed density (for lead or copper) and caliber. The estimated stability factor can be inaccurate, as the exact projectile length is not known. The hunter should independently check whether his barrel twist rate is sufficient for the selected projectile.
The expansion velocities are rough estimates. The assumed expansion velocities are only rough estimates. Some projectiles can expand at slower velocities than assumed, and others may only expand sub-optimally at the assumed limit.
Effective range is not modeled. The minimum energy limit and the minimum velocity for expansion apply when the projectile impacts the animal. The velocity on the graph is the velocity at the muzzle, and while it may be high, the projectile slows down in flight because of drag and loses energy along the way. These lower limits therefore place an upper limit on the range at which the game can be harvested. How quickly the velocity decreases depends on the projectile’s ballistic coefficient, which is not modeled or considered by this tool. It is the hunter’s responsibility to know his rifle and his cartridge load, and the limits of its effective range.
Further reading. Additional information on projectile selection and effective game killing can be read in an excerpt from Nathan Foster’s books: https://www.ballisticstudies.com/Knowledgebase/Effective+Game+Killing.html