It's fun to use formulas to predict your teen's height – as long as you take such predictions with a grain of salt. Shoe size generally is proportional to height, so it's used in many height-predicting formulations. Such formulations sometimes take the parents' height into account, as well. Unfortunately, the results you get are far from reliable.
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In the teen years following puberty, growth of 3 to 5 inches each year is common. A sudden increase in your teen's shoe size at puberty likely indicates he's on the verge of such a growth spurt, but his shoe size itself is not a good predictor of your teen's ultimate height, according to the InteliHealth article "Can We Predict Height?" by Dr. Robert H. Shmerling of Beth Israel Deaconess Medical Center. In fact, there's no reliable way to predict a teen's ultimate height with any precision, according to Shmerling.
Many factors determine your teen's ultimate height. One is how long his lengthiest bones, such as the femur in the upper leg and fibula in the lower leg, ultimately become. This is determined by growth plates that allow for elongation. When your teen finishes growing, usually about age 17, these plates close, preventing bones from getting longer. Gender, hormones, genes, overall health and nutrition are other factors.
While shoe size is a poor predictor of ultimate height, there is a relationship that exists between the two. There is a stronger relationship between shoe size and height when you consider girls and boys in separate categories, according to the "Edexcel GCSE Mathematics" textbook by Keith Pledger and associates. The formula for boys is height in centimeters equals 5.3 times shoe size plus 133. The formula for girls is height in centimeters equals 4.5 times shoe size plus 140. Divide your answer by 2.54 to convert it to inches. You can use this formula to calculate a teen's existing height based on shoe size or shoe size based on existing height. Such numbers are estimations, notes Pledger.
You also can estimate a teen's height in inches by doubling his shoe size and adding 50. This what is known as a "quick" relationship rather than an on-the-nose accurate correlation, notes "Elementary Statistics," by Robert Russell Johnson and Patricia Kuby. For example, if your shoe size is 10, your height might be 71 inches as opposed to the 70 inches that the formula would provide.