How to Count Jelly Beans in a Jar

By Ariel Balter

You’re trying to guess closest to the number of jelly beans in a jar. You aren’t allowed to take them out and count them, so you need to be tricky. The best you can do is to estimate. You can do this by assuming that the jelly beans are fairly evenly distributed within the jar, and employing some basic geometry. First the height and circumference of the jar must be determined, using jelly beans as the unit of measurement. The volume of the jelly beans can then be calculated using a mathematical formula.

Bean Counting

Count the number of jelly beans that intersect with a line stretching from the top of the jar to the bottom. To make the line, you can stretch a piece of string, lay down a piece of tape or hold up a strip of paper. Count every jelly bean that the line crosses. This is the height of the jar in jelly beans.

Count the number of jelly beans that intersect with a line that goes around the jar. Use the same method as above. If you can’t reach all the way around the jar, go half way around and multiply by 2. This is the circumference of the jar in jelly beans.

Calculate the volume of the jar in jelly beans using the following formula: volume = circumference squared x height / (4 x pi).

Round to the nearest jelly bean unless you think there might be broken pieces in the jar.

Tip

If the jar is not a cylinder, you can use the same process, but use the formula for that geometric shape. A rectangular solid like a fish tank is easier, while a ball shape is harder.

About the Author

Ariel Balter started out writing, editing and typesetting, changed gears for a stint in the building trades, then returned to school and earned a PhD in physics. Since that time, Balter has been a professional scientist and teacher. He has a vast area of expertise including cooking, organic gardening, green living, green building trades and many areas of science and technology.