Here is a sign that shows a 4 minutes 1 pound of Lego because that $8.99. What go this say about the circulation of Lego blocks? thickness included.

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Yes, it's true the I have pondered the price of Lego bricks before, by looking up the expense and number of pieces in assorted sets. Here is the data, and also a attach to my initial analysis.


I arrived at a price of about 10.4 cent per piece. Ah, however what about the price per mass, in ~ $8.99 per quarter-pound? This of course requires an ext data.

It's not complicated to uncover the mass of a Lego. Simply plop that sucker top top a balance and boom—there is her mass. Determining the volume is tougher, due to the fact that Lego pieces space not solid. Sure, I could drop the pieces right into water and find the volume by displacement, however that wouldn't be really interesting. The mass come volume ratio (something ns like speak to density) likely would be consistent since the piece are probably made native the same material.

Instead, I will certainly look in ~ two various kinds the volume. First, the exterior volume. Imagine a simple Lego brick:


I deserve to measure the height, length, and width with a normal lengthometer (some might contact this a ruler). What around the bump on peak (I believe Lego calls castle studs.)? i will overlook them—this isn't the genuine size anyway. Using these measurements, I deserve to calculate the volume in cubic centimeters.

But there is another volume measurement in devices of Lego—the studs. Because that the brick above, it seems clear the the length and also width are two studs long. What about the height? If you take it the thinnest Lego piece, which each other a slice, you find that 3 of them is the same height as one "normal" brick.

And so I will assign this "normal" brick a height of 3 slices, although i am certain Lego has particular term for this dimension. To uncover the volume, I simply multiply size times broad times height. However, a height unit isn't the very same as a length or width unit, therefore this might seem meaningless. Ns think I will certainly stick with the volume measure in centimeters.

Lego offers plenty of kinds that pieces. Ns am going come stick v the straightforward shapes—no committed pieces. Here's a look at the stuff i measured:


The data looks fairly linear—well, linear sufficient for me. The steep of this right is likewise a great way to estimate the density of a Lego piece. Slope is characterized as the rate that the vertical variable (mass) alters with respect to the horizontal variable (volume). This is as with mass split by volume—the density. Looking in ~ the slope of this installation line, the median Lego density is 0.565 g/cm3. This seems plausible. I constantly like to compare densities of thing to that of water which is 1 g/cm3. The Lego density is reduced than water so that they would certainly float—assuming the the air remains inside the the piece. Again, this is reasonable.

But why does the data look prefer it has actually two linear functions mixed together? Probably because there room two Lego densities. In this study, I just examined single-height block or the three-height blocks. The shorter ones offer much less empty space—this would yield a higher density 보다 the higher blocks. That's simply my guess—you deserve to examine Lego density further as homework.

How carry out I connect the Lego density to the price per pound? First, I can determine the price per gram through a straightforward unit conversion. This would certainly be 7.9 cent per gram. Currently using the 10.4 cents per piece, I deserve to do the complying with unit trick:


If ns invert that, I get 1.35 grams every piece. This might be understood as the mean mass of a piece in a kit—if the $8.99 per 4 minutes 1 pound is realistic. What would certainly a 1.35 gram Lego item look like? based on my data the would autumn somewhere between the tall 2x2 and the high 4x1 brick.

How around just one homework question. Discover a ratio of Lego piece such the the median mass is exactly 1.35 grams. Friend should be able to see mine mass data if you click the plotly graph above. Friend will require that or you will require to recognize your very own Lego fixed data.


Rhett Allain is an combine professor of physics at Southeastern Louisiana University. That enjoys teaching and also talking about physics. Periodically he takes points apart and also can't put them back together.

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