Millimetres and litres: a guide to choosing the right sized box
Usually, customers ask for cardboard boxes of a particular size, which is why on most packaging suppliers websites, you’ll find them listed showing the internal dimensions given in millimetres. That means you know exactly how much packing space you have to work with.
But sorting out packaging problems isn’t always that straightforward. Every now and then, for example, someone might need a box of a particular volume instead. That might be because packaging is required for something which can be adapted to suit the available space, such as packets of small things (powders, seeds, flour, etc). In packaging, loose fill packing peanuts are sold by volume (usually 425 litre bags).
With most websites having only a limited number of fields with which to provide essential information for packaging buyers, there isn’t usually going to be room to display volume, so if that is what you are after, you may have to revisit long-forgotten skills from your schooldays.
Let’s start with the maths
Working out the volume of a carton is actually pretty straightforward, as long as you have a calculator to hand. The first thing you need to do is multiply the length by the width by the height. That gives the number of cubic millimetres. To calculate the number of litres, you then divide that number by a million.
As an example, let’s take a box measuring 406 x 356 x 203mm. If you multiply 406 x 356 x 203 (and this is the bit you really need the calculator for), you discover that this box contains 29,340,808 cubic millimetres (mm³).
Divide that by a million, and you get a volume for that box of 29.34 litres.
To help you narrow down your search a little, here is a short list of cube boxes by volume:
152 x 152 x 152mm = 3.51 litres
203 x 203 x 203mm = 8.37 litres
254 x 254 x 254mm = 16.39 litres
305 x 305 x 305mm = 28.37 litres
350 x 350 x 350mm = 42.88 litres
406 x 406 x 406mm = 66.92 litres
457 x 457 x 457mm = 95.44 litres
500 x 500 x 500mm = 125 litres
610 x 610 x 610mm = 226.99 litres
So far, so relatively easy.
What about a polythene bag?
This is where it gets complicated. As stated above, to work out a volume, you would normally need three dimensions (length, width, height). Standard polythene bags have only two dimensions (length and width), but is still able to expand to hold things. Can you work out the maximum volume?
The answer is that you can – approximately – but you may need better than your school maths to work it out. A Wikipedia page dedicated to what is known as the ‘paper bag problem’, but which applies equally to polythene, tells us that a very rough maximum volume for a bag with one open end would equate to:
w³(h/(πw) – 0.071(1-10(-2h/w)))
where w is the shorter side, and h the longer.
In maths, you need to do your calculations within the inner enclosed brackets first, and then work your way out.
For a polybag measuring 300 x 450mm:
1. -2h/w = -900/450 = -2
2. 10-2 = 0.01
3. 1-0.01 = 0.99
So, we now have:
w³(h/(πw) – 0.071(0.99))
4. 0.071 x 0.99 = 0.07
5. πw = 942.48
So, we now have:
w³(h/(942.48) – 0.07)
6. h/942.48 = 0.48
7. 0.48 – 0.07 = 0.41
So, we now have:
w³ x 0.41
8. w³ = 27000000
9. 27000000 x 0.41 = 11070000
That means we have 11070000mm³. Once again, to get the volume in litres, divide that number by a million.
10. 11070000/1000000 = 11.07 litres
Alternatively, you might find it quicker to fill your bag with something like flour, then empty it into a measuring jug. That would work as well.
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