Calculating Maximum Possible Erect Penis Size

[catoshka]

Sometimes I like to create characters that are more scientifically (or mathematically) accurate. I mean, have you ever wondered if that dick on your OC is even possible? So this is a guide to calculate the maximum penis size of your character. Full disclosure, I don't claim this to be the most scientifically accurate way to find the max penis size, but this is the method I came up with.

So how exactly does a penis get hard? Well the answer is simply blood. During an erection the blood vessels in the penis relax allowing more blood to flow in. The blood is trapped in the penis, thus it gets hard. This fact is important to calculate the maximum penis size because you can only lose so much blood before it gets dangerous for your body. For an average adult you can lose roughly 10% of your blood and still be fine.

The next things to know are the statistics that I've found online claim that the average erect penis is 5.16 inches long, 4.59 inches in girth. That means an erect penis would be roughly 8.65 cubic inches in volume.

A realistic penis girth is from 4.5 inches to 7 inches. So we'll need to pick a number within this range.

Finally the last thing to know is that the average penis requires 4.4oz of blood to form an erection. I can't verify this but it will have to suffice. Close enough for our purposes.

Once you know all these facts, the first step is to calculate the Blood Volume of your character. Lets say my character is a futanari so she has a female body type. I want her height to be 5ft 4in tall, and I also want her weight to be 26Lbs. So we'll go online look for a blood volume calculator (the one I used was https://www.omnicalculator.com/health/blood-volume) Then we'll simply plug the numbers in and we get that she has 125oz of blood in her body. Divide this number by 10, and we'll get the amount of maximum blood my futanari OC can put into her erection.

So here's where the science gets a bit shaky because I have no idea if what I'm doing is even scientifically accurate. I'm no doctor or biologist but hey I can do maths, that counts right? So we'll need to get a "maximum size coefficient". You may think, that sounds like it might be complicated to do but actually it's not. All you need to do is divide the maximum amount of blood your OC can put into their erection by 4.4oz, the average amount of blood that fills up an average penis. In our case it will be 12.5oz/4.4oz giving us roughly 2.84 rounded to the nearest 2 decimal places.

Now use the coefficient we just calculated and multiply it by the average penis volume of 8.65. In our case it will be 2.84x8.65= 24.57 cubic inches!

The last steps involve deciding how girthy you want the penis to be, I want my futanari OC to be quite THICC so I'll give her 6 inches in girth. Now to calculate the length of her penis, we'll approximate it by assuming that the penis is like a cylinder. A cylinder's volume is given by the area of a circle multiplied by the length. However "girth" simply translates to "circumference" and cross-section of the penis translate into "area of the circle". So we need to divide the girth by 2pi (for simplicity let's say it's 6.28) to get the radius of the penis cross-section, then we'll use it to calculate the area of the penis cross-section. So 6 divided by 6.28, which gives us 0.96 in radius. We'll square this number giving us 0.91 and multiply it by pi to get the area which is 2.87.

Now we already know that penis volume is 24.57 cubic inches, all is left to do is divide the volume by the area of the cross-section and we now know that her maximum penis length is 8.56 inches!

BONUS - Too long, I want the numbers now!
Fear not, I've made a graph.

Explanation of the graph.
A person can safely lose 10% of the blood in the body, thus we can dedicate 10% of this blood to form an erection.
Average female has 144oz of blood. 10% of this is 14.4oz.
Average male has 192oz of blood. 10% of this is 19.2oz.
4.4oz is the amount of blood an average penis needs to get hard.

The average penis is 8.65 cubic inches in volume.
14.4oz divided by 4.4 is 3.27. Multiplied by 8.65 is 28.29 cubic inches.
19.2oz divided by 4.4 is 4.36. Multiplied by 8.65 is 37.71 cubic inches.

Pick a girth between 4.5 and 7 (the realistic range of penis girths). Divide it by 6.28, square it and multiply it by 3.14. Then use this number to divide 28.29 (female/futanari) or 37.71(male) to get your penis length.

TL;DR - Just make the penis whatever size you like.

 

[TheShepard256]

We could get more accurate penis sizes if we used more accurate formulae, which is especially important for those with non-human-like penises. All of the following will be based on the formulae found on the TiTS wiki. With radius = thickness ratio*length/12, the human penis is as follows:

Shaft size = pi*(length - radius)*radius^2
Tip size = (2/3)*pi*radius^3
Total size = shaft size + tip size = pi*(length - radius/3)*radius^2
In terms of length and thickness ratio: = pi*(length^3)*(1 - ratio/36)*(ratio^2)/144

Which is basically a cylinder (the shaft) with a hemisphere (the tip) at one end. The following flags (which are used to determine the shape of the penis) affect these in the following ways:

Blunt: tip size = pi*radius^3
-> total size = pi*length*radius^2 (basically a cylinder, though this assumes no other flags are modifying the size)
-> length & ratio: = pi*(length^3)*(ratio^2)/144
Flared: multiply tip size by 1.3
-> size w/o Blunt = pi*(length - 2*radius/15)*radius^2 = pi*(length^3)*(1 - ratio/90)*(ratio^2)/144
-> size w/ Blunt = pi*(length + 3*radius/10)*radius^2 = pi*(length^3)*(1 + ratio/40)*(ratio^2)/144
Double-Headed: tip size = (4/3)*pi*(radius/2)^3 + (pi/2)*(radius)^3 (I have no idea what this is supposed to represent)
-> size w/o Flared = pi*(length + 5*radius/6)*radius^2 = pi*(length^3)*(1 + 5*ratio/72)*(ratio^2)/144
-> size w/ Flared = pi*(length + 13*radius/12)*radius^2) = pi*(length^3)*(1 + 13*ratio/144)*(ratio^2)/144
Tapered: multiply both tip size and shaft size (i.e. the entire volume) by 0.75 = 3/4

Dividing the average penis volume of 8.65 cubic inches by (4.4 ounces converted to cubic inches) gives a dimensionless quantity of ~1.134, which means that any given volume of blood (in any unit system) can support a penis of a volume ~1.134 times the given volume. So, once you have the total amount of blood in your character's body, multiply that by 0.1134 to get max penis volume and put that equal to whichever equation best fits your character's penis. I personally find this to be easier and more intuitive than taking 10%, dividing by average penis blood content then multiplying by average penis volume, since once you get 0.1134 it's just one operation rather than three.

I've included versions of each equation that depend only on the length and thickness ratio because some (like myself) prefer to maintain girth proportionally to length; after all, having a width of 2" is much different on a 6" penis than it is on a 12" one, which is different again to on a 24" one. Simply substitute the desired thickness ratio (such that width = length*ratio/6) and you'll get an equation depending only on length, which is easily solvable. If you want a specific width/girth instead, convert the desired width/girth to radius and plug that in to get the length-only equation.

Note that this assumes your character only has one penis; if they have more, then that blood volume*0.1134 must be shared between all of them, which creates a range of maximum values for each unless you can figure out an exact relationship between the sizes of each. It also ignores the size of any knots those penises might have, which would presumably require even more blood due to their knotting function.

For example, my Steele is a 2m (6'7") tall herm with a mass of 93.7kg (206.6lbs); using the linked calculator and averaging all three female results gives her a total blood volume of 6,041.666.., mL (212.637oz), giving her a max penis volume of 685.125mL (24.113oz). With a single tapered penis (ignoring her knot and other flags) and the default thickness ratio of 1, that means, by this method, she has a theoretical maximum penis length of just over 35cm (14").