You've probably seen the word. It looks like a typo for the world's biggest search engine, but it’s actually the mathematical inspiration behind it. A googol is a specific number. Specifically, it is a 1 followed by 100 zeros.
It sounds manageable, right?
We deal with big numbers constantly. National debts are in the trillions. Global populations are in the billions. We’ve become desensitized to zeros. But here’s the thing: a googol isn’t just "big." It’s larger than the number of atoms in the observable universe. When you start talking about how big is a googol, you aren't just doing math; you're pushing the physical limits of reality itself.
The accidental name of a giant
Back in 1920, an American mathematician named Edward Kasner was trying to find a way to get kids interested in the concept of infinite vs. finite numbers. He asked his nine-year-old nephew, Milton Sirotta, to come up with a name for a 1 followed by 100 zeros. Milton blurted out "googol."
Kasner liked it. It sounded silly. It sounded approachable. But the math behind it is anything but childish.
The actual notation for a googol is $10^{100}$. In a world where $10^6$ is a million and $10^9$ is a billion, $10^{100}$ feels like it should just be "a bit more." It isn't. Mathematics is exponential, not linear. Every time you add a single zero to the end of a number, you aren't just adding a digit; you are multiplying the entire previous value by ten.
Do that 100 times.
Putting the scale into perspective
To really understand how big is a googol, we have to look at the universe. If you took every single atom in every star, every planet, and every grain of cosmic dust in the observable universe, you’d have a lot of matter. Astronomers estimate there are roughly $10^{80}$ atoms in the known universe.
Think about that.
If you counted every single atom, you would still be 20 orders of magnitude short of reaching a single googol. To reach a googol, you would need 100,000,000,000,000,000,000 (that’s 100 quintillion) copies of our entire universe, all stuffed into a bag, just to equal the number of atoms matching a googol.
It’s a number that exists almost entirely in the realm of the theoretical because there is nothing in our physical reality to fill that volume. You can't have a googol of apples. There isn't enough space in the fabric of spacetime to fit them.
Why the name Google is actually a misspelling
Larry Page and Sergey Brin didn't just pick a quirky name out of a hat. They wanted to signify that their search engine was designed to organize an "infinite" amount of information. They settled on "Googol."
However, when they went to check if the domain was available, a student named Sean Anderson searched for "https://www.google.com/search?q=google.com" by mistake. Page liked the misspelling better. It was shorter. It was punchier.
But the original intent remains: a googol represents a scale of data that is basically unfathomable. Even today, with the massive indexing power of modern AI and server farms, the total number of web pages on the internet doesn't even come close to $10^{15}$, let alone $10^{100}$. We are barely scratching the surface of Milton Sirotta’s number.
The Googolplex: When a googol isn't enough
If you think a googol is a headache, let's talk about the googolplex.
A googolplex is a 1 followed by a googol of zeros.
$$10^{\text{googol}} \text{ or } 10^{(10^{100})}$$
You literally cannot write this number down. Not because it would take a long time—though it would—but because there isn't enough matter in the universe to act as ink and paper. If you tried to write a googolplex on small slips of paper, you would run out of atoms in the universe before you were even 1% of the way through the zeros.
Even if you could write zeros on individual atoms, you'd still run out of atoms.
Carl Sagan once pointed out that a googolplex is so large that if you filled the entire volume of the observable universe with fine dust particles, the number of ways you could arrange those particles is still smaller than a googolplex. It is a number that defies physical representation.
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Real-world math where these numbers actually appear
Does anyone actually use these numbers? Sorta.
In thermodynamics and quantum mechanics, we deal with "combinatorial explosions." If you have a deck of 52 cards, the number of ways you can shuffle them is $52!$ (52 factorial). That’s roughly $8 \times 10^{67}$. That's getting close to our atom-count from earlier.
Now, imagine a slightly more complex system. Maybe a computer password or a sequence of DNA. The number of possible states a system can be in often surpasses a googol very quickly.
Theoretical physicists like Roger Penrose use massive numbers when calculating the "entropy" of the universe at the Big Bang. When you start calculating the probability of a "Boltzmann Brain" (a brain spontaneously forming in a vacuum due to random fluctuations), the numbers involved make a googol look like pocket change.
The heat death of the universe
Perhaps the most haunting use of these scales is in the timeline of the universe's end.
In about $10^{100}$ years, physicists predict the "Heat Death" of the universe. By this point, even the most massive black holes will have evaporated via Hawking Radiation. The universe will be a cold, dark, empty void where no energy can be exchanged.
Basically, the life of our universe—from the Big Bang until the very last black hole disappears—is roughly a googol years long.
It is the ultimate timer.
Beyond the Googol: Graham’s Number
Honesty time: as big as a googol is, it’s basically zero compared to Graham's Number.
In the world of "serious" mathematics, Graham's Number is so large that it cannot be expressed with powers of ten. Mathematicians have to use something called "Knuth’s up-arrow notation" just to describe how to calculate it. If your brain actually tried to hold all the digits of Graham’s Number at once, your head would technically collapse into a black hole because the information density would exceed the Schwarzschild radius of your skull.
Seriously.
How to use this knowledge
Knowing how big is a googol won't help you balance your checkbook. But it does change how you view the world. It reminds us that our human experience is tucked into a very tiny, very specific slice of reality.
If you want to play with these concepts further, here are a few ways to wrap your head around the scale:
- Try the Rice Grain Visualization: Imagine a chessboard. Put one grain of rice on the first square, two on the second, four on the third. By the 64th square, you have $1.8 \times 10^{19}$ grains. That’s enough to cover the entire country of India in a layer of rice meters deep. Now realize you are still 80 zeros away from a googol.
- Check out the "Powers of Ten" video: The classic 1977 film by Charles and Ray Eames is still the best visual guide to the scale of the universe.
- Look up the "Wait But Why" blog on big numbers: Tim Urban breaks down these scales with stick figures and humor that makes the existential dread much more palatable.
The next time you type a query into Google, remember the zeros. You're interacting with a brand named after a number that the universe isn't even big enough to hold.
Next Steps for Exploration:
To deepen your understanding of mathematical scales, research Hawking Radiation to understand why $10^{100}$ years is the "deadline" for the universe. Alternatively, look into Shannon's Number, which calculates the number of possible chess games—it's roughly $10^{120}$, making a googol look tiny in the world of board games.