How Many Pennies Are In 0 – Let’s start with a 12-by-12-inch piece of cardboard, which is exactly 1 SF. As you can see from the pictures, the tape measure shows that we have 12 inches on both sides, although it may be hard to see the small numbers.
We start by placing pennies on the edge of this 12-inch cardboard and it turns out to be a perfect fit: 16 pennies side by side measures exactly 12 inches (one foot) because the diameter of a penny is 0.75 inches (or 3/) is 4 . inches).
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We added an additional 15 cents to “fill” the other side of the square cardboard, as you can see here:
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Simple math can tell us how many pennies fit in one square foot in this straight pattern (16×16=256) without actually filling the square of cardboard with pennies. We decided to do it anyway to show other details and to show you how nice it looks. Here we will add, row by row, 16 cents each.
It is worth noting that the pennies do touch each other. If an opening/space is needed around every penny, for example for grout, changes will need to be made.
So, how many cents fit in one square foot? 256 cents per square foot if the rows are straight
Not one cent covers the edge and there is no space left at all – at least that’s what mathematics tells us. If you see little imperfections in the picture below, that’s because we placed all 256 cents by hand and they’re just sitting there, not glued.
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If a penny were square in shape instead of round, with a side of 0.75 inches, the cardboard underneath would be completely covered with 256 square cents. But because the penny is round, you can see the cardboard between the pennies.
Here is a close up on one corner of the square cardboard. Although the tokens are in contact with each other, there is enough space between them and this is due to the straight row pattern/arrangement.
And here’s another view of the same 256 brand new shiny pennies sitting in straight rows on exactly one square foot of cardboard.
The first row of 16 stuivers remains the same and the second row is moved half a stuiver to the right. Then we can also push the entire second row up (as you look at the photo) until it touches the first row of pennies.
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We push each even row (2nd, 4th, 6th,…) half a hundred to the right and then the whole row up a little to touch the previous row. With each row pushed up a little, we should get some space at the bottom of the cardboard.
Here’s more of a visual: if you push a row with a half cent (A), the half cent overlaps the edge of our square foot (B).
Overlap cannot occur if your exact one square foot (SF) project has sides/walls like a tray. And for larger projects, each SF of cents can overlap the next SF until you reach the final side of your project and can’t fit another full cent.
So, by pushing 8 rows of halfpennies to the right and then up a bit, our original 16 rows of pennies were ‘pushed up’ closer, revealing quite a bit of extra space (C) at the bottom of the carton.
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Can we lose 2 rows of cents there? We certainly can. Not only that, there will be some space left after that that we won’t go into (mathematically), but some ‘slices’ will still fit in the small room on the bottom left.
There we have the 2 extra rows of pennies (above) and space left for ’16 slices of pennies’ lined up with the bottom of the carton.
What about the top of the cardboard? It will fit 16 more over small ‘pennies’, lined up with the edge, to make our square foot…full.
And the overlapping pennies on the right make up for the blanks on the left, so no further explanation is needed here.
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Simple math gives us the total number of whole cents (18×16=288) plus about 16 ‘slices’ at the bottom of the carton and another 16 small discs at the top.
The topic “How many whole cents are in the 32 slices” may be the title of a new article, which is outside the scope of this page. But if you’re a math genius who wants to give it a shot, let us know and we’ll publish your paper and give you credit.
A quick look says that the 32 slices can make up about 6-8 cents, but let’s wait for Einstein’s confirmation.
Pennies per square foot (sf) in offset pattern: 288 plus about 6-8 pennies “cut” at the top and bottom of cardboard The total can be 294-296 pennies per SF.
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What if your perfect square foot was a tray (or something similar) with edges/sides preventing the pieces from overlapping … like the 9 cents do in the picture above or below.
So what then? Someone might say “let’s cut the 9 overlapping pennies in half and fill the left side with the 9 halves”. We absolutely do not recommend cutting pennies. Just don’t include the 9 overlapping cents and the right side will be identical to the left.
Also slide the whole thing down so that the top and bottom have identical spaces as the edge of the square foot.
The straight pattern we saw earlier had larger blank areas with 4 rounded sides and now with the offset pattern we have smaller blank areas between pennies with 3 rounded sides. (Hey, where did one side go? Hmm…)
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Let’s compare the close-ups of both setups one by one. You can clearly see the pennies much closer together with smaller empty areas in the offset arrangement compared to the straight row pattern with larger empty areas between the cents.
Remember that in both patterns the pennies will still touch and if you want a grot for your project, it’s best to have space around each penny.
In short, here’s the comparison of each penny pattern on square foot cardstock, hoping it sheds some light…
If you need the pennies to have a space for tile or other reasons, you probably need our Real Penny Tile Sheets (handmade web-back penny tile sheets).
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Our handmade coins are 224 pence each. There are small spaces between the pennies as space for tile (get 20% off at The Tile Shop for tile and tiles).
The entire sheet is just under 1 SF to fit in 12-by-12-inch shipping boxes.
If you are a math genius and want to tackle the ’32 cut paper’, let us know and we will publish it here with full credit. “How many cents in a roll?” my son asks. “Fifty,” I reply. “One, two, three, four,” he begins to count. “Six seven eight nine ten!” He declares with utter excitement.
Minutes later, piles of pennies are in front of him. His little fingers grasp the stacks and move them in perfect rows. “Done!” he declares after counting and stacking all the pennies. “How many nickels in a roll?”
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“5, 10, 15, 20…” he counts as he piles up the nickels. When all the nickels are counted, he looks up and asks, “How many quarters in a roll?”
“Oh yeah,” he says and the counting begins again. “10, 20, 30, 40, 50 … wait how many coins in a roll?” “Fifty,” I reply and he picks up where he left off. “60, 70, 80…”
When I look at my son, I go back to my own childhood. Counting coins is a family tradition. I guess the roots of my own passion for personal finance started when I was just four years old.
I heard the familiar sound long before I saw it. The distinct sound of coins clicking in a metal case. My father kept his change in an old box with blue and orange cheese curls at the bottom of his closet.
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Each time he took it into the kitchen, where he counted and tossed his coins. As he walked, the coins shook and jingled before him.
As soon as I heard the sound, I ran to the table, pulled out a chair and fell on it. I didn’t want to miss a moment of the money counting process.
“We’ll have to count,” he replied, but I always tried to guess the amount before throwing them out. I wanted to hold the container and feel how heavy it was. Of course, the weight and number of coins never gave any clue. A can of pennies is worth much less than a set of quarters and half dollars. It turned out that weight was not a good predictor.
My father unfolded the newspaper, spread it across the table and poured out the quarters, dimes, cents and nickels onto the black and white words below. The moment the coins appeared, the unmistakable smell of
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