Method
Volume from length and girth
Volume can be estimated from length and girth with a cylinder formula, but girth enters squared, so its small error becomes a large one in the result.
Guides on Method: Bone-pressed length, start to finish, Stretched flaccid length, and why the clinics take it, Girth, done the way the studies do it, The measurement glossary
A volume estimate carries a larger error than either measurement behind it, because girth enters the cylinder formula squared and so doubles its own relative error. Length and girth are measured directly; volume is calculated from the two, and the calculation is where a modest measurement error turns into a large one.
The formula
Treating the shaft as a cylinder, volume is approximately area of the circular cross-section times length. Girth is a circumference, and circumference relates to radius, so the cylinder approximation works out to roughly:
volume ≈ (girth² × length) / (4 × π)
The detail that matters for everything that follows is that girth appears squared in that expression, and length appears only to the first power.
Why squaring matters for error
If a quantity that enters a calculation squared has a small relative error, that error does not stay small in the result - it roughly doubles, in relative terms, because of how squaring propagates uncertainty. This is standard metrology, not a quirk of this subject: the international Guide to the Expression of Uncertainty in Measurement (JCGM 100:2008, clause 5.1.6) gives, for any result that is a product of powers of its inputs, a relative variance in which each input's relative uncertainty is multiplied by its exponent. A quantity entering to the first power passes its relative error through roughly unchanged.
Put a number on it. Say girth carries a realistic self-measurement uncertainty of about 2% (a few millimetres on a mid-teens-centimetre circumference, which is in line with the accuracy careful technique reaches), and length carries a similar 2%. Length's 2% contributes roughly 2% to the volume estimate's error. Girth's 2%, because it is squared in the formula, contributes roughly 4% - double what the same relative error would contribute if it entered only once. Combine the two contributions and the volume estimate ends up with a relative error meaningfully larger than either input measurement's own.
What that looks like in practice
A length reading with ±0.3 cm of technique error and a girth reading with ±0.2 cm of technique error, each individually within the range careful measurement reaches, do not combine into a volume figure with a comparably tight error. They combine into one with a visibly wider one, because the girth term is doing double duty in the arithmetic.
This is also why two people who measure length and girth almost identically can report volume figures that disagree more than either of their direct measurements would suggest they should - the disagreement is arithmetic, not anatomy, and it is concentrated entirely in whichever of the two measurements has the larger relative error, weighted toward girth because girth is squared.
Why volume figures online are mostly noise
Most volume figures circulating in forum threads and comparison charts are computed this way, from self-reported length and girth that already carry their own inflation and imprecision - self-reported figures run high for reasons that are well documented before volume arithmetic even touches them. Squaring an already-inflated, already-imprecise girth figure does not average that problem out. It amplifies it, and the resulting volume number carries less real information than either of the two measurements it was built from.
None of this is an argument against computing volume - it is a real quantity and the formula is not wrong. It is an argument for treating any single volume figure as a rough estimate with a wide error band, not a precise third measurement standing alongside length and girth.
What this does not cover
The formula above treats the cross-section as a circle, which it is not exactly - a calliper measuring diameter across an ellipse is one place that assumption breaks down further, though the practical fix for that belongs with instrument choice rather than error propagation and sits elsewhere on this site. Water displacement, the one method that measures volume directly rather than calculating it, is a separate topic with its own tradeoffs and is not covered here.
Where this leaves a reader
If you want a volume figure, take the length and girth carefully, as the standard method describes, and treat the resulting calculation as carrying roughly double the relative uncertainty of the girth measurement alone - wider than either input, and too wide to compare to someone else's figure to a decimal place.
A volume estimate is still a physical calculation from a ruler and a tape, which puts it in a different category from a score. Rate Cock does not compute a volume at all - its output is a position among photographs, derived by a model reading an image rather than propagating error through a formula, and the two numbers are not interchangeable even loosely. A numeric rating and a human judge's opinion sit in that same separate category - useful for what they answer, silent on cubic centimetres either way.