Subject: percentage differences
Name: michael
Who are you: Other

how do I calculate the percentage difference of a certain box size.
for example. How much percent smaller is this box: 8.4mm x 6.3mm to this box: 9.35mm x 7mm


Hi Michael. Percentage difference isn't really a term we use in mathematics. We do use percentage change, but that has the element of time associated with it. It is calculated according to this formula:

(L - E) / L * 100%

where L and E are the two values (Later and Earlier) you are comparing. Note that which one is L and which is E makes a difference! That's why we have the convention of phrasing things in a particular way when it comes to percentage change.

If you don't have a time frame, then the best you can do with a percentage difference is to choose one of the measurements as your reference value. However, this arbitrary choice certainly means that you might get a different percentage than if you chose the other measurement as the reference value. Here's an example:

Let's say d is Donna's height and d = 2 meters. m is Michael's height and m = 2.2 meters. Then "Michael is 10% taller than Donna" would mean (m - d) / d * 100% = 10% because Donna is the reference value. And if we stick in the values of m and d, we find that it works out.

But if we said "Donna is 9.1% shorter than Michael", that would mean (d - m) / m * 100% = -9.1%. And this works too! We've changed reference frames.

This seems a little strange initially because we think that the difference should be the same either way, but it isn't. Even with subtraction you can see that the difference of 2 and 2.2 (2 - 2.2) is not the same as the difference of 2.2 and 2 (2.2 - 2).

With your question, I would say that if you are comparing the sizes of boxes, you should be comparing volumes, so first calculate the volume of each box and then you can give the percentage difference in volume referencing a particular box.

Hope this helps,
Stephen La Rocque.