How this works, and where it's weak

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Methodology version 1.3 · last reviewed 9 October 2026 · What changed

What this calculates

Within Range currently estimates one component of a humane hunting outcome: the probability that a shot lands inside a circular vital-zone proxy under the inputs supplied. A vital-zone proxy is a simplified circle standing in for the chest cavity's heart-lung region, the target area used to convert your group size into a hit probability at each range. It is a modelling simplification, not an anatomical diagram; see "Vital-zone proxies" below for how directly each species' value is sourced.

The result is the first 5 m range sample where estimated placement confidence falls below the percentage you selected. It is not a validated probability of rapid incapacitation, recovery, or an ethical shot.

Impact energy is plotted for context. It does not set the confidence boundary: the dataset's energy figures are legal or informal conventions, not validated species-specific predictors of humane outcome.

How it works

The trajectory calculation uses the manufacturer's published ballistic coefficient, muzzle velocity and test-barrel length, together with altitude, temperature and wind. Manufacturer velocity is not a substitute for chronograph data from your own rifle.

If you enter your own barrel length, published velocity is adjusted using Hodgdon Powder Company's published barrel-length testing: roughly 25 fps per inch of difference from the manufacturer's test barrel. This is a single average rate applied to every cartridge, not a measured value for your specific rifle, and Hodgdon's own testing found magnum and overbore cartridges can vary more than this average predicts. Leave the field blank to use the published velocity as-is.

Your group size is converted from observed extreme spread to a point estimate of radial dispersion, then combined with wind uncertainty. The group must have been shot from the position you select. Position is recorded as scenario context; the model does not add a position penalty because the previous coefficients were not measured field-dispersion data.

When you choose a comparable-session summary from Practice, the calculator instead uses a one-sided 95% upper confidence bound on dispersion. Only groups with the same rifle/load profile, practice distance, position and shot count are pooled, and groups recorded with different versions of a load, or with no recorded load, are kept apart. This bound is conditional on the centred circular-normal model; it is not a claim that 95% of shots will hit. The calculator applies it as the same angle at every distance it models. That is a modelling assumption, not capability shown at distances other than the one you practised at.

The resulting circular bivariate-normal model is compared with the species' circular vital-zone proxy at each range. It assumes the group is centred on the intended point of aim.

The Practice page's recent-versus-previous comparison is observed history only. It compares two three-group medians inside the same setup, distance, position and shot-count stratum. It does not prove that capability changed, apply a recency adjustment or change a calculator input.

Guided practice drills hold a user-selected setup, distance, position and shot count constant while groups are recorded. Every linked group counts toward the recording target, including groups that are not eligible for the centred calculator model. Reaching a drill target is a data-collection milestone, not a capability or humane-shot result.

If you provide a distance being considered, “What changes this result?” reruns the same placement model with one input changed at a time. It may show a closer distance, a lower wind-uncertainty value, a smaller future practice-group benchmark, or another position only when directly comparable evidence exists in this browser. These are conditional scenarios, not instructions or evidence that a shot is humane.

A worked example

One scenario followed through the model, computed by the calculator itself when this page was built: the 6.5 Creedmoor 143 gr ELD-X at the manufacturer's published velocity, a red deer (200 mm vital-zone proxy), a 1.5 MOA 3-shot group from prone, 3 m/s wind called to within ±2 m/s, 300 m altitude, 12°C and an 80% target. The example is illustrative, not advice.

1. Group to spread. A 3-shot group's width averages 2.409 times the underlying spread, so 1.5 MOA ÷ 2.409 = 0.62 MOA.
2. Wind. At 200 m the solver predicts 0.26 MOA of drift per 1 m/s of crosswind, so a ±2 m/s call adds 0.51 MOA.
3. Combine. √(0.62² + 0.51²) = 0.81 MOA, which is 4.7 cm at 200 m.
4. Hit chance. For a 10 cm radius circle, 1 − exp(−10² ÷ (2 × 4.7²)) = 89.6%, above the 80% target.
5. Walk the distances. Repeating this every 5 m, placement confidence first falls below 80% at 225 m. That is the headline.
6. How sure is the group? One 3-shot group could come from a true spread between about 0.6× and 2.3× the estimate, which moves that boundary to anywhere between 135 m and 255 m. More comparable groups narrow this range.

