Before we uncover how plenty of pennies deserve to fit in one square foot, we must ask part questions...

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any minimum room required between pennies?what pattern?are over there sides come the square foot and no penny can overlap any kind of edge?other

Let"s begin with a item of cardboard that measures 12 by 12 inches, i beg your pardon is specifically 1 SF. Together you can see in the pictures, the tape measure reflects we have 12 in. On both sides, even though it might be hard to view the little numbers.



We begin placing pennies ~ above the edge of this 12 in. Cardboard and it outcomes in a perfect fit: 16 pennies next to each other measure precisely 12 inches (one foot) since the diameter the a coin is .75 in. (or 3/4 of an inch).

By the way, as you deserve to see, we supplied all brand new pennies for this demonstration.

1 SF cardboard and 16 pennies on its edge

Simple math deserve to tell us exactly how many pennies fit in one square foot in this directly pattern (16x16=256) without actually filling the square cardboard through pennies. We chose to execute it anyway in order to display other details and for you to see exactly how beautiful that looks. Here we go, adding row after heat of 16 pennies each. 

Worth mentioning right here is the the pennies do touch every other. If a gap/space is forced all approximately each penny, say for grout, changes must be made.   

Slowly including up pennies...

So, how plenty of pennies have the right to fit in one square foot?256 pennies every square foot if the rows are straight

No coin overlaps any kind of edge and there"s no an are left whatsoever - at least that"s what mathematics tells us. If you view slight imperfections in the photo below is due to the fact that we placed all 256 pennies by hand and also they are just sitting there, no glued.

If a penny was square shaped rather of round, with a .75 in. Side, the cardboard listed below would be completely covered by 256 square pennies. But due to the fact that the penny is round, you can see the cardboard in in between pennies.

Notice the empty area between any 4 pennies is quite large and has actually 4 rounded sides (more top top this later).After closely placing every penny by hand, right here it is: 16 rows the 16 pennies each.

16 pennies per directly row x 16 rows = 256 pennies

Here"s a close-up on a corner of the square cardboard. Also though the pennies space in call with each other, there"s still rather some room in between them and that"s due to the straight rows pattern/layout. 

Close-up on directly rows of pennies

And here"s another view the the exact same 256 brand brand-new shiny pennies sitting in straight rows top top a precisely one square foot cardboard.

256 brand brand-new pennies on a 1 SF area
How many pennies can fit in 1 sq. Ft. If we readjust the sample to staggered/offset rows?

The very first row that 16 pennies stays the same and we relocate the 2nd row to the ideal by fifty percent a penny. Then we can also push up (as friend look at the picture) the whole second row till it touches the very first row of pennies.

We"ll push every also numbered heat (2nd, 4th, 6th, ...) to the best by half a penny and also then the entirety row up a little bit to touch the previous row. Through every row propelled up a little, we should acquire some room in ~ the bottom of the cardboard.

Beginning of offset/staggered rows that pennies

Here"s more of a visual: advertise a row by half a coin (A) outcomes in fifty percent a coin overlapping the edge of our square foot (B). 

Overlapping can"t happen if your an accurate one square foot (SF) project has actually sides/walls choose a tray. And also for bigger projects, each SF that pennies have the right to overlap ~ above the next SF until you with the finish side of your project and also cannot fit another full penny anymore.

So, pushing 8 rows to the best by fifty percent a penny and then up a little, our 16 initial rows of pennies got "squeezed upwards" closer together and revealed rather the extra room (C) in ~ the bottom of the cardboard.

Can we fit 2 an ext rows that pennies there? We certain can. Not only that but there will be a little bit of room left after that which we"re no going to (mathematically) acquire into, but some much more "slices that pennies" will fit in the little room left below. 

There we have the 2 extra rows of pennies (above) and room left because that "16 slices of pennies" aligned v the cardboard"s bottom edge.

How about the optimal side that the cardboard? another 16 super tiny "slices that pennies" will certainly fit in there, aligned v the edge, to do our square foot... Full.

And the overlapping pennies on the ideal side, compensate because that the north spaces top top the left, for this reason no much more explanation needed here.

Easy math offers us the total variety of whole pennies (18x16=288) plus part 16 "slices of pennies" at the bottom that cardboard and also another 16 tiny slices in ~ the top.

The subject of "How countless whole pennies room in the 32 slices" can it is in the location of a new article i m sorry is beyond the objective of this page. But if you"re a genius mathematician who desires to offer it a shot, let united state know and also we"ll publish your article and give you the credit.

A fast eyeballing says that the 32 slices can comprise for around 6-8 pennies but let"s wait because that Einstein"s confirmation.

Here"s the humble conclusion...

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Pennies per square foot (sf) in offset pattern:288 plus about 6-8 pennies "sliced" at peak & bottom that cardboardThe total could it is in 294-296 pennies per SF

What if your perfect square foot to be a tray (or similar) through edges/sides which don"t enable pennies come overlap... Like the 9 pennies carry out in the above or below picture.

So what then? Someone might say "let"s reduced the 9 overlapping pennies in fifty percent and to fill the left side through the 9 halves". We totally advise against cutting pennies. Simply, not incorporate the 9 overlapping pennies and also the best side will certainly be identical to the left.

Also, on slide the totality thing down so the top and bottom will have actually identical spaces to the sheet of the square foot. Pennies per SF is 279 in this situation (288-9=279).