Is it a bell curve

Close to it near the middle, less certainly in the tails: the nomograms in Veale et al. (2015), BJU International, assume a normal bell curve. That assumption is what lets a mean and a standard deviation stand in for the whole curve, and it has a specific place where it is worth being careful.

Why the assumption is doing real work

A normal distribution is fully described by two numbers - the mean and the standard deviation. Once you assume normality, every percentile follows from those two figures by a fixed formula, which is what makes a nomogram possible to draw at all without plotting every individual measurement. That is exactly how the reference charts were built: Veale et al. (2015) calculated a weighted mean and pooled standard deviation for each measure, then simulated 20,000 observations from the normal distribution to generate the nomograms.

If the real distribution were meaningfully different in shape - skewed, with a longer tail on one side, or with two separate humps - the same mean and standard deviation would produce a curve that misrepresents the actual population at some percentiles while looking fine at others.

Where it holds up

For a physical measurement like length, taken across a large clinically measured sample, a roughly normal shape is what you would generally expect, and it is broadly what the pooled data show across most of the range. Most men cluster near the mean, with the count falling off in both directions in the pattern the normal curve predicts, and that middle section is where a nomogram reading is on its most solid ground.

This is also the section most measurements land in, since the middle of this particular distribution is unusually crowded relative to its own range - which is exactly the condition under which a normal-curve approximation is easiest to trust, because there is a lot of data in the middle to check it against. Seeing that middle crowding directly, rather than taking the shape assumption on faith, is what reading an actual length histogram lets you do.

Where to be more careful

A physical length cannot go below zero, which means the true distribution cannot be perfectly symmetric all the way out - a normal curve technically extends in both directions forever, and this one cannot. The NIST/SEMATECH e-Handbook of Statistical Methods gives the normal distribution's range as minus infinity to infinity, which no length can match. In practice this only matters far from the mean, well past where almost anyone measuring themselves will land, but it is the honest reason the assumption is an approximation rather than an exact description. The shape is also an empirical question rather than a given: in Nguyen Hoai et al. (2021), Andrology, clinic records of 14,597 Vietnamese men did not follow a normal distribution when tested with a Kolmogorov-Smirnov test, and the authors reported medians instead.

The tails are also where the pooled sample thins out fastest. The pooled totals are also smaller than the headline suggests for some measures - Veale et al. report 14,160 men for stretched length but only 692 for erect length and 381 for erect circumference - and the count of measurements several standard deviations from the mean is small, so a nomogram's accuracy at the extreme percentiles rests on less data and more on the shape assumption than its accuracy near the middle does. The reasons the tails carry less certainty than the middle are worth reading on their own, separately from the normality question itself.

What this means for reading your own percentile

If your measurement sits within a couple of standard deviations of the mean - which covers the great majority of readings - the normal-curve assumption behind the nomogram is on firm ground, and the percentile it gives you is trustworthy to within the measurement's own error.

If your figure sits well out toward either tail, treat the stated percentile as a rough indication of direction rather than an exact figure. That is not a flaw specific to this dataset - it is true of any percentile drawn from a finite sample at its extremes - but it is worth knowing before quoting a tail percentile as if it carried the same precision as one near the middle. It is the same reason a rating hub's public score distribution is more informative read as a whole shape than as a single number lifted from one end of it.

None of this is a reason to distrust the nomograms in general. It is a reason to read them the way any statistical tool should be read: with attention to where the underlying assumption is doing light work and where it is doing heavy lifting. Near the mean, the normal curve and the real data are hard to tell apart. Out at the edges, the curve is extrapolating past where much data exists to check it against, and a careful reader treats that extrapolation as an estimate rather than a fact.

None of this touches a separate kind of number entirely: an assessment, rather than a percentile, is what a service like Rate Cock or a human judge provides, and it does not rest on a distributional assumption at all because it is not derived from a population curve in the first place. An AI-estimated figure from a photograph is a third thing again - not built from a measured distribution at all, whatever percentile language surrounds its output.