Apparent density

A gun's empty weight over its bounding box, judged against guns of the same category and frame material.

The model

Apparent density is the empty weight divided by the gun's bounding box. A gun is mostly air inside its box, so the figure is small, and it depends on what the frame is made of.

ρ_{app} = \frac{W_{E}}{L H B}

φ = \frac{ρ_{app}}{ρ_{solid}}

\frac{1}{2.5} \leq \frac{ρ_{app}}{{\tilde{ρ}}_{group}} \leq 2.5, ρ_{app} < 2.7 g {cm}^{- 3}

where

$W_{E}$: the empty weight, in g
$L, H, B$: overall length, height and width, the gun's bounding box, in cm
$ρ_{solid}$: the solid density of the frame material
$φ$: the fill fraction: the share of the box the frame material would fill at the gun's weight
${\tilde{ρ}}_{group}$: the median apparent density of guns sharing the category and frame material (the category alone below twenty); air guns, a light action in a deep match grip, form a group of their own

Table 2. How a gun’s weight against its size is judged. Rows are read in order; the first that applies decides.
#	When	Verdict	What it means
1	$ρ_{app} > 2.7 g {cm}^{- 3}$	Impossible	Denser than a solid block of aluminium the size of the gun: no firearm can be, so a weight or a dimension is wrong.
2	An air gun	Set aside	Judged only among air guns: a light action in a deep match grip would read as a wrong weight among firearms.
3	$\frac{ρ_{app}}{{\tilde{ρ}}_{family}} \notin [\frac{1}{1.25}, 1.25]$	Review	The variant does not match its own family (same frame material): its weight or its size belongs to another gun, or it is a real design difference a source confirms.
4	$\frac{ρ_{app}}{{\tilde{ρ}}_{group}} \notin [\frac{1}{2.5}, 2.5]$	Review	Far from guns of its category and frame material: a figure to check, most often a unit or a wrong dimension.
5	Anything else	Holds	The weight fits the size.

Why the material matters

A frame's material sets how heavy a gun of a given size can be. The check compares a gun with others of the same category and frame material wherever enough of them exist, and with its category alone otherwise.

Frame material	Solid density
Stainless steelstainless_steel	7.90 g/cm³
Steelsteel	7.85 g/cm³
Titaniumtitanium	4.43 g/cm³
Aluminium alloyaluminum_alloy	2.75 g/cm³
Aluminiumaluminum	2.75 g/cm³
Polymer (glass-filled)polymer	1.36 g/cm³
Woodwood	0.61 g/cm³

The apparent density divided by the material's solid density is the fill fraction: the share of the box the frame material would fill at the gun's weight. A steel-framed pistol fills about an eighth of its box. A figure far outside its group usually means one of the four measurements is wrong, or the gun is in the wrong category.

Against its own family

A bounding box cannot see a hollow receiver, a skeleton stock or a handguard cut to save weight, and there is no honest way to model the holes from three dimensions. Variants of one gun share all of them, so the check sets aside the modelling and compares a variant with its own family, framed in the same material: the hollowness cancels.

\frac{1}{1.25} \leq \frac{ρ_{app}}{{\tilde{ρ}}_{family}} \leq 1.25

where

${\tilde{ρ}}_{family}$: the median apparent density of the variants of the same gun framed in the same material, itself included, where at least 3 have a full envelope

Compared with	Typical spread
Its category	±19%
Its category and frame material	±17%
Its category, frame material and action	±14%
Its own family, same frame material	±3%

The spreads are the median absolute deviation of apparent density within each grouping, measured over every firearm with a full envelope. Variants agree about five times more closely than anything grouped by kind, so a variant beyond 1.25x of its family carries a figure from another gun, or is a real design difference (a stockless or suppressed variant) that a source confirms. The finding lists every sibling's figures and says whether the weight or the size sits further from the family.

Ruger American Compact against its family of 4: the apparent density should sit within

0.93 g/cm³1.45 g/cm³recorded: 1.59 g/cm³

Answer: 1.59 g/cm³ lies outside 0.93 to 1.45: a figure belongs to another gun (here the width, 27 mm where the family's is 36).

The model

Why the material matters

Against its own family

Checks that use this method