In this article, I attempt to determine an average value for the mass of a single grape, and to develop a (relatively) simple formula for approximating how many pounds of grapes to buy given a desired number of individual grapes.

For convenience of purchasing, grocery stores sell grapes by mass, with stems and packaging included. If all you want to do is eat some grapes, this is fine. However, if you want to consume or distribute a precise number of grapes, an interesting problem arises: What mass of grapes should you buy (with stem and packaging included) to end up with the desired number of grapes?

Spaniards! In Spain, it is traditional to consume precisely 12 grapes at the stroke of midnight on New Year's Eve, to symbolize good luck over the coming 12 months. Part of my family hails from Spain, and for many years we have hosted a large New Year's Eve party for as many as 80-100 family and friends. It has become a tradition at this party for us to prepare and distribute pre-measured packages of 12 grapes for group consumption at midnight.

So, each December we are faced with the problem of needing to buy as many as 1000 or more grapes, and figuring out how many n-pound bags to buy in order to end up with enough individual grapes. Traditionally, we have solved this problem by significantly overbuying, which usually leaves us with a freezer full of surplus grapes until at least mid-March.

I have often longed for a more precise solution to this problem. Although I assume adherents to this tradition must face this problem frequently, I have been unable to find any relevant discussion of average grape mass online. So, I decided to do my own research.

In December 2017, Adam Cordingley and I purchased 3 brands of grapes at our local Kroger. They were:

- Agricola red grapes (PLU 4023)
- Frusan green grapes (PLU 4022)
- Vincent B. Zaninovich & Sons green grapes (also PLU 4022)

For one bag of each brand of grape, we recorded the individual mass of between 30 and 40 grapes using a kitchen scale which was precise to the nearest gram. We also measured the total mass of all the grapes in the bag, the total number of grapes in the bag, and the combined mass of the stems and packaging (all 3 brands came in lightweight plastic bags).

Graps mass(g) | Number of grapes |
---|---|

3 | 3 |

4 | 9 |

5 | 14 |

6 | 4 |

Total number of grapes in bag | 155 |

Total mass of grapes + stems + bag | 792 g |

Mass of stems/bag | 15 g |

The Agricola grapes we weighed had an average mass of 4.63 g, with a standard deviation of 0.85 g. The average mass of all the grapes in the bag was higher (5.0 g), but this diference is well within the standard deviation. The grapes we weighed came from several different clusters throughout the bag, so I think it's unlikely the difference was caused by settlement during shipping.

We weighed 39 Frusan green grapes:

Graps mass(g) | Number of grapes |
---|---|

2 | 1 |

3 | 0 |

4 | 2 |

5 | 2 |

6 | 4 |

7 | 11 |

8 | 9 |

9 | 6 |

10 | 4 |

Total number of grapes in bag | 136 |

Total mass of grapes + stems + bag | 1012 g |

Mass of stems/bag | 20 g |

The Frusan grapes we weighed had an average mass of 7.36 g, with a standard deviation of 1.77 g. The average mass of all the grapes in the bag was 7.29 grams, which was very close to the average of the grapes we randomly selected.

We weighed 41 VBZ & Sons green grapes:

Graps mass(g) | Number of grapes |
---|---|

2 | 2 |

3 | 3 |

4 | 5 |

5 | 7 |

6 | 13 |

7 | 6 |

8 | 1 |

9 | 3 |

10 | 1 |

Total number of grapes in bag | 142 |

Total mass of grapes + stems + bag | 952 g |

Mass of stems/bag | 14 g |

The VBZ & Sons grapes we weighed had an average mass of 5.68 g, with a standard deviation of 1.84 grams. The average mass of all the grapes in the bag was 6.61 grams. Like the Agricola grapes, this was greater than the average mass of the grapes we measured, but well within the standard deviation.

Based on the data collected, I draw the following rudimentary conclusions:

- Red grapes appear to be lighter than green grapes on average. However, there was also significant variation in average mass between the two brands of (nominally identical) green grapes. So, maybe we just bought an unusually light bag of red grapes.
- In bags of grapes this large (700g - 1kg, which seems to be a common size in American grocery stores), the mass of the stems and lightweight plastic packaging is probably negligable.
- Thus, it's probably OK to assume a linear relationship between the desired number of grapes and the mass of grapes to purchase.
- However, to account for potential variation in average grape mass from brand to brand and batch to batch, it's probably a good idea to add some safety margin (say, 10%) to the calculated mass of grapes to purchase.

This is my best guess at calculating what mass of grapes to purchase to recieve a desired number of grapes. When doing this in real life, I would probably buy 10-15% more grapes by mass than I calculated I needed, unless I really didn't want any extra grapes and was willing to make an additional trip to the grocery store in case I ended up with too few. I could add more significant figures to these numbers, but given the apparent variation in grape mass that would probably be unwise.

For red grapes (PLU 4023), I would assume an average mass of 5 grams, or roughly 1 pound for every 90 desired grapes.

For green grapes (PLU 4022), I would assume an average mass of 6-7 grams, or roughly 1 pound for every 65-75 desired grapes.

My hunch is that grapes vary significantly in mass depending on various factors, including manufacturer, growing region, geographical & annual weather patterns, fertilizers used, etc.

To further refine my model, it will be necessary to weigh many more grapes, from many different manufacturers and batches. Ideally, I would also have data available from grapes purchased in many different locations.

I will continue to measure grapes each year. If you are interested in this project and want to send me data you've collected yourself, feel free to do so via email to grapes@johnholbrook.us. Please include the following information:

- Grape Manufacturer, type, and (ideally) PLU
- Location you purchased the grapes (store name and city is fine)
- Total number of grapes you weighed, and the mass distribution (or your raw data for each grape)
- Total number of grapes in the container
- Type of container in which grapes were packaged
- Total mass of the grapes, stems, and container (just as it appeared in the store)
- Total mass of the container and any stems (weighing these together or separately is fine).
- Any other information/data you deem relevant.