One of the frothiest stories to bubble forth from the shit-tastic Rio Olympics this week was the sudden, inexplicable greening of not one, but two Olympic pools.

Actually, there is an explanation: algae. Lots of them. Algae thrive in warm, still water, especially when there’s plenty of sunlight to break down pesky, antimicrobial compounds like chlorine. Alternately, the viridescent hue might have been caused by a simple chemical imbalance. But you know what every closeted 12 year old on the internet assumed it was?

Piss.

As reputable outlets like The Guardian and New Scientist felt compelled to point out, the greening of the pools was not the result of a mass urination perpetrated by Olympic protestors or, I dunno, drunk gymnasts. But as Twitter polls this week indicate, a sizable portion of the public remains unconvinced:

As confusion, fear, and outrage swept the civilized world, my colleagues and I started to wonder: how much pee would it actually take to turn an Olympic pool green? To find out, I spent yesterday afternoon researching the human bladder, color theory, and 10th grade algebra.

The basic premise of my investigation was simple. As every first grader knows, blue + yellow = green. But when you’re trying to figure out how much yellow is needed to get from a particular shade of blue to a particular shade of green, things can get hairy fast. I soon realized I was going to need to make some assumptions.

The first thing I needed was a representative image of Rio’s Olympic pools before and after the Incident. I chose the image below, because it’s relatively well lit, shows us a contaminated and uncontaminated pool in the same frame, and doesn’t have any obvious Instagram filters.

### Assumption #1

This is a representative image of the color of Olympic pools in Rio before (left) and after (right) the alleged mass urination. Note that the pool on the left is a diving pool while the pool on the right is a swimming pool, which might affect the color balance somewhat owing to different depths. For simplicity, we are assuming that the color of the two pools should be one and the same.

Armed with a sample, I downloaded the iOS app “True Color,” which allows one to determine the precise, mathematical proportions of red, blue, yellow, and white comprising a user-selected region of an image. At just \$2.99, it was a steal.

After randomly selecting a handful of spots in both pools and averaging the results, I arrived at some rough estimates of their color compositions:

Pool Color Before Incident: 28% Yellow, (72% Blue + White)

Pool Color After Incident: 31% Yellow, (69% Blue + White)

In essence, the diving pool became 3% “more yellow” following the Incident. Now before we figure out how much urine that equates to, we need to make another assumption.

### Assumption #2

Human piss is pure, unadulterated yellow.

It looks like this.

This is arguably a much worse assumption than #1, for reasons I’ll discuss momentarily if you haven’t already guessed. But for now, let’s roll with it, because it simplifies the math. Standard Human Urine™ is yellow like a sun-kissed sunflower.

Finally, we must make one last, very important assumption.

### Assumption #3

For every bladderful of vivd yellow excrement a human empties into the pool, he or she kindly removes a corresponding volume of pool water. In other words, the total volume of the pool does not change. We can safely assume this is correct, because the pool on the right in our representative image is not overflowing with piss-water.

Whew! Now, we can set up a simple system of equations to solve for the amount of urine needed to turn an Olympic pool green.

Given:

Pre-urination pool (PUP) = 28% Yellow

Post-urination pool (POUP) = 31% Yellow

Estimated volume of an Olympic diving pool = 1886 cubic meters = 1,886,000 Liters (based on an estimated average depth of 4.5 m, FINA), and estimated horizontal dimensions of 18.3 × 22.9 meters (iSport Diving)

Volume of “yellow” in the pool after urine is added = 1,886,000 × 0.31 = 584,660 Liters

x = amount of water left in the PUP after draining

y = amount of urine added to the POUP

We can set up two equations:

x + y = 1,886,000

0.28(x) + y = 584,660

Now, all we need to do is rearrange terms and solve the system for y:

y = 584,660 - 0.28(x)

x+ (584,660 - 0.28(x)) = 1,886,000

0.72x = 1,301,340

x = 1,807,417

y = 1,886,000 - 1,807,417 = 78,583

SOLUTION: It will take a full 78,583 Liters of Standard Human Urine™ to turn that sucker green.

That’s a lot of wizz!

According to Continence.org, a healthy adult bladder can hold up to 600 milliliters of urine. Assuming the Incident was perpetrated by a group of standard, full-bladdered adults, and assuming nobody peed twice, you’d need:

78,583 /0.6L = 130,972 full human bladders to turn an Olympic pool green

That is an awful lot of desperate bathroom-goers—it is close to half the population of Iceland. The mind boggles to imagine that many humans attempting to urinate in a pool over the course of a single night without attracting notice.