In 2004, an English academic reported that he had devised a scientific formula to calculate maximum high heel height.
The heel height formula looked both straightforward and scientific: It read simply: Heel height = Q x [12 + (3 x Shoe Size / 8)].
But there was a problem. As we will see, the scientist was not really being serious.
Nevertheless, how does the formula stack up today?
Can you really calculate a maximum heel height with a formula?
The big clue to the fact that this heel equation is not really scientific is the explanation of what is meant by “Q” in the formula. In fact, Q (which is defined as the “sociological factor”) is a separate equation in itself.
It reads: Q = [P x L x (Y + 9)] / [(T + 1) x (A + 1) x (Y + 10) x (L + 20)].
According to the inventor of the formula, this “Q factor” takes into account matters such as the price of a high heel, its “wow factor” and its fashionability in determining maximum heel height.
The formula also factors the experience of the heel-wearer and the amount of alcohol she has consumed into the equation.
Of course these matters are far removed from what are surely the physiological factors that would actually determine a theoretical maximum heel height.
Some involve subjective judgment such as the wow factor, which is defined as “P” – the probability the shoes will land you a date or other flattering attention.
Others, such as the effect of alcohol, will have a different impact on different women.
Indeed the only objective biological matter taken into account by the formula is the shoe size. But to conclude that a bigger foot can take a higher heel is hardly revolutionary.
Another clue that the equation is somewhat tongue in cheek is found in the words of its inventor, Paul Stevenson, a nuclear physicist at the University of Surrey in England.
“It’s not supposed to be taken too seriously,” Stevenson told HealthDay when the news first broke.
But could the high heel formula actually work?
Calculating maximum heel heights put to the test
To test the formula, we will take a highly popular modern heel as our base example.
The shoe we have chosen is Kate by Christian Louboutin, a style which Louboutin introduced in November 2020 as a version of his iconic So Kate but in lower heel heights. Since its introduction the heel has continued to prove very popular.
Q factor inputs
First, we must calculate the Q factor. These are the inputs we have chosen.
P factor: this is the “wow” factor, or the probability that the shoes will land you flattering attention.
Kate is a really eye-catching shoe, with what Louboutin describes as “a plunging silhouette that reveals just enough toe to leave a little something to the imagination”.
We say that Kate has a 90% chance of landing flattering attention when worn, which calculates as a p factor of 0.90.
L factor: the L factor is the list price of the shoes, in British pounds. Kate retails for £595, giving an L factor of 595.
T factor: this is the time elapsed since the shoe was the height of fashion. We can’t find an explanation of how this is calculated (is it years, months or seasons?), but the HealthDay article does say that a zero means the heel is “red-hot”.
Kate is red-hot at the moment so we’re happy to set the T factor at 0.
A factor: this is the number of units of alcohol consumed while wearing the high heel. We will defer to the UK’s Drinkaware website which states that a typical-strength 125ml glass of champagne has around 1.5 units of alcohol.
For our exercise, we will assume that the heel wearer has had half a bottle of champagne (which is three 125ml glasses).
This is 4.5 units of alcohol, an A-factor of 4.5.
Y factor: this is the number of years of experience in wearing high heels. We’re going to take a round number here, and assume a y factor of 10.
Q factor calculations
We now present the Q factor and our inputs above to calculate the Q factor.
Q = [P x L x (Y + 9)] / [(T + 1) x (A + 1) x (Y + 10) x (L + 20)].
Q= [0.9 x 595 x (10 +9)] / [(0 + 1) x (4.5 + 1) x (10 + 10) x (595 + 20)]
Q = 10,174.5 / 67,650
Q = 0.15039911
Therefore our Q factor is 0.150 to three decimal places.
Heel height calculations
Next we must input the Q factor and shoe size into the heel height calculations, using the formula: Heel height = Q x [12 + (3 x Shoe Size / 8)].
The average American women’s shoe size is around a size 8.5 but the shoe size in the formula is in UK sizes. A size 8.5 US heel converts to a UK size 6.5.
Here’s our workings:
Heel height = Q x [12 + (3 x Shoe Size / 8)].
Heel height = 0.150 x [12 + (3 x 6.5 / 8)].
Heel height = 0.150 x 14.4375.
Heel height = 2.165625
Finally, we need to convert the heel height from cm to inches (the formula produces a result in centimetres). This converts to a heel height of just 0.85 inches.
Conclusions
According to the heel height formula, the maximum heel height for a woman with average-sized feet who is wearing expensive, on-trend heels and who has worn heels for 10 years and consumed 3 glasses of champagne is just 0.85 inches.
0.85 inches is basically a flat. It is a long way from the 4 inch Kate pump which our hypothetical wearer is trying to turn heads in.
We know that lots of women can wear a 4 inch heel, even after a modest 3 glasses of champagne. And certainly with 10 years experience in heels.
The formula also produces a number that is so low that it practically is saying any heel is too high in these circumstances.
We don’t think those conclusions are realistic based on lived experience.
For that reason, we consider that the maximum heel height formula should not be taken seriously. Which is the conclusion we expected its inventor came to himself.