Where the numbers come from

Every recommendation-affecting dataset value declares the fields it supports, its evidence class, how the app uses it, the source URL, and the date it was accessed. The build fails when required source coverage is missing.

The model-use labels have specific meanings:

• Calculation: the value enters the mathematics.
• Eligibility: a conservative guardrail controls whether a result is produced.
• Context only: displayed information that cannot change the recommendation.

Manufacturer intended use is an eligibility guardrail, not evidence of humane terminal performance. A target or varmint projectile is not assessed for deer. A manufacturer-designated hunting projectile can enter the placement model, but that designation alone does not prove reliable terminal behaviour on a particular NZ species.

How accurate is the trajectory?

The solver is tested against manufacturers' own published velocity and trajectory tables at their standard conditions. Every build fails if any point differs by 2% or more. The largest differences today:

So across these tables the model stays within 0.7% on velocity and 7 mm on trajectory out to 457 m. That agreement is with manufacturers' calculations, not with measured bullet flight, and it says nothing about your rifle's actual velocity.

Which BC band. Hornady publishes ELD-X BCs at three speed bands. The dataset uses the Mach 2.25 figure, which matches Hornady's own trajectory tables; Hornady recommends its slower Mach 1.75 figure beyond 600 yd. For the 6.5 Creedmoor 143 gr ELD-X (G7 0.314 in use), the slower band would add 0.6% drop and remove 2.6% energy at 300 m, and 2.0% drop and 5.7% energy at 600 m. Long-range figures are therefore slightly optimistic.

What overseas field research adds

A UK study by Aebischer, Wheatley and Rose (2014)analysed 2,281 first shots recorded by 102 deer stalkers. Shooting stability, support, practice, distance and time available were associated with field outcomes. This supports paying attention to the conditions behind your practice evidence.

Those outcomes are different from this calculator's estimate: hitting an animal is not the same as landing inside a vital-zone proxy, and a recorded first-shot kill is not proof of immediate incapacitation. The original dataset contains only 19 shots at 300 m or beyond. Its findings do not supply a personal shooting penalty, a long-range guarantee or NZ validation.

Manufacturer expansion guidance also needs context. A projectile family's stated impact velocity does not establish penetration or a humane outcome for every species and presentation. Such guidance does not currently change the placement-confidence boundary.

Where this model is weakest

It is a placement model. Projectile-specific terminal behaviour, shot presentation, physiological incapacitation and recovery probability are not yet quantified. The result must not be described as a complete humane-outcome probability.

Small samples. A manually entered group or direct single-session prefill still drives the headline as a point estimate, but the calculator now shades the plausible range for that single group (see the worked example above). The Practice page's comparable-session option instead uses a model-conditional one-sided bound. Both still assume a stable process and do not model changing skill, cold-bore offset, time pressure or recency.

Firing solution. Range-estimation error, zero error, sight height, elevation correction error and aiming bias are not modelled. The placement calculation therefore assumes a correctly centred firing solution and may be optimistic.

Wind treated as all-directional. Wind uncertainty only moves shots sideways, but the model adds it to a circular spread, as if it also moved them up and down. That makes the model more pessimistic about wind than it should be, which partly and accidentally offsets the vertical errors listed above. The planned fix is to model sideways and vertical error separately and add range-estimation and velocity error together, so no result moves outward on its own.

Long range. Published fixtures used to validate the trajectory implementation extend to about 450–460 m. Results beyond that are extrapolations of the point-mass model.

