Introduction

An analysis on vaginal length by some anonymous and potentially unqualified person on the internet. This must be bullshit. I don’t want to lament over such stereotypes. I would be skeptical as well. After all, where is the data supposed to come from. However, the combinatorial force of the pandemic and the ingenious lockdown policies in the first world graciously allocated me with an abundance of free time. It was during this time back in 2020 that I “stumbled” upon some videos hosted by our good friends from Pornhub which contained a rich and comparable data set that only had to be extracted with my newly found supply of time.1 Despite the obvious caveat that I have basically zero knowledge of gynecology I think this may nonetheless be the best analysis on this subject. Take a look and decide for yourself.

Literature Review

Searching through Google Scholar I found a number of other studies on vaginal length. The studies and the key results are summarized in the table below (Both tables have the same order). Most of them were conducted in the United States. The average vaginal length in those studies ranged from 6.27 to 11.51 centimeters. From what I understand, the measurements were taken in a normal, unaroused state.2 Throughout the analysis length is measured in centimeters (cm) and weight in kilograms (kg).

Literature Review - Studies

Literature Review - Summary Statistics

Data and Sample Characteristics

The data comes from professional or semi-professional adult actresses, primarily from the Czech Republic, who underwent a so called “Gyno” exam.3 In total, the data set includes data on the height, weight and vaginal length of 159 women. Vaginal length was usually measured in sitting and standing position. The women were asked to push a plastic dildo marked with “cm’s” as far as possible into their vagina.4 Before insertion the women were “stimulated” for a couple of minutes . If and to what extent the subjects were aroused by the stimulation is not clear. For the calculations that follow, I use the average of the vaginal length in sitting and standing position. The correlation between both measures is very high at 0.88 and should not impact the results.

The table below shows the data set as well as some summary statistics for the height, weight and body mass index (BMI).

Data Set

Sample Summary Statistics

Analysis of Vaginal Length

Now, with all the boring stuff out of the way we can go on to use some more elaborate machinery to calculate the good old average and some related friends. The table below shows the results. The mean vaginal length in this sample is 12.78 cm with values ranging from 7.5 cm to 17 cm.

In order to get a better sense of the results it is useful to see how the values are distributed. The plot in the left tab shows how many women in our sample fall within a certain range (e.g. greater than 12cm and smaller or equal to 13cm). Clearly, most observations are centered around the mean and roughly symmetrically distributed (skewness = -0.48). The sample standard deviation of the mean is 1.74. Consequently, the 95% confidence interval for the population mean of vaginal length is given by [12.51, 13.05]. In other words, if we repeated the measurements a 1000 times with different women, we would expect that the average would fall within the confidence interval about 950 times. The plot in the right tab shows the empirical distribution function. It does not count how many observations fall in a given bucket. Instead, it tells you what fraction of women have a vaginal length that is smaller than or equal to a given value (e.g. 12cm, 13cm etc.). For example, the vaginal length is smaller than or equal to 10cm for only about 5% of women in this sample. As another example, about 70% of the women in this sample have vaginal length that is smaller than or equal to 14cm.

Histogram

Empirical Distribution Function

Let’s compare these numbers to the other studies on vaginal length. The graph below plots the point estimates, represented by the dot, as well as the 95% confidence intervals of vaginal length for the other studies included in the literature review. The current study is highlighted in red. Compared to the other studies, the average vaginal length based on this data set is higher. This effect is statistically significant because the confidence intervals do not overlap. What explains these differences? One obvious and potentially the biggest factor is probably the level of arousal. What’s also interesting is that the differences among the other studies appear to be larger than one would expect purely based on sampling variation.

Relationship between Height and Vaginal Length

Given that we also have information on height, it seems natural to ask whether height is related to vaginal length. A scatter plot which plots height against vaginal length is probably the simplest way to approach this question. In addition, I estimate a simple linear regression model where vaginal length is the dependent variable and height is the explanatory variable.

