Pi Day! Today’s Special: The Human Body

Happy Pi Day!  Pi Day is definitely one of my favorite holidays, right up there with Halloween and 4th of July.  We normally celebrate Pi Day with a variety of Pi-foods.  Tonight we are having Pi-pperoni Pi-zza and for dessert we are having double cream blueberry pie (I just double the cream part, and use a really big deep pie pan).  

Happy March 14, Pi Day! / Photo by Bodymybody.com

What is Pi day? Pi day is celebrated on March 14, which can be shortened to 3-14 which is very similar to 3.14, the rounded off number for pi.  Ta da!  Pi day!  Sometimes abbreviated with the Greek letter, π, pi is mathematically equivalent to the ratio of the circumference of a circle divided by the diameter.  It has been calculated to over a trillion places beyond the decimal point, and doesn’t have a pattern.

While the human body doesn’t have any mathematically exact ratios like pi, it does have some other interesting, approximate ratios, both internally and externally.  

Body Mass Index or BMI

One common ratio that you have often heard about is the Body Mass Index, or BMI.  It is calculated using kg for weight and m for height.  The BMI is calculated by dividing the body mass by the square of the body height.  The resulting number is often used by doctors to categorize the patient into four different categories–underweight, normal, overweight, and obese.  BMI is a very general number and easy to calculate.  However, it is limited in its accuracy and how useful the resulting data is.  For example, BMI does not accurately reflect muscle mass and sometimes extremely fit people are categorized as obese.  Also, extremely short people and extremely tall people are sometimes improperly categorized.  Regardless, here is the BMI calculator from the National Institutes of Health.


Speaking of proportions, a newborn baby’s weight is approximately 5% of its adult weight.  The weight of the baby’s brain is about 25% of its adult brain weight [1]. It would make sense then, that the weight of a baby’s head is 25% of its body weight [2]. That’s a heavy head! No wonder it takes them so long to hold their head up.

Ape Index

My favorite name for a ratio of the human body is the “ape index.” The ape index is the ratio of your arm span to your height. Typically, your arm span matches your overall height from head to toe, giving you an ape index of 1.  Your ape index is usually expressed in terms of inches.  For example, if you are 6 feet tall, and your arm span is 6’ 2”, you would have an ape index of +2.  If you are 6 feet tall and your arm span is 5’ 9”, you would have an ape index of -3.  Many rock climbers believe that having an index greater than 1 provides a competitive advantage.  

This gorilla has an ape index greater than 1 / Photo by Raul654 and available via CC 3.0

Attractiveness and the Golden Ratio

The golden ratio can be used to describe attractiveness of human facial features.  The Golden Ratio is often seen in nature.  It is described mathematically as

The Golden Ration / Image available in the public domain

In this example, a+b is 1.61% larger than a.  Also, a is 1.61% larger than b.  Alternatively, b is 0.61% the size of a, and a is 0.61% the size of a+b.  After a variety of rectangles are built using this and overlaid on a face, a mask can be calculated showing the optimum attractiveness.  This optimum attractiveness is the distance between eyes, the distance between the eyes and the lips, the width of the face versus the height of the face, and many other calculations and variables that all work out to the Golden Ratio.  This blog explains it very well.  

I found a neat calculator overlaying the mask over a variety of photos, and your own photo.  Jessica Simpson is a near perfect match–me, not so much.

Golden ratios used to calculate attractiveness. / Photo by Bodymybody.com. Mask overlay by www.intmath.com


Your height can be approximated in several ways.  Again, your arm span is approximately your height.  In figure drawing, it is common to draw a person about 8 heads tall, including the head.  18 fists (measured across the knuckles) is also an approximation for height.

Your height is also approximately 7 times the length of your foot and 10 times the length from your wrist to the tip of your middle finger.  Detectives can use this approximation when estimating the height of a criminal based on a footprint found at the scene.  

An old wives tale says that the height of a child at two years old, doubled, is an estimate of their adult height.  While researching this tale, I found some clinical reasoning to justify it.  At two years old, the child, barring any illnesses, hormone imbalances, etc, has reached their growth chart percentile that they will follow that percentile as they grow [3].    

Vitruvian Man, approximating height to arm span, by Leonardo da Vinci / Image available in the public domain

Your Organs

Internal organs can have a large variance in size due to the size of the owner.  Even if two people are similarly sized, the size of the organs can vary person to person.   I was able to find some estimates of sizes and weights of some organs.  

  • The brain accounts for about 2% of a person’s body weight.  [4]
  • The heart is a relatively small (no bigger than a clenched fist), accounting for approximately 0.3% of the body weight of an adult [5].  The weight of blood is about 9% of the body weight [6].
  • Your stomach is about the size of your fist.  The stomach is super stretchy though, and can expand up to 40 times its size if you eat a large meal.  Knowing that your fist is about the size of your stomach is sometimes used as weight loss advice, so you know about how much to eat.
  • In an adult, the liver is 2-2.5 % of the body weight.  During infancy though, the liver accounts for 5 % of the body weight [5].
  • The largest organ of your body is your skin.  It accounts for 12-15% of your body weight [7].  
  • While not typically categorized as an internal organ, but still an organ on your insides, bones weigh about 15% of your body weight.  This can vary based on diet, exercise, and disease.

Penis Size

Jokes abound correlating hand, foot, and shoe size to penis size.  However, a peer reviewed, scientific study conducted in 2002 shows no association between shoe size and penile length [8].  Hand size is correlated to foot size [9], so it follows that there is no association between hand size and penile length.

