How much beer would a bar need to get the entire adult population of Britain drunk?
Here’s a fun mathematical analysis for you!
If you’ve ever spoken to anyone that has worked in a pub, I am fairly confident you have been told numerous times about how unique and eye-opening the experience can be. Bonus points if it’s somewhere that is pretty much always busy, no matter the time of day.
As a lover of mathematics and statistical modelling, this very interesting thought popped in to my head. How many pints would a bar need to pour, per hour, to get, and keep, the entire adult population of Britain drunk?
Let’s break it down piece by piece, and see where our answer will take us!
Let me throw in a little disclaimer here saying that I don’t think anyone should be getting to this point.
It’s bad enough having to clean up someone’s uhm … mess.
This is purely hypothetical. And if everyone in Britain reads this, please don’t all come to my place of work at once. Thanks!
Okay. let’s lay down some guidelines for our calculation.
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Firstly, we will be including only Britain’s adult population. Sorry kids, but you’re not jumping over our fence.
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We’ll also assume that each pint is drunk instantaneously. This one’s for the older crew. No sipping your Guinness for two hours.
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To keep things simple, we will be giving everyone beer. We’ll calculate values for both Bud Light (at 3.5%) and Leffe (strongest at 6%).
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We will take averages for things that vary across different people. Alcohol metabolism is affected by things like body weight, ethnicity, even age. So we will try and take uniform values for those measurements to represent your average person.
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Oh and just to clarify, we’re not using any AI generated content as sources for statistics, or otherwise.
With that out of the way - let’s begin!
So how many adults are there in Britain?
According to Google’s own collected data, there were 68.3 \text{ million} people (including under-18s) in Britain in 2023. Worldometer gives us a slightly higher value of 69.4 \text{ million}.
Let’s assume this is 70 \text{ million} for our calculation. This is a slight overestimate from our data, but the population has likely grown anyway from time of recording so it’s a reasonable figure.
Our first step is to purge the youth. It was actually quite difficult to find a definitive source for the number of children in the UK, so we will take government data from the 2021 Census as our rough source.
According to the UK Government, the total number of children in Britain for each age group in 2021 was…
3\space 323\space 055 children (0-4 yrs)
3\space 524\space 635 children (5-9 yrs)
3\space 596\space 015 children (10-14 yrs)
2\space 039\space 535 children (14-17 yrs)
If we add these values up, we get a total of \boxed{12 \space 392 \space 240} children (0-17 yrs).
We can subtract this from our original value of 70 million to work out just the number of adults in the UK.
If we subtract this from our figure of 70 \space 000 \space 000, we get a total of \boxed{57 \space 607 \space 760} adults in this country.
That’s a lot of people!
Yep! That’s our first step complete.
Now we’ve got our people statistic, it’s time to get a little more mathematical. Let’s take a look at alcohol metabolism in humans, and state the legal definitions of intoxication.
Intoxication depends on a measure called the blood alcohol concentration, or BAC. This essentially tells us how much alcohol is in a person’s blood at any time. The UK defines the legal drink-driving limit at 80mg of alcohol per 100ml of blood, or 0.08\%.
Now interestingly, the amount that this value increases per unit of alcohol consumed, is dependent on a person’s weight. To account for this difference, we will take average values. The average weight for males in the UK is 85.8 kg, while the average weight for females is 72.8 kg.
Assuming there are the same number of males and females in Britain, taking the mean value for both of these statistics gives us a value of 79.3 kg.
This is an average of how much an adult in Britain weighs.
So how do we work out someone’s blood alcohol concentration, if we know their weight?
This is where it gets interesting.
The Widmark formula allows us to calculate this value. It is as follows:
The 0.62 value is an average of the ‘metabolism constant’ for alcohol across biological sexes. This is actually 0.55 for women and 0.68 for men. We are taking an average of these to get 0.615 \approx 0.62.
Cool! So how much does a single pint affect this value?
Let’s work it out numerically!