Scatterplot

Linear Regression Model

Judging from the scatter plot, there seems to be a weak positive relationship between height and vaginal length (correlation coefficient = 0.24). The output of the regression model confirms that this relationship is statistically significant. The R-Squared of the model is 0.0596. Thus, about 6% of the variation in vaginal length can be explained by variation in height which confirms our visual hunch that height does not seem to be a strong predictor of vaginal length. From the output of the regression model we can infer that a woman that is 175cm tall is expected to have a 1.3 cm longer vagina than a woman with a height of 155cm (i.e. height coefficient estimate of 0.065 * 20 (175-155)) .

Probability of Bottoming Out

To “bottom out” is when one is having sex and the penis reaches the cervix, or the top part of the vagina, and can go no deeper.5 Thus, one can ask how likely is a man going to “bottom out” a women when having sex. In order to estimate the probability, we need information on the distribution of vaginal and penis length. For vaginal length, I use the data from this study and for penis size I rely on estimates from calcsd.info which aggregates various studies on penis size. Their estimate of the western average erect penis length is 14.7cm (standard deviation: 2.14cm).6 Another source of uncertainty comes from the fact that the estimate in this study might slightly underestimate the “true” vaginal length because the measurements were taken in a rather artificial environment. Of course, this is rather speculative. In general, the case for underestimation is stronger if “true” vaginal length refers to the maximum vaginal length when the level of arousal is at its peak. However, if we are interested in the typical vaginal length during a real sexual encounter the estimates might already by very accurate. In any case, I use different multipliers from 5% to 25% to inflate the measured values and then show how different estimates of vaginal length affect the probability of bottoming out. Personally, I think multipliers of 20% or more are rather unlikely. The table below displays the summary statistics for different scaling factors including the measured sample values.

Great, but how do we arrive at the probability that a man bottoms out a women? It’s relatively simple. We do the following:

  1. Draw one random observation from the distributions of vaginal and penis length. 7
  2. Compare the two values. Note that, if we are interested in the probability that a man with a given penis size would bottom out, we would use this specific value (e.g. 15cm) and not the value drawn from the distribution.
  3. Repeat this process many times (e.g. 10000). If the penis length is greater than the vaginal length 5000 out of 10000 times, the estimated probability of bottoming out would be 50%. The results below are based on 1 million simulations for a given comparison (e.g. multiplier of 1 and a penis size of 15cm).

The bar plot below gives you the probability of bottoming out for different penis lengths and different estimates of vaginal length. Let’s look at the dark blue bars which show the probability of bottoming out under the assumption that the result we obtained from the sample in this study is correct (i.e. scaling factor = 1). In this scenario, men with a penis size of 10cm are expected to bottom out a woman about 8% of the time. The probability increases to 100% for penis lengths of 18cm or more. The other bars have exactly the same interpretation. The only difference is that we apply other scaling factors to the measured vaginal lengths to account for the possibility that the measured values slightly underestimate the true values due to the rather artificial setting in which the measurements were taken. The scaling factors range from 1.05 (5%) to 1.25 (25%). How does the picture change if we assume that the average vaginal is 10% higher (scaling factor = 1.1) than the estimate in this sample suggests. In this case, a man with a penis size of 15cm has a 68% probability of bottoming out compared to 92% under the baseline scenario in which we assume the sample estimate is correct (scaling factor = 1). For penis lengths of 19cm or more the probability of bottoming out is very high irrespective of the assumptions we apply. Even if we assume that the sample estimate for the 159 women is 25% below the true value, the probability of bottoming out for a men with a penis size of 19cm would still be 96%.

