11/11/2013 08:45 pm ET Updated Jan 23, 2014

"That's Not Normal!" The Statistics of Penis Size

As everyone knows, there's nothing guys like talking about more than math. No, wait, that's not right, it's...oh, yeah: dicks! Guys like nothing better than talking about their dicks! But I believe that guys will talk about math, as long as that discussion centers on their dicks. As we Americans rank 21st (out of 23 advanced nations) in math scores, I say: whatever works. I'm still thinking about a strategy to get women talking about math--possibly something involving shoes or guys putting down the toilet seat--well, promising to put down the toilet seat. Let's start with a simple--if, as we'll see, somewhat dubious--assumption: that penis size follows what statisticians call the "normal distribution". If you measure a large number of guys' erect penises (which, depending on your gender and sexual orientation, could be the high point of your year or a slow day in the bar) and make a bar graph (possibly a row of erect penis graphics of varying lengths, but the math doesn't require that), from smallest to largest, of how often each value occurred, you'd get the familiar bell-shaped curve, with the two tapering-to-0 "tails" indicating that there are few very large or very small cocks, and the fat middle indicating a great many average-sized cocks--again, if cock size is normally distributed. If you know where the weighted middle of the bell (the mean) is and how far out it stretches (the standard deviation, which, it might surprise you, doesn't involve cross dressing) in either direction, you can estimate how many men have smaller cocks than you. Let's pretend an all-knowing entity (the opposite of Bill O' Reilly, speaking of dicks) told us that the mean of all dick sizes in the world is 5.877 inches with a standard deviation of .825 inches (numbers I cribbed from the Ansell study). That gives us the following table:

Size Of Your Dick (inches)

Percent Of Population With Smaller Dicks





























*Geek alert: cumulative distribution function values for 13 and 13.5 inches were so close to 1 as to be indistinguishable by Excel and the Apache Commons Math library, due to numerical precision issues.

Assuming you accept these numbers (and you'd have reason not to, as we'll see), if you're a guy sporting a respectable if not eye-popping (unless you have terrible aim) 6-inch member, over half the men you meet should bow to your kingly scepter, though you probably shouldn't actually tell them so, because of how they might pop you in the eye. But: the unofficial world's largest penis observed (by, I'm sure, quite a few people) is about 13 ½ inches. Despite a technical issue (solvable with a bit of effort, which is why I didn't solve it) that prevented an exact-enough calculation of the numbers for men with 13 and 13.5 inch penises, we see that even a 12-inch penis should only, according to these calculations, occur once in 17,321,537,028,348 guys, or about 5,000 times the world's population of men, and 320 times the number of guys who have ever lived on earth. So clearly, at least with respect to the more tripodal males, dick-size is not normally distributed; we find far too many anacondas among the trouser-snakes. In the middle, our numbers look a bit more believable, and as for the pubically stubby, well, they can continue buying SUVs and guns.

Difficulties abound in collecting data on this emotionally-fraught subject. In what might represent the best example of science tending to demonstrate the incredibly bleeding obvious (which I like to call, rather obviously, the "no shit, Sherlock" effect), we note that self-reported penis sizes tend to be rather larger than--in the immortal words of Wikipedia's article on penis size--"staff-measured" penis sizes. I feel confident that, asked to participate in a self-measurement survey, I would immediately demand a yardstick. Tell no small lies about how not-small you are.

On the subject of penile veracity, the prevalence of 8- and 9-inch dicks self-attributed to Web commenters would seem far higher than we expect from the distribution. Three explanations for this effect suggest themselves: 1) even in the middle, penis size does not follow the normal distribution, B) Internet commenters have far larger penises than the population as a whole (certainly the commenters on my articles do, even the women), or iii) Internet commenters are giant lying liars who lie. Comments on porn videos featuring men of average endowment frequently heap scorn on these performers, leading us to suspect that a mechanism similar to the "he who smelt it dealt it" law familiar from the field of fart-attribution might be at work: he who mocked it has a tinier cock...than it. (I am a statistician, not a poet. And well I know it.) (And by "statistician" I mean: guy that took a statistics class and got an "A".) (Well, a "B", but close to an "A".) (Fine: it was a "B-".) I think we might take as a kind of psychological rule of thumb that the more expansive your claims for the pipe-wrench-like proportions of your tool, the more likely we are to be discussing one of those screwdrivers used to adjust eyeglasses.

Returning to our discussion of the penis-size distribution, debate abounds, especially on adult message boards frequented by gay statisticians, about this larger-than-expected number of larger-than-expected penises. As we've noted, with respect to more edificial penises, more exist than the normal distribution would predict. (I found the most interesting--and mathematically astute--discussion of this topic on this Web forum.) We observe many more large penises (especially while watching porn) than can be accounted for by the means and standard deviations in the surveys. Even if the normal distribution describes well the majority of dick-sizes in the middle, we see too many big dicks, and not just on Wall Street. I cannot say definitively that normality fails with respect to the size of men's junk, but I can say that gay men seem very invested in the existence of a large number of men with big dicks. No shit, Sherlock.

We can perhaps find in evolutionary theory the reason for the rarity of both cocktail-weenie- and kielbasa-sized tube-steaks. Humans have the largest penises of all the primates, considered both as a proportion of body size and absolutely. (If you think yourself lacking, consider dating orangutans--they will swoon with admiration for your giant schlong, or perhaps hit you with a coconut.) Scientists speculate that walking upright provides the explanation: the rearrangement of the human vagina that resulted from the hominid switch in posture favored longer penises; smaller ones fell short and their owners failed to reproduce. But, as the human vagina ranges in depth from only about 3 to 6 inches (very approximately; data on this measure are much harder to come by--you should excuse the expression--than data on penis size), too much length could present an evolutionary challenge too: painful coitus, perhaps resulting in the woman giving it up as a bad job, with the same result as Mr. Shorty: no Little Big Men for you. Sure, the human vagina possesses a remarkable elasticity and during childbirth stretches to an astonishing degree--but not without extreme pain and a vastly different set of circumstances from those obtaining during intercourse. So, while visually interesting, the ten-inchers of song and story (not to mention that 1-in-17-trillion 13.5-incher) present their owners with a reproductive challenge, though not one as severe as that faced by those on the other side of the curve; they are largely, as we used to say about a gentleman's pocket hankie, for showing, not for blowing. Thus, my sincerest sympathy to all you commenters about to tell us about your 99.99997th percentile boy-bits.

A couple of notes to stats geeks (i.e., those of you who got an A in statistics and/or took more than one stats class): as might be expected from such noisy data, sample means from different studies vary quite a bit (from 5.1 inches to 5.9, with a 95% confidence interval from 4.23 inches to 7.53) as do standard deviations. Data from the Ansell study show a positive skew, with a median below the mean; at least one other study skews negatively. Put the graphing calculators back in your pocket protectors, boys and girls; we're just having fun here.

Also, like Frank Burns in Robert Altman's M*A*S*H, if I made any mistakes in this article, they are God's will or someone else's fault.