Verification of the accuracy of a Fermi estimate

• By Olivier Diotte
• Published Sep. 29, 2016
• (Updated Oct. 10, 2016)

In a previous post, I detailed my Fermi estimation for vegetarianism.

How far from the truth was my estimate?

Well, going by Google's nutritional fact sheets, romaine lettuce is 108 calories/head while ground beef is 332 calories/100g.

Searching for the grazing space needed for cows gives us this link from the US Natural Resources Conservation Service which tells us that the rule-of-thumb is 1.5 to 2 acres per cow calf pair and their own calculation comes up to about 1.8 acre/(cow*year). So, if anything, we're overestimating the energy efficiency of meat-eating.

We had estimated 10 meals/3 lb of ground beef. human metabolism requires about 2500 calories [1] . So we get 3 lb / 2.2 lb/kg * 332 calories/0.1 kg / (2500 calories/2 [2] meals) ≈ 5.4 meals for each 3 lb of ground beef (which seems reasonable given we're neglecting breakfast as well as the corn and potatoes in a pâté chinois).

We estimated about 700 lbs of meat from a single cow. Estimates vary on what a cow weighs, but the NRCS link above puts it at 1200 lbs, this one gives a Holstein's weight (the breed I'm familiar with) as between 1000 to 1800 lbs, this one puts it at 1000 lbs and gives us an estimate of 430 lbs of retail meat from that. From that, they exclude things like heart and probably tongue too, but I doubt these account for much. Adjusting for a maximum weight Holstein and padding some, we get somewhere close to the 700 lbs estimated.

As for the lettuce, we had estimated 9 times as much food at a rate of 30 lettuces heads/day. 108 calories/head * 30 heads/day = 3240 calories/day, much more than both what's needed and what we get from the meat equivalent. I couldn't directly confirm the size of a lettuce head or how much space is needed to grow them, but this link has pictures which show lettuce heads being grown very close to one another as well as one in a person's hand and a visual estimation seems to agree with the estimation.

One last datapoint that could tip the scale would be things like water usage or the amount of fertilizer used. Taking a quick look around, it looks like vegetables win the water contest hands down again.