What can we say about the probability of bottoming out more generally. For example, let’s say you live in a small city with a 100 couples. In how many of those 100 relationships would we expect the man to bottom out the woman. Looking at the bars for the category “overall”, we see the answer is 75 under the baseline scenario (scaling factor = 1). If we assume the sample estimate underestimates the true vaginal length by 10% (scaling factor = 1.1) the answer would be 58.8

Conclusion

Key takeaways:

  • The average vaginal length is close to 13cm which is higher than previous studies have indicated.
  • The maximum vaginal length in this sample is 17cm. Thus, very high values of 20cm or more are probably extremely rare.
  • There appears to be a only weak relationship between height and vaginal length and the magnitude of the impact is rather small.
  • Men with a penis size of 12cm or less have a relatively low probability of bottoming out a woman. In contrast men with a penis size of of 19cm or more are almost certainly going to bottom out a woman.

Appendix

The appendix calculates the probability of bottoming out with slightly different assumptions. Remember that the key step is to compare values for penis length and vaginal length. The values for vaginal length come from our sample of 159 women. Thus, every time we draw from the distribution of vaginal length we get one of the 159 actually measured values. In my opinion, this seems like a natural way to do it. However, an alternative would be to use the sample mean and sample standard deviation from our sample and draw from a normal distribution characterized by these values. This affects the results, because our sample distribution is slightly skewed to the left, implying that the share of small values is higher than under a normal distribution. Conversely, the share of high values is lower than under a normal distribution. This is depicted by the graph below which overlays the histogram of the sample values with a normal curve which takes as its arguments the sample mean and the sample standard deviation.

The summary statistics under a normal distribution are shown in the table below. We see that the 99.5% Quantile is already higher than the maximum in our sample.

Following the same steps as before gives us the following probabilities for bottoming out. As expected, the probability of bottoming out for large penis lengths falls slightly compared to our initial analysis in the main section. Apart from that, the results are very similar.

  1. The analysis was basically sitting on the sideline for the last 2 years. So the publication is long overdue.↩︎

  2. In one study by Pendergrass et al. (1996), it appears that the posterior wall was (partially) distended (i.e. stretched) when measuring. They note on page 181: “However, mean posterior lengths which represent the greatest lengths of the vaginas as measured with calipers (8.84cm) and strings (10.23cm) are consistently shorter than the mean length as measured with rods (11.51cm). It is unclear whether the discrepancy of about 1.25cm or 0.5 inch is caused by a failure to introduce the molding material completely into the posterior fornix or by distension of the posterior wall when the rod is inserted”.↩︎

  3. The fact that they are professional or semi-professional adult actresses does not make the measurements less representative for the general population (of European women). This would require, that there is some sort of positive selection for women with higher vaginal length in porn. In my opinion, this is pretty implausible.↩︎

  4. If you search for “Foxy Sanie Gyno” on Pornhub you will see an example of how the measurements were taken (at around 27:30). Most or all of the other videos are no longer on Pornhub. But I guess they are still available on gyno-x.com (requires paid subscription).↩︎

  5. Urbandictionary.com. This is not meant to take a stand on whether this is desirable or not.↩︎

  6. The estimate of the eastern average erect penis length is 13.4cm (standard deviation: 1.45cm). Under these assumptions the probability of bottoming out in a random sexual encounter would be: 59%, 48%, 37%, 29%, 22%, 16% for the different multipliers from 1 to 1.25.↩︎

  7. For the simulations a small amount of random variation (“jitter”) is added to to the vaginal lengths because the measurements are rounded. Thus, a measured value of 13cm does not mean the length is exactly 13cm. It could be 12.95cm or 13.05cm or some other value close to 13cm. We have to take this into account. Otherwise, a man with a penis size of 13cm would never bottom out a woman with a measured vaginal length of 13cm. In reality, however, he would bottom out some (those with a vaginal length of slightly below 13cm) but not others (those with a vaginal length slightly above 13cm).↩︎

  8. This assumes that there is no matching between vaginal and penis length. Put differently, women with longer (shorter) vaginas are not more likely to be in a relationship with men who have longer (shorter) penises.↩︎