Vital-zone proxies. Red deer uses a cross-species whitetail proxy, and sika uses a value from a different sika subspecies. Fallow, chamois, rusa deer, feral goat, feral pig, white-tailed deer and sambar values are species-specific expert guidance, not clinical measurements. Expert sources disagree for fallow: the 250 mm used here (Australian Deer Association) is larger than the 20 cm vitals depth in the table used for most other species, which would give a more cautious result. White-tailed deer and sambar weight bands use the only figures DOC publishes ("40 kg plus"; "up to 157 kg" and "average 245 kg"), so they are reference points rather than measured ranges. None changes shape for broadside, quartering or frontal presentation. Feral goat's weight range is itself a borrow from chamois's own DOC-sourced figures, since DOC states only sex-average weights for goats, not a min/max. Wapiti's value is a cross-subspecies proxy too: the source table treats it as equivalent to NZ wapiti, but NZ's actual Fiordland population is a wapiti-red deer hybrid, not pure Rocky Mountain elk.

Impact-energy references. Red deer's and white-tailed deer's 1,356 J value is the converted 1,000 ft-lb US rule of thumb, a convention built around whitetail-class deer. The 2,000 J values are from German hunting law, not NZ welfare research. For sika, fallow, chamois and feral pig (wild boar), this is a literal fit: each is one of German law's own eight regulated deer/game categories. Rusa deer, sambar and feral goat are not German-regulated species; their 2,000 J figures are convention-borrowed from a relative already on this list (sika/fallow for rusa, red deer and rusa for sambar, chamois for feral goat) rather than a literal regulation of that species itself. Wapiti's 1,356 J value is a different convention family again: a genuinely elk-specific minimum from Colorado's big-game regulations, one US state's rule, not a national standard and not related to the German figures above. All of these remain on the chart only to show how the trajectory compares with familiar references.

New Zealand validation. The model has not yet been calibrated against NZ field-practice or hunting-outcome data. Personalised, position-matched practice data and prospective local validation are still required.

Not legal or safety advice. This model's output is a number under stated assumptions, never a guarantee, a safety certification, or a substitute for your own judgement.

Ballistic energy reference and recoil comparisons

The free Energy Charts & Cartridge Comparison uses the same point-mass trajectory solver with standard sea-level, 15°C, no-wind assumptions. Curves are enabled only for documented loads cross-checked against manufacturer velocity checkpoints within 2%. This numerical agreement is not independent live-fire validation; source pages do not always disclose their atmospheric conditions.

Reference distance is limited to 400 m. Velocity is interpolated at exact metric distances and kinetic energy is derived from the same velocity. Constant G1/G7 coefficients approximate drag that varies with speed; barrel and ammunition variation remain unmodelled. No reference energy threshold or recoil result enters the placement-confidence, Capability, Practice or DOPE calculations.

Free recoil uses conservation of momentum, including powder gases at SAAMI’s 1.75× muzzle-velocity approximation for high-powered rifles. Reviewed factory loads do not publish powder charge, so factory recoil is unavailable. Optional user-entered powder masses create labelled sensitivity scenarios only. Free recoil is not felt recoil and no muzzle-device reduction is inferred.

What changed

• 9 October 2026 (version 1.3). Added the overseas field-research explanation and linked learning resources. Clarified why animal-hit and first-shot outcomes differ from circular placement confidence, and why manufacturer expansion guidance does not establish a species-specific humane outcome. Calculator values, eligibility and results are unchanged; NZ validation remains open.
• 26 September 2026 (version 1.2). Added white-tailed deer and sambar, and disclosed that expert sources disagree on the fallow vital-zone size.
• 26 September 2026 (version 1.1). Added this change log, the worked example, the equations, the trajectory accuracy table and the BC band caveat. Disclosed the all-directional wind treatment. The calculator now shades the plausible range for a single group; headline results are unchanged.
• Version 1.0. Methodology as first published. Earlier changes are recorded in the project's commit history.