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March 14th is Pi Day, the one day each year when math nerds everywhere trade their calculators for forks and celebrate π (pi) the tastiest way possible with actual pie. As a math nerd whose work encompasses food and the environment, I’ve decided to mark the occasion by calculating the environmental footprint of a single slice of key lime pie. Maybe two slices… purely in the name of science, of course.
The way we typically calculate an environmental footprint is to look at the impact of each ingredient and process involved. Let’s start with the ingredients for the crust and the pie:
- 1.5 cups Graham cracker crumbs
- 1/3 cup sugar
- 6 tablespoons butter
- 5 egg yolks (assuming each egg is 2 oz)
- 14 oz sweetened condensed milk
- ½ cup key lime juice (I always use fresh lime juice, about 4 squeezed limes)
We have a couple of challenges right away. Graham crackers and sweetened condensed milk are both products with multiple ingredients. To simplify, I will assume that the graham crackers are mostly wheat flour and that the sweetened condensed milk takes double that amount of milk plus a half cup of sugar. I also didn’t have butter as one of the ingredients in the database I searched, so I assumed it takes 20L of milk to make 1 kg of butter. Our base ingredients are then listed below with impact data per kg of the product (or per L for the milk). The environmental impact information comes from Poore & Nemecek’s (2018) paper in Science. The mean is listed along with the 5% and 95% confidence intervals in parentheses.
| Land (m2yr/kg) | Water (L/kg) | GHG (kgCO2e/kg) | |
| Flour (bread) | 3.9 (1, 10) | 648 (2, 3369) | 1.6 (0.7, 3.1) |
| Sugar | 2 (1.1, 3.5) | 620 (7, 3567) | 3.2 (0.6, 5.6) |
| Milk | 9 (0.8, 32.2) | 628 (19, 2664) | 2.8 (1.3, 7.1) |
| Limes (citrus fruit) | 0.9 (0.3, 1.8) | 83 (0, 245) | 0.4 (0, 0.7) |
| Eggs | 6.3 (4.3, 8.8) | 578 (139, 1033) | 4.6 (2.8, 8.5) |
Since our only major process in this instance is preheating the oven to 375° Fahrenheit and baking for 15 minutes, we can assume there is no land or water footprint, just a greenhouse gas (GHG) footprint from the electricity usage.
Note that for the eggs, if we assume we toss the egg white, all the impact of the whole egg needs to be assigned to the yolk; if we assume the yolk is about half the weight, that means the impact doubles. For our purposes, we use the rest of the egg for future cooking, so we only count the half of each egg that we use.
Now, we multiply the amount of each ingredient by its impact. For mean land impact, we have:
1.5 cups flour * 0.2 kg / cup * 3.9 m2yr/kg + (0.3 cups + 0.5 cups) sugar * 0.2 kg / cup * 2 m2yr/kg + (28 oz milk + 3oz butter * 20L milk / kg butter) * 0.028 kg / oz * 9 m2yr/kg + 4oz lime * 0.028 kg / oz * 0.9 m2yr/kg + 5 oz egg * 0.028 kg / oz * 6.3 m2yr/kg = 25 m2yr on average. If we lucked out and had the 5% lowest impact ingredients, it would be only 3 (or more than 80, if we had the 5% worst impact ingredients) This means that the land area used to produce this pie would need about 25 square meters in cultivation for a year.
We can repeat the same process for the water footprint. In this case, we’d get 1931 L (!) on average for my whole pie, with 68 on the low end and 8318 on the high. Put another way: the difference in volume between low, mean, or high-end water consumption could range from 9 cups worth of coffee to 240 cups all the way to 1,000+ cups.
For GHG, the ingredients alone are 8.6 (mean) kgCO2e, with half that if we had the lowest 5% impacts and double it for the highest 5%. But we also need to add in the energy for baking. We’ll assume we have a 3kW oven and we’re cooking for 25 minutes (10 to preheat and 15 minutes of cooking) so about 1.5kWh total. If we’re on a coal grid, this is about 1kg of CO2e per kWh, while a renewable grid would be about 0.2kgCO2e/kWh. Where I live in Massachusetts, natural gas is the most common fuel, so we’ll assume an emissions factor of about 0.2kgCO2e/kWh.
So, we have an additional 0.3kg from the baking process.
Now, I bet you thought I was going to cheat and not actually use pi, the mathematical constant that relates the circle’s radius to its circumference, in any of my calculations. Let’s assume I cut a 3-inch slice (at the edge). The circumference of my 9-inch pie is 9”*3.14… or about 28.3”. Three inches of this is about 11% of my pie. So, my single piece is (for an average ingredients’ impact) about 3m2yr of land, 200 L of water, and 1 kgCO2e.
Those values are big enough to feel real — a land surface area roughly equivalent to a typical dining room table, a 20-minute shower, and enough CO2 to weigh more than two cans of soda in your hands... But what do they all mean? Should I feel good or bad about my slice of pie?
In truth, it’s very difficult to know with any certainty what the real footprint is, or how to reduce it. It would be one thing if my slice could be sourced from the best practices. But even the companies who make these ingredients often don’t know which farms their products came from, much less the footprint from those farms. So how can they, and by extension, we, make better choices? There are choices I can make, of course — perhaps substituting a (typically) higher-impact ingredient with a (typically) lower impact ingredient and sending a market signal that environmental performance is important to me. I can also make sure I’m not wasting ingredients or the food I make, so I don’t drive needless resource use. But these aren't solving the core issue: that in producing all foods, we must use dramatically fewer resources — and quickly.
In the end, I figured my best bet was to raise the issue for lots of smart, motivated people (that’s you, readers!) so we can come up with solutions together at scale. First nerd to crack the code gets a free slice of pie.