How many millilitres of pure alcohol are in a pint of Bud Light? A pint (~568ml) of Bud Light in the UK is sold at an ABV of 3.5%.
But what does this actually mean? Essentially, out of the 568 millilitres in the pint, around 3.5% will be pure alcohol.
3.5 \% of 568 ml gives us around 19.88 ml of alcohol per pint.
So Bud Light has about 20 millilitres of pure alcohol per pint. But our formula wants grams of alcohol, not millilitres!
No problem! Pure alcohol weighs about 0.789 grams per millilitre.
19.88 millilitres of alcohol per pint \times 0.789 grams per millilitre gives us around 15.69 grams of alcohol, per pint.
We can use this to finish our calculation. Let’s plug in our grams value (15.69) and our average body weight in grams (79300) into the BAC formula above.
So we get a value of around \boxed{0.032\%}.
This is how much a person’s blood alcohol concentration will increase for each pint of Bud Light consumed.
Right. So what’s the next step?
Now we know how much our drunkenness value per person is increasing for each pint, we can figure out how many pints it will take for them to initially get over the threshold of 0.08\%, which is our legal definition of “drunk”.
This is not a hard calculation, though! If we see how many times 0.0319\% goes into 0.08\%, we get a value of 0.08 \div 0.0319 \approx \boxed{2.51}.
In other words, a person would need to consume just over two and a half pints of Bud Light - in one go - in order to legally be considered “drunk”.
Based on this data, we would need each person to consume 2.5 pints at the beginning of the experiment in order to initially get drunk. This will put us at exactly 0.08\%. However, the rate will start to drop immediately.
We’re making progress! What do we need to calculate now?
Hold up - not so fast. Let’s look at another alcohol metabolism statistic first!
- Blood alcohol level decreases at a rate of about 0.015\% per hour.
- So if we start at 0.08\%, our level will have dropped to about 0.065\% after one hour of consuming our last drink.
We need to consume a specific amount of beer per hour in order to keep our number above 0.08\%.
We already know that 1 pint of Bud Light raises our BAC by 0.031\%. If our BAC is dropping by 0.015\% every hour, how much Bud Light will we need to drink each hour to re-raise our level back to what it was before?
By dividing the values, we can get the fractional portion of a single pint that pushes our BAC up by 0.015, negating the effect. This gives us 0.015 \div 0.031, which is around 0.48 pints per person per hour.
Put simply, around half (48\%) of a pint of Bud Light consumed per hour will counter the body’s natural metabolism of alcohol, and allow us to continue enjoying being drunk. This is also roughly equivalent to 2.08 hours, between each full pint needed per person, to remain drunk.
Remember how we said the rate starts to drop immediately after our first 2.5 pints? We want to stay above 0.08\%, not dip below. So we actually need to consume this additional half pint at the beginning of our experiment, too. Every person needs to drink 3 pints in the first hour, and then an additional half pint every hour to stay above our BAC threshold.
Our alcohol calculations are complete! Now we just need to scale it up to … well, nearly sixty million people.
Unfortunately so. Thankfully for us as mathematicians (not for the workers, though), this is quite an easy calculation. With 57 \space 607 \space 760 people to serve, we would need to initially pour about 57 \space 607 \space 760 \space \times 3 pints in order to get the ball rolling.
And that is about 172 \space 823 \space 280 pints just at the beginning.
To keep everyone drunk? Every hour, we would need to pour an extra 28 \space 803 \space 880 pints. That works out at around 48000 pints per minute, or 8000 pints per second. All that just to keep Britain’s adult population at a stable level of drunkenness. It’s safe to say that we may be dealing with some clean-up, and it’s going to be quite long!
I hope you enjoyed this deep dive into some data! I’m going to update this thread with some appendix information when I get a chance. We’ll also add in the calculation for a stronger beer - obviously we would need less of them.
I thoroughly enjoyed researching this. Do let me know if you have more burning questions you want me to work out!
- Saen, Collectives Forum Developer