How to win a guess the number of jelly beans in a jar contest

Photo by theilr

Question: Can you do better than guessing to win a jelly bean counting contest?

Answer: Let me count the ways

  1. There are approximately 930 jellybeans in a gallon. If you know the volume, then a simple ratio will give a good estimate.
  2. Estimate in two steps. If you can see the bottom of the container, and the container is at all regular and not uneven, count the number of visible jellybeans you see. For jellybean ends, count half. Then estimate the height of the container in jellybean widths. Multiply the two numbers for a low estimate. Round up a little to get a little closer.
  3. Not all jellybeans are created equal. But for a regular shaped jar, a jellybean jar is about 20% air. To estimate the volume of a single jellybean, fill a cup with water to the overflow point while the cup is sitting in an empty saucer. Add 10 jellybeans to the cup and allow the water to overflow into the saucer. Measure the volume of the water collected in the saucer. If you have a syringe, one milliliter is the same as one cubic centimeter. If you have a scale, one cubic centimeter of water weighs one gram. Divide by 10 to get the volume of a jellybean. A liter is 1000 milliliters. A gallon is 231 cubic inches and 3785 cubic centimeters. Divide by the volume of your jellybean to get your number of jellybeans per standard container, all melted down without any air spaces. Multiply this number by 80% to get a good guess for jellybeans with air gaps. If you get a number different from 930 per gallon, email me at
  4. The volume of a straight wall cylinder is π * radius * radius * height.  π is the symbol for Pi which is approximately 355 divided by 113. The volume of a cone is one third the volume of the same height and diameter cylinder. If the cone has the top chopped off, then calculate the volume of the missing piece and subtract that from the volume of the whole, un-truncated cone. Try here for other shapes.
  5. Take a digital picture of the filled container. Count the number of shapes you see. For a cylindrical jar, multiply by 6. OK, that is a pretty rough guess, and likely to be wrong. A better estimate is to also count the number of jellybean lengths in width. Multiply by the number of beans you saw in the photo and divide by 2.

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