In common US usage, the heights of tall things are sometimes converted to a "number of stories". The thinking is that people can better compare heights to similar tall buildings that they might have seen.

The US conversion is usually: $$\text{Number of stories} = \text{Round}\Big(\frac{\text{height in feet}}{10}\Big)$$

I assume that something similar is used in metric countries like: $$\text{Number of storeys} = \text{Round}\Big(\frac{\text{height in meters}}{3}\Big)$$

I am assuming that like most things that are common usage, this conversion is not correct in practice.

What is a more accurate height of a building story?
How does this cause confusion when comparing the height of a building in "stories" to the actually number of stories?

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    $\begingroup$ I assume you're talking about in public media (news, blogs, etc.) I honestly haven't seen it, usually the exact or rough measurement is given in metric units. Perhaps because a meter or a kilometer is easy to visualize. Perhaps because dividing a measurement into 3 to give an arbitrary or subjective value is unnecessary. $\endgroup$ – Sam Weston Mar 8 '15 at 0:40
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    $\begingroup$ @SamWeston Maybe I just assumed incorrectly, and it really is just a US thing. $\endgroup$ – hazzey Mar 8 '15 at 0:42
  • $\begingroup$ California's Capitol Building comes to mind; an annex was added many years after its original construction, which has a different story height, so although the buildings are contiguous you can only move directly between them on levels where the floors are in about the same spot. I looked for a good picture but this was the best I found, looking from the original building into a hallway of the annex on one of the levels that matches up. $\endgroup$ – Air Mar 8 '15 at 4:48
  • $\begingroup$ @EnergyNumbers - Regarding the edit - "story" and "stories" are not misspellings; they're just the American spellings. Not typos. Note the use of "storeys" for non-American countries. $\endgroup$ – HDE 226868 Mar 8 '15 at 13:07

There's a handy-dandy table here:

                                           Office      | Residential/hotel | Function Unknown 
                                                                             or Mixed-Use 
floor-to-floor height (f)                  3.9m        | 3.1m              | 3.5m 
Entrance lobby level floor-to-floor height 2.0f = 7.8m | 1.5f = 4.65m      | 1.75f = 6.125m 
Number of mechanical floors above ground   s/20        | s/30              | 2/25
(excluding those on the roof)

Height of mechanical floors                2.0f = 7.8m | 1.5f = 4.65m      | 1.75f = 6.125m 
Height of roof-level mechanical            2.0f = 7.8m | 2.0f = 6.2m       | 2.0f = 7.0m 
areas / parapets / screen walls

H = Building height
f = Typical occupied floor-to-floor height
s = Total number of stories

m = meters

These numbers are just averages.

Using this, it is possible to derive the height of an office building: $$H_{\text{office}}=3.9s+11.7+3.9(s/20)$$ The same can be done for a residential building: $$H_{\text{residential}}=3.1s+7.75+1.55(s/30)$$ The page then gives some comparisons of real buildings and the variation from the formula. However, while the "aggregate" variation for residential buildings (for example) comes out to 0.36%, a better indicator of accuracy would be to take the absolute value of the variation.

So, in summary: The average height depends on the function of the building (i.e. office vs. residential). But there are, of course, deviations from these figures.

  • $\begingroup$ It is interesting that a group tried to distill it down to a formula. Interesting site. $\endgroup$ – hazzey Mar 8 '15 at 0:51
  • $\begingroup$ @hazzey Indeed. I was skeptical of their legitimacy at first, but some background checks indicate that they're reliable. The formulae, though, do deviate quite a bit in some cases. But after all, there are some things (e.g. spires) that formula can't account for. $\endgroup$ – HDE 226868 Mar 8 '15 at 0:53

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