Before any estimation: what does a million words actually feel like?
At a comfortable adult reading pace of around 250 words per minute, reading the entire Harry Potter series back-to-back would take about 72 hours of continuous reading. If you read for an hour a day, that's three months. For reference, the series is longer than War and Peace (about 580,000 words) and in roughly the same range as the complete Lord of the Rings including appendices (about 1.1 million words).
So we're looking for a number somewhere around a million. Let's see if we can get there from what we already know.
Step 1: Number of Books
Seven. This one is exact.
Step 2: Average Pages Per Book
This is where the estimation earns its value. The books vary considerably:
- Philosopher's Stone (book 1): thin — around 220 pages
- Order of the Phoenix (book 5): very thick — around 800 pages
- The middle books fall somewhere between
A reasonable average across all seven is around 450 pages per book. You don't need it to be precise — you need it to be in the right neighbourhood.
One thing worth noting: the series almost triples in length from first to last. Book 1 is about 77,000 words; book 5 is about 257,000. That's a massive variation, which is exactly why averaging is a useful technique rather than a limitation — it's designed to handle this kind of spread.
Step 3: Words Per Page
A standard novel page has roughly:
- 30 lines of text
- about 10 words per line
That gives approximately 300 words per page. You can verify this on any novel sitting near you — the number usually lands between 250 and 350 depending on font size and margins.
Step 4: Words Per Book
450 pages × 300 words = 135,000 words per book
Step 5: Total Across the Series
135,000 × 7 = 945,000 words
The Real Number
The actual total word count of the Harry Potter series is approximately 1,084,000 words.
Our estimate of 945,000 is within about 13% of the real figure. For a calculation using nothing but rough averages and publicly known facts, that's a very strong result.
Fermi estimate
~945,000 words
True answer
~1,084,000 words
Within 13% of the true answer using nothing but rough averages.
Why Averaging Works Even When the Range Is Wide
It might seem like averaging over books that vary from 77,000 to 257,000 words would produce a useless result. But the estimation works because the errors go in different directions. The shorter books pull the average down; the longer books pull it up. The product of several rough estimates, when the errors aren't all skewing the same way, tends to land near the true mean.
This is one of the core insights behind Fermi estimation: you don't need each assumption to be accurate. You need the assumptions to be reasonable, and for your errors to be relatively balanced. When those conditions hold, the final product is often closer than you'd expect.
How to Use This in a Game Context
On Magnitudle, this question would ask you to estimate the total word count of the Harry Potter series. The order-of-magnitude scoring means that landing anywhere from around 500,000 to 2 million words would earn a high score — you've correctly identified that the answer is "about a million words." Getting there by working through pages and words per page, rather than guessing randomly, is exactly the kind of reasoning the game rewards.
For a similar exercise in a completely different domain, see How Many Oscar Nominations Have Ever Been Given Out? — the same decomposition approach, applied to a question about a century-long institution.