You probably think you know what a big number looks like. Maybe it’s a billion. That’s a nine-zero monster that describes the world population several times over. Or a trillion—the kind of number usually reserved for national debts and the market caps of companies like Apple or Microsoft. But honestly? Those are tiny. In the grand playground of mathematics, a trillion is barely a rounding error. Once you move past the stuff we use to count money, the names of really big numbers start getting weird, fast.
Most of us stop counting at a trillion. Why wouldn't we? It’s a massive scale. But the naming system, specifically the "Standard Dictionary" system used in the US and UK, keeps going until your brain basically melts.
🔗 Read more: Why You Still Can't Download Power BI Mac and How to Actually Use It
The Confusion Between Billions and Milliards
Here’s the first thing people mess up. Depending on where you grew up, a "billion" might not be what you think it is. In the United States, we use the Short Scale. Every new name is 1,000 times larger than the last. So, a million times a thousand is a billion.
But if you’re in parts of Europe or talking to someone using the Long Scale, a billion is actually a million million. That’s $10^{12}$ instead of $10^{9}$. In that system, the number $10^{9}$ is called a "milliard." It’s confusing. It’s messy. Most of the English-speaking world officially switched to the short scale decades ago—the UK made the jump in 1974—but the legacy of the long scale still haunts old textbooks and international finance.
If you want to sound like an expert, remember that the "bi" in billion refers to the number of groups of six zeros in the long scale ($10^{6 \times 2}$), whereas in the short scale, it's just... well, it's just the next step up.
Climbing the Ladder to Infinity (Sorta)
Let’s look at the names you’ve probably never heard of. After a trillion comes a quadrillion. That’s 15 zeros. It’s a number so large that if you had a quadrillion pennies, you could cover the entire land surface of the Earth in a layer nearly half an inch thick.
Then you hit the quintillion ($10^{18}$), the sextillion ($10^{21}$), and the septillion ($10^{24}$).
By the time you reach a yottillion, you’re dealing with numbers that describe the total number of atoms in a medium-sized room. But mathematicians didn't stop there. They kept naming things. There’s the vigintillion, which is a 1 followed by 63 zeros. If you’re writing that out, you’ll be there for a minute.
Why do we name them?
It feels like a hobby for people who love Latin roots. Honestly, it kind of is. We don't "need" a name for $10^{303}$ (a centillion), but we have one anyway. In physics, scientific notation—like $10^{50}$—is way more practical. Using names of really big numbers is more about the poetry of scale than the utility of math.
The Goose Egg: The Story of the Googol
If you’ve ever used a search engine, you’ve interacted with a misspelling of a very famous big number. In 1920, mathematician Edward Kasner asked his nine-year-old nephew, Milton Sirotta, to come up with a name for a 1 followed by 100 zeros. Milton said "googol."
It stuck.
A googol is massive. It is larger than the number of elementary particles in the observable universe, which is estimated to be around $10^{80}$. Think about that. You can’t even find enough "stuff" in the known universe to count up to a googol.
But then there’s the Googolplex.
A googolplex is 1 followed by a googol of zeros. You literally cannot write this number down. Not because you don’t have enough paper, but because there isn’t enough space in the universe to hold the ink. If you tried to write a googolplex in standard form (1,000...) and you wrote each zero on a single atom, you’d run out of atoms long before you finished the number.
When Numbers Get Truly Scary: Graham's Number
For a long time, Graham's Number held the Guinness World Record for the largest number ever used in a serious mathematical proof. It was used by Ronald Graham in the field of Ramsey Theory.
You can't use "zeros" to describe Graham's Number.
The number is so large that the observable universe is far too small to contain a digital representation of it. Even if you turned every bit of matter into a hard drive, you couldn't store it. If your brain actually tried to hold all the digits of Graham's Number at once, your head would literally collapse into a black hole because the information density would exceed the Schwarzschild radius of your skull.
That’s not a joke. That’s physics.
To write it, we have to use something called Knuth's up-arrow notation.
- $3 \uparrow 3$ is 27.
- $3 \uparrow \uparrow 3$ is $3^{3^3}$, which is 7,625,597,484,987.
- $3 \uparrow \uparrow \uparrow 3$ is a tower of powers of 3 that is 7.6 trillion layers deep.
Graham's Number is way, way bigger than that. It’s built in 64 layers, where each layer determines the number of arrows in the next layer.
TREE(3) and the End of Logic
Just when you think Graham's Number is the king of the hill, something like TREE(3) comes along.
TREE(3) comes from a branch of mathematics called graph theory. It involves a game with colored seeds and trees. While Graham's Number is unfathomably large, it is essentially zero compared to TREE(3).
If you tried to imagine the difference between them, you’d fail. Humans aren't wired for this. Our brains evolved to count things like "three mammoths" or "twenty berries." Once we get into the realm of fast-growing hierarchies, the names of really big numbers become abstract symbols for "more than everything."
Why This Matters in 2026
We live in an era of big data. We’re constantly talking about "exabytes" of data or "petaflops" of computing power. Understanding the scale of these names helps us visualize the complexity of the world we’re building.
When a tech company says they are training an AI on trillions of parameters, they are using the lower rungs of this infinite ladder. As we move toward quantum computing and more complex simulations of the universe, we’re going to need these names more than ever.
Actionable Insights for Navigating Large Scales
If you want to apply this knowledge or dive deeper into the world of "googology" (the actual term for the study of large numbers), here is how to handle the scale:
- Audit your scale: When reading international news, check if they are using the short scale or the long scale. A "billion" dollar investment in a 1950s British document means something very different than it does today.
- Use Scientific Notation: For anything larger than a trillion ($10^{12}$), stop using names. It leads to errors. Use $10^n$. It’s cleaner and prevents you from confusing a quadrillion with a quintillion.
- Visualize by Comparison: Don't just look at the zeros. One million seconds is about 11 days. One billion seconds is about 31 years. One trillion seconds is about 31,700 years. That jump—from a human career to the existence of civilization—is the best way to feel the weight of these names.
- Explore the Fast-Growing Hierarchy: If you’re a math nerd, look up the Ackermann function. It’s a great introduction to how numbers can grow faster than our ability to name them.
The universe is mostly empty space and massive numbers. Learning the names of really big numbers is just our way of trying to put a fence around the infinite. It doesn't always work, but it’s a fascinating way to see just how small our everyday world really is.