A calculation to see how many cups of coffee you would need to drink in order to kill yourself.

by David Ng

By DAVID NG

I’m in full on marking mode right now, which also means my uptake of coffee has increased significantly. Consequently, I’m procrastinating and thinking about strange things – such as lethal doses – especially for things we scientists particularly indulge in (like coffee, alcohol and, yes – the free cookies at Departmental seminars). So let’s look at the fatality of coffee drinking? And yes, for the scientist, the first place to look a little deeper is the vaulted MSDS (or Material Safety Data Sheet).

For those not initiated in this lingo, MSDS are those documents that provide risk assessment and health considerations for any and all reagents, compounds, molecules, chemistries you might care to use in a laboratory setting. Of course, the most press worthy value it often provides is the “lethal dose.” Which, according to wiki is:

the median lethal dose, LD50 (abbreviation for “Lethal Dose, 50%”), LC50 (Lethal Concentration, 50%) or LCt50 (Lethal Concentration & Time) of a toxic substance or radiation is the dose required to kill half the members of a tested population.

Anyway, I thought it might be interesting to do some back of the envelope calculations to bring to you, some information on how many cups of coffee to avoid drinking, so as to not kill yourself.

However, this calculation is not as easy as it sounds, because there’s a certain amount of kinetics that needs to be taken into consideration. So, let’s first start with a few facts and figures to get the ball going.

To begin with, if we’re going to focus on coffee, probably its most potent chemical component from an oral lethal dose point of view is the caffeine. However, from a purely empirical perspective, it might actually be its water content that will kill you in the end. In other words, if you drink lots of coffee and plan on doing it to induce a fatality, it might be interesting to see what scenarios are necessary for that death to be caused by too much caffeine versus too much water.

In any event, here are the numbers to concern ourselves with:

1. Average weight of a human: From wiki:

In the United States National Health and Nutrition Examination Survey, 1999-2002, the mean weight of males between 20 and 74 years of age was 191 pounds (86.6 kg, 13 st 9 lb); the mean weight of females of the same age range was 164 pounds (74.4 kg, 11 st 10 lb)

Let’s use 80kg as an average.

2. A single cup of coffee on average contains about 250ml of water, and about 135mg of caffeine (link).

3. Lethal dose (oral intake for a rat, which has similar metabolism – although we should note, not identical metabolism) is about 192 mg/kg for caffeine and 90 mL/kg for the water.

4. However, the other part of the equation is we need to evaluate involves rates of elimination.

The half-life of caffeine–the time required for the body to eliminate one-half of the total amount of caffeine–varies widely among individuals according to such factors as age, liver function, pregnancy, some concurrent medications, and the level of enzymes in the liver needed for caffeine metabolism. In healthy adults, caffeine’s half-life is approximately 4.9 hours.

And for water – this was a little harder, because water turn over rates I found, tended to revolve around the idea of an individual not imbiding in crazy amounts of fluids. So, for the sake of our calculations, I’ll go with the following piece of information:

It’s Not How Much You Drink, It’s How Fast You Drink It! The kidneys of a healthy adult can process fifteen liters of water a day! You are unlikely to suffer from water intoxication, even if you drink a lot of water, as long as you drink over time as opposed to intaking an enormous volume at one time. As a general guideline, most adults need about three quarts of fluid each day. Much of that water comes from food, so 8-12 eight ounce glasses a day is a common recommended intake. You may need more water if the weather is very warm or very dry, if you are exercising, or if you are taking certain medications. The bottom line is this: it’s possible to drink too much water, but unless you are running a marathon or an infant, water intoxication is a very uncommon condition.

O.K. so let’s do the math.

First, an oral lethal dose for an 80kg human would extrapolate to 15,360mg of total caffeine. This technically is equivalent to the amount of caffeine absorbed from drinking 113 cups of coffee really really really quickly. However, the reality is that this figure would instead result in a fatality due to water intoxication since 113 cups is close to 30 litres of water.

So let’s try a different tact: by focusing on a safe water ingestion figure (i.e. 15 litres per day when spread reasonably). This works out to 60 cups of coffee over a full day, or approximate one cup every 24 minutes. Anyway, this is some pretty nasty math to figure out (since it’s a half life calculation with continual replenishing going on). Anyway, if you do the math, what you find is that at the end of a 24 hour period, that average body would have retained a little less than 2500mg (this is based on some very rough back of the envelope calculations). Not even close to the 15,000 or so milligrams needed to reach the lethal dose. Presumably still not a healthy thing to do, but within the context of our LD50, it sounds doable.

And the funny thing is, by the next day, that 2500mg would have been metabolized or cleared itself and only about 50mg of this is left behind. Which means that the net total amount of caffeine still in a person’s system if he or she were to continue drinking a cup of coffee every 24 minutes for a 48 hour period is 2550mg (2500mg + 50mg).

It turns out that your body is potentially quite capable of dealing with such a heavy coffee dosage, because that new 2550mg level becomes 53mg by the next 24hours – therefore three days of drinking a cup of coffee every 24 minutes will result in a net retention of 2553mg (2500mg + 53mg) and so on.

I haven’t had a chance to extrapolate this over the full year (365 days), but I’m pretty sure that even a constant coffee drinking regime (1 cup every 24minutes for the full year) wouldn’t work out to a retention amount above the lethal dose.

All to say that your body pretty much kicks ass in its remarkable metabolism. Now, it’ll be interesting to maybe dig a little deeper with regards to how messed up a person gets with that base 2500mg inside them (as I’m sure the case will be). As well, not sure what the deal would be with 15 litres of expresso shots per day – that may just about be enough!

(This is partly reprinted from a post I wrote in good old Scienceblogs.com).

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