Interestingly, the ratio between the length of the second finger (pointer finger) to the length of the fourth finger (ring finger) on the right hand does show a statistically significant association to penile length [10].  The second digit to fourth digit ratio has previously been associated with high fetal testosterone and high testicular activity.  The ratio is calculated as follows:

Digit ratio=(pointer finger length)÷(ring finger length)

If your right hand pointer finger measures 7 cm and your right hand ring finger measures 7.25 cm, your digit ratio would be:

Digit ratio=7÷7.25=0.96

The smaller that ratio is, the larger the size of the stretched flaccid penis (which is an approximation of an erect penis [11]).  Here is a graph pulled from the study showing the relationship between stretched penile length and digit ratio.   

Penile length graphed against digit ratio / Graph available from In Ho Choi, Khae Hawn Kim, Han Jung, Sang Jin Yoon, and Tae Beom Kim as found in the Asian Journal of Andrology in 2011. It is licensed under CC 3.0.


I stumbled across a fascinating study while researching this post.  It is not related to human body size, but it is related to body size of mammals.  The data was collected at Zoo Atlanta using high speed cameras or video.  The study concluded that the size of the animal does not significantly change the duration of urination.  The study discovered that all mammals above 3 kg in weight empty their bladders over nearly constant duration of 21±13 seconds.  This is due to a much higher flow speed of larger mammals (think elephant) versus more of a drip from smaller mammals [12].  If you would like to watch slow-motion pictures of a rat, a goat, a cow, or an elephant urinating, follow this link.

Large mammals, such as elephants, urinate at a higher flow speed than smaller mammals / Photo on left by Fiona Henderson, Photo on right used with permission from Yang, Patricia J., Jonathan Pham, and And Jerome Choo. “Duration of Urination Does Not Change with Body Size.” Ed. David A. Weltz. Proceedings of the National Academy of Sciences of the United States of America 111.33 (2014): 11932-1937


Graph showing the relationship between body mass and urination time. / Graph used with permission from Yang, Patricia J., Jonathan Pham, and And Jerome Choo. “Duration of Urination Does Not Change with Body Size.” Ed. David A. Weltz. Proceedings of the National Academy of Sciences of the United States of America 111.33 (2014): 11932-1937. PNAS. National Academy of Sciences


There are numerous ratios for the human body, and I have only listed a few.  Do you know of another interesting one?  Let me know in the comments! Happy Pi Day!


References Cited

[1] Oppehheim, Leah. “Mass of a Newborn Baby.” The Physics Factbook. Ed. Glenn Elert. Hypertextbook, 2002. Web. 11 Mar. 2017.

[2] “Fast Facts about Your Body.” Did You Know? Did You Know?, 07 Feb. 2010. Web. 11 Mar. 2017.

[3] Bishop, Shawn, and Siobhan Pittock, MD. “Child’s Height at Age 2 May Predict Adult Height.”Mayo Clinic News Network. Mayo Clinic, 24 Sept. 2010. Web. 11 Mar. 2017.

[4] “Brain Facts and Figures.” Brain Facts and Figures. Web. 11 Mar. 2017. <https://faculty.washington.edu/chudler/facts.html>.

[5] Gambino, Stephanie. “Mass of a Human Heart.” The Physics Factbook. Ed. Glenn Elert. Hypertextbook, 2006. Web. 11 Mar. 2017.

[6] Lee, LanNa. “Volume of Blood in a Human.” The Physics Factbook. Ed. Glenn Elert. Hypertextbook, 1998. Web. 11 Mar. 2017.

[7] Fridman, Igor. “Surface Area of Human Skin.” The Physics Factbook. Ed. Glenn Elert. Hypertextbook, 2001. Web. 11 Mar. 2017.

[8] Shah, J., and N. Christopher. “Can Shoe Size Predict Penile Length?” BJU International 90.6 (2002): 586-87. BJU International. Blackwell Publishing Ltd, 13 Sept. 2002. Web. 09 Mar. 2017.

[9] Oommen, Anitha, Avinash Mainker, and Tom Oommen. “A Study of Correlation between Hand Length and Foot Length in Humans.” Journal of the Anatomical Society of India 54.2 (2005): 55-57. Research. Researchgate.net, 20 Apr. 2015. Web. 11 Mar. 2017.

[10] Choi, In Ho, Khae Hawn Kim, Han Jung, Sang Jin Yoon, Soo Woong Kim, and Tae Beom Kim. “Second to Fourth Digit Ratio: A Predictor of Adult Penile Length.” Asian Journal of Andrology 13.5 (2011): 710-14. Asian Journal of Andrology. Shanghai Materia Medica, Shanghai Jiao Tong University, 04 July 2011. Web. 11 Mar. 2017.

[11] Wessells, H., and J. W. McAninch. “Penile Length in the Flaccid and Erect States: Guidelines for Penile Augmentation.” The Journal of Urology 156.3 (1996): 995-97. PubMed. U.S. National Library of Medicine. Web. 11 Mar. 2017.

[12] Yang, Patricia J., Jonathan Pham, and And Jerome Choo. “Duration of Urination Does Not Change with Body Size.” Ed. David A. Weltz. Proceedings of the National Academy of Sciences of the United States of America 111.33 (2014): 11932-1937. PNAS. National Academy of Sciences. Web. 11 Mar. 2017.

This website and information contained herein is meant for informational purposes only. You assume full responsibility and risk for the appropriate use of this information.


Leave a Reply

Your email address will not be published. Required fields are marked *