Volume by displacement

Volume is the one figure on this site that length and girth cannot give you directly. There is exactly one method that measures it rather than estimates it from other numbers, and it is Archimedes' method - submerge the object, read how much water it displaces. It also happens to be the method almost nobody actually manages to use here, for reasons worth being specific about.

The direct method

Fill a container with a known, marked volume, note the level, submerge the object fully, and read the new level. The difference between the two readings is the object's volume, and the physics behind it is exact - this is not an approximation the way a formula from length and girth is. Displacement is how volume gets measured for genuinely irregular shapes in a lab, precisely because it does not care what shape the object is.

Why it does not work well here

Three practical problems stack up. State: an erection has to be sustained and stable for the seconds it takes to submerge and read, which is a harder condition to hold than it is for a length or girth reading taken in the open. Seal: full submersion in a container narrow enough to give a readable displacement means the water line has to be read against a body part rather than a fixed rigid edge, and small differences in how deep it goes in change the reading. Resolution: a household measuring jug or cylinder is graduated coarsely relative to the volumes involved, so the level difference for a change of even a centimetre in length can fall well within one graduation - the container itself becomes the limiting factor before the method does.

None of these is fatal in principle. Together they are why displacement, despite being the theoretically correct method, does not show up as a practical technique anywhere in this site's method posts.

What circulates instead

The figure people actually use is a cylinder-formula estimate: treat the shaft as a cylinder, take length and girth (or a diameter derived from girth), and calculate volume from the two. It is fast, it uses instruments this site already covers, and it is available to anyone who has already taken length and girth for other reasons. It is also only an approximation, because a real cross-section is not a perfect circle and the shaft is not a perfect cylinder along its length - and because girth enters the formula squared, a girth reading's own error grows substantially by the time it reaches the volume figure. Taking that girth reading itself accurately is a precondition for any of this being worth calculating at all, since the formula can only be as good as the two numbers fed into it.

Comparing the two errors

Displacement, done well, has essentially no formula error - it measures the actual shape rather than approximating it - but in practice its achievable precision is limited by the state and container problems above, which are hard to control tightly at home. The cylinder estimate has no state or container problem, since it reuses length and girth readings you can take carefully and repeatably, but it carries a built-in formula error from treating a non-cylindrical shape as one, amplified by the squared girth term. In practice the formula estimate, taken from careful length and girth readings, is usually the more reliable number to hold onto - not because it is more accurate in principle, but because its error is easier to reason about and bound than the practical error a household displacement setup actually achieves.

What this has nothing to do with

None of this maps onto a rating. An image-based estimate does not measure volume or anything else physically - it infers a figure from visual pattern in a photograph, which is a different kind of process from either method here - and a rating service's score is not a physical quantity with an error bar in the sense either displacement or the cylinder formula has one, being a position in a distribution of images rather than a measurement. A person's stated opinion is not a volume estimate either, and a human judge offering an impression is not implicitly doing arithmetic on a length and girth. Rate Cock's rating answers a different question from any of the numbers on this page - it was never trying to be a cubic centimetre figure, so there is no error comparison to be made between it and either method above.