Trying to figure out how many jelly beans there are in a mason jar or gallon jug? Here's our method of getting the number, but you can jump to the bottom and just use the calculator too.
One way to do it is to figure out the volume of the jar and divide that by the volume of a jelly bean.You want to get the volume of the inside of the jar, so you should subtract the thickness of the glass from the diameter. Mason jars typically has a 3/8" thickness.
To calculate the cubic inches inside a jar or other cylinder shaped object, you will need to know the diameter (minus the glass thickness) and height of the jar then apply the following formula:
Let's say our jar is 8 inches in diameter and 12 inches in height.
- Subtract the glass thickness from the diameter (8 - .375 = 7.625)
- Half of the circle's diameter equals it's radius (7.625 / 2 = 3.8125)
- Square the radius (3.8125 * 3.8125 = 14.53515625)
- Multiply the height by the squared radius (12 * 14.53515625 = 174.421875)
- Multiply that by pi 3.1416 (192 * 3.1416 = 547.9637625)
So we know our jar is 547.9637625 cubic inches.
Jelly Bean Volume
If our jelly bean dimensions are 3/4" by 1/3", that would be equal to .75" x .333333". We would use the jelly bean's dimensions to repeat the steps used for jar volume, which would give us 0.06544986910006544 cubic inches per jelly bean.
Jelly beans have odd, uneven shapes and won't fill all the available space of a jar. They don't pack together nicely, which means there will be small, unfilled voids in between all those jelly beans. We need to figure out what percentage of our jar does not contain jelly beans. You could add sugar to a cup filled with jelly beans so that it is filled to the top. Then strain out your jelly beans and measure how much sugar you have using tablespoons. If you have 3 and a half tablespoons of sugar, you can estimate that there is a 21.875% void in between your jelly beans. 16 TBSP = 1 Cup, 1 Cup divided by 16 TBSP = .0625, 3.5 TBSP of sugar x .0625 = .21875
To make things even more precise, repeat your jelly bean/sugar test 3 or 4 more times, then get the average value of those results. For our purposes, we'll just stick to using the first result of 21.875%. We'll use that to subtract from our jar volume, since we know 21.875% of our jelly bean jar will have unfilled voids. So 547.9637625 (jar cubic inches) multiplied by .21785 = 119.8670730 (void cubic inches). And 547.963762 - 119.8670730 = 428.096689 cubic inches of jelly bean space.
We'll divide our available jelly bean space by the cubic inches per jelly bean. 428.096689 / .06544986910006544 = 6540.833387237015
Our 8"x12" jar can hold approximately 6540 jelly beans. That's a lot of jelly beans.
For reference, here are some common jar dimensions:
- Ball 16 oz Pint Mason Jar outer dimensions are 5.2 height by 3.2 diameter - which could hold approximately 390 jelly beans
- Ball 32 oz Quart Mason Jar outer dimensions are 6.9 height by 3.9 diameter - which could hold approximately 804 jelly beans
- Ball 128 oz Gallon Jar outer dimensions are 10.5 height by 5.7 diameter - which could hold approximately 2792 jelly beans