How do I calculate how many banker´s boxes will fit under a 10x10 tent?

May 5, 2019 8:08 PM

YANMMT (You Are Not My Math Teacher) but can you help me figure out how many banker´s boxes will fit under a 10x10 tent? Tent has a 6´valence but I´ll call it 5´ cos I don´t want to tower the stacks of boxes too crazy high. Tent height x width x length: 60¨x 120¨x 120¨ ; Box height x width x length: 10¨x 12 ¨x 15.¨ I could divide each tent dimension by the box dimension to arrive at 6 x 10 x 8 = 480 boxes fit in a tent. (Volume of tent divided by volume of the boxes = the same number). But I´m afraid that I´m missing something. Does the fact that the numbers all divide evenly mean that this will work? Or is there something I must take into account so as to consider that even though we can break a box into length/width/height we have to ensure we treat it as one whole unbroken thing in real life? Thank you!
posted by red_rabbit to Grab Bag (12 answers total)

Your boxes won’t perfectly fill the volume of your tent, there will be empty/‘wasted’ space. So a calculation based on volume alone will overestimate how many boxes will fit. I’m a bit confused by the dimensions and geometry of the tent and the boxes: I assume the boxes are rectilinear but most tents are not... is it domed, prismatic, other?

If you can specify the tent geometry more clearly (maybe a labeled diagram?) I’d be willing to help you get a more realistic estimate, another tack is to take your number based on volumetric analysis and reduce it by about 20% and figure it will probably fit.
posted by SaltySalticid at 8:17 PM on May 5, 2019 [1 favorite]

I'd say you can't really pack them to the edges (presumably you're putting them into the tent to protect them from the weather, and if they touch the walls, then they'll get wet from condensation, etc.)

So, width x length of tent is 120x120 inches, and that means you can pack in 9x7 boxes. ((120 / 12) - 1 = 9, (120 / 15) - 1 = 7).

(60 / 10) - 1 = 5.

so, 9 x 7 x 5 = 315 boxes per tent will fit without touching the walls or ceiling.

Edit: If the ceiling is not a horizontal plane (very likely for a tent), then you can probably fit a few more in the top center region.
posted by smcameron at 8:23 PM on May 5, 2019

I think you are basically right. You would then need to adjust if the measurements are not exact - the tent might vary by a few inches, there are probably tent poles within the perimeter of the tent. Another question is whether the lids on the box extend out an extra fraction of an inch.

Finally, depending on what you are doing, the boxes may not be sturdy enough to stack 6 high, especially if you are going to leave them for a long time.

Also, do you need to be able access the interior boxes? if so, then you will need to allow for aisles which will limit the number of boxes significantly.
posted by metahawk at 8:48 PM on May 5, 2019

If the tent is 120x120 and the boxes are 12x15 (ignoring heights for now), then you can lay 10 boxes with their 12" sides facing one side. You can have a total of 8 rows of boxes, because 8x15 = 120. So you have 80 boxes in a layer. (If you're okay with having the boxes right up against the edge of the tent, which as smcameron points out is probably not a good idea.) If you assume you can stack them 5 ft (60 inches) high, then since they're 10 inches tall you can have 6 layers. 6x8 = 480, which is what you came up with. So you were basically right, but consider how close to the edge you want them to get and maybe go with smcameron's figure instead.
posted by Redstart at 9:02 PM on May 5, 2019 [1 favorite]

Response by poster: The tent is an EZ-up with no walls, like this one.

The bankers´boxes are ones like these.

This is an intermediate step in clearing out a 4BR house that´s filled with mostly books and papers. Don´t think we´ll leave them more than 24 hours.

Not planning to access the boxes beyond load / unload, so no need for aisles.

We will allow for box lips + tent poles, good call.

I´m equally curious about the true reality of things as to the math problem...is it really as simple as multiplying and dividing as I´ve laid out? Or is there something more funky to consider?
posted by red_rabbit at 9:03 PM on May 5, 2019

Yeah, the math smcameron lays out seems like it makes sense. Pack the boxes full, and you should be good to go. I'd give some consideration to whether you want to protect from blown rain/snow, which is what I'd worry about in this case.

Personally, I'd just use a tarp.
posted by sagc at 9:08 PM on May 5, 2019 [2 favorites]

You did the math right--it was a coincidence that the numbers worked out evenly. If, say, the tent was 125 inches on each side, you would have gotten 125/12=10.41 and 125/15=8.33. You'd round down because you can't have partial boxes, so you would still have 6x10x8=480.

Also I'm with sagc, I'd just use a tarp. You might want a tarp anyhow, and also want to put them on a tarp, if you are somewhere with a lot of dew.
posted by lemonade at 9:28 PM on May 5, 2019 [4 favorites]

I worked in a warehouse where we packed pallets for delivery to Amazon that had to have very specfic max dimensions. DIfferent size boxes. There is available software for free or trial version that will not only tell you how many, but also the configuration to get there. Here is one such software package. There are others. This is just the first one that came up on the search.
posted by AugustWest at 1:19 AM on May 6, 2019

Not answering your math question but in the event of rain, have you got them sitting on top of pallets or something? Thirding the tarp idea.
posted by bonobothegreat at 3:16 AM on May 6, 2019

To have more confidence in your (correct!) answers to math problems, I would recommend reading a little bit about Polya's problem solving process, which is a way to think about the steps involved in solving a math problem, originally written by a famous mathematician and mathematical educator.

In this case, commenters above solved the problem by setting up equations to model the scenario. It sounds like this is what you did as well. Polya recommends trying two different methods, in order to check your reasoning - which is what you did in doing the volume calculation as well as the length, width, and height calculations! I would recommend drawing a picture or diagram to help visualize the scenario, as well.
posted by eviemath at 3:22 AM on May 6, 2019 [1 favorite]

You can't just do it by volume, because if, say, the widths don't fit evenly, then it doesn't matter if the volumes fit evenly. So you need to look at how many you can fit across, how many you can fit deep, and how many you can fit high, and then do that math. In your problem they do, so it worked out fine, but if the boxes had been, say, 11 inches wide, even if the volume had worked out, they wouldn't have lined up properly on the floor.
posted by gideonfrog at 4:18 AM on May 6, 2019 [1 favorite]

Are you trying to protect against rain, sun, wind, heat, animal attack, theft? If rain, then possibly wind will blow rain in from the side. If sun, then you're more interested in the volume and shape of the shadow of the tent, and the sun moves relative to the boxes.
posted by at at 12:53 PM on May 6, 2019