My gym is in the basement, and part of the first floor, of a 7-floor building. But it also has access to the back stairwell that climbs the full height of the building to the rooftop, where workouts sometimes happen, but that’s not really the point. We also use the back stairwell for plain old stair climbs, which seems to be one of the more (good-naturedly) grumbled-about exercises.
A couple days ago, a class I was in was climbing the stairs, and Tahnee complained about how, in a class the day before, the instructor made them do “a ton of stairs.”
In that “man, I’m tired” funk that happens during a workout, my mind wouldn’t let that go. How much is “a ton of stairs?” Sure, it’s intended idiomatically, but that doesn’t mean we can’t calculate it literally as well. Stairs have mass, do they not? It may be tough to weigh them when they’re already installed, but what is life without obstacles to overcome?
Here’s some stuff that I found:
Possibility 1: As a rough estimate, each tread in the stairway is about 44 inches wide and 11 inches deep. The rise is also solid, and that’s about 7 inches tall. So each step has a surface area of 792 square inches (5.5 square feet). According to this article from The Sheet Metal Shop, metal stairs (I didn’t mention it before, but the stairway is metal, presumably steel; it certainly clangs a lot as we climb) are typically made from 12 gauge steel sheet. Now, that article does come from 1910, so technology may have changed somewhat, but I’m going to go with it.
Why? Well, this chart from the Engineering ToolBox shows the different gauges of metal. I was guestimating that the sheeting on the stairs was maybe a tenth of an inch thick, which happens to be… 12 gauge. It’s close enough for the ludicrously imprecise work that I’m doing here. It’s my website, I don’t need to be any more accurate than I want to be (even though I do tend to show my work a lot more than other sites).
So, also from that chart, 12 gauge steel sheet weighs 4.375 pounds per square foot. That means that each step weighs 24.0625 pounds, so one ton of stairs would be 83.11 steps.
As you might have guessed from the fact that I’ve done all of these calculations, I’ve also counted the number of stairs. (I find it helps me get through a workout to know how close to being done with it I am so I can check-off progress, and yes, I know I’m weird.) 83 stairs is just a little over 4 flights. Which is less than I expected. And that’s arguably way too high, because…
Possibility 2: That only includes the bits of the stair where your feet go. What about the railings and support and stuff? I’m not sure what the Queen’s Rules on Converting Stair Climbs to Mass say (mostly because if the Queen has such rules the whole world needs to step back and take a serious look at what it’s doing with its life), but one could certainly argue that they should be taken into account as well.
It’s surprisingly difficult to find information about how much complete stairways weigh. One estimate comes from Redd Team: a 32-inch-wide, 4-step stair weights 145 pounds. But those are aluminum, which they say weighs 30% as much as steel. So to math it out, a steel stairway that’s 44 inches wide would weigh about 664 pounds per four steps. So a ton of stairs would only be 12 steps. The trouble with that analysis, however, is that the Redd Team’s staircase includes a landing, which may muck with the estimate. On the other hand, the stairs at my gym probably have more in the way of support and railings. I’ll go with it, since I can’t find any other information.
So there you have it: A ton of stairs is either 12 or 83 steps. I will finally be able to sleep now.