Fermi estimates

"It is better to be roughly right than precisely wrong." — John Maynard Keynes

Last week I found myself in an argument about climate change with a friend who insisted we couldn't possibly know how much human activity contributes to global warming. When I mentioned various scientific models, he dismissed them as "just guesses." This got me thinking about the strange relationship we have with estimation and uncertainty. Many people seem to believe that if we can't know something precisely, we can't know it at all. This is a dangerous fallacy. In reality, there's a vast and useful territory between complete ignorance and perfect knowledge. Enter Fermi estimates.

What are Fermi estimates?

Fermi estimates (named after physicist Enrico Fermi) are rough calculations made with limited information to arrive at reasonable order-of-magnitude approximations. They're a powerful cognitive tool that allows us to navigate uncertainty and make better decisions even when precise data is unavailable.

Fermi was famous for his ability to make good approximate calculations with little or no actual data. Perhaps his most famous demonstration came at the Trinity test in 1945, when he dropped pieces of paper during the atomic blast and used their displacement to estimate the bomb's yield—a calculation he made in seconds that proved remarkably close to the official value determined much later through detailed analysis.

The core insight behind Fermi estimation is that breaking complex problems into simpler parts often reveals paths to reasonable approximations. Even when we don't know the exact answer to a big question, we often know enough about its components to triangulate a useful range.

Consider the classic Fermi problem: "How many piano tuners are in Chicago?"

Most people's immediate reaction is "How could I possibly know that?" But we can approach it step by step:

Chicago's population is roughly 3 million people
Average household size is about 2.5 people, so approximately 1.2 million households
Perhaps 1 in 20 households has a piano, giving us 60,000 pianos
Pianos might need tuning once a year on average
A piano tuner can perhaps tune 5 pianos per day, working 250 days per year = 1,250 pianos/year
Therefore, Chicago needs about 60,000 ÷ 1,250 = 48 piano tuners

Is this exact? No. But it's likely correct within an order of magnitude, which is remarkably useful given our starting point of complete ignorance.

Fermi estimates as a cognitive flashlight

I like to think of Fermi estimates as cognitive flashlights. They don't illuminate everything, but they help us avoid stumbling in complete darkness.

Consider some examples where Fermi thinking proves valuable:

Personal finance: "Can I afford this house?" becomes a calculation about income, expenses, and time horizons rather than a gut feeling.
Climate policy: "How much would it cost to replace all coal plants with nuclear?" can be roughly estimated even without detailed engineering studies.
Pandemic response: "How many hospital beds might we need?" can be approached through estimates of population, infection rates, and hospitalization percentages.

In each case, the Fermi approach doesn't give us certainty, but it moves us from complete ignorance to informed uncertainty—a far better position for decision-making.

Overcoming common biases

Fermi estimation helps counteract several cognitive biases:

Anchoring bias: By forcing us to build estimates from scratch, we avoid being unduly influenced by initial numbers we encounter.
Availability bias: The structured approach helps us avoid overweighting vivid or recent examples in our thinking.
Scope insensitivity: Breaking problems down helps us properly scale our responses to different magnitudes of problems.

These benefits extend beyond just making estimates. The Fermi approach instills a quantitative mindset that improves decision-making across domains.

Pitfalls to avoid

While powerful, Fermi estimation isn't without hazards:

False precision: Don't mistake your estimate for an exact answer. Always remember the uncertainty involved.
Overlooking crucial factors: Sometimes a single overlooked variable dominates the calculation. Always ask, "What might I be missing?"
Multiplicative errors: When multiplying several estimated quantities, errors compound exponentially. Be especially careful with long chains of multiplication.
Status quo bias: We often unconsciously bias our estimates toward familiar values or outcomes that seem "normal" based on our experience.

Practical applications for everyday rationality

You don't need to be estimating nuclear yields to benefit from Fermi thinking. Consider these everyday applications:

Time management: "How long will this project take?" breaks down into component tasks and reasonable time estimates.
Nutrition: "How many calories am I consuming?" can be roughly estimated without detailed tracking.
Environmental impact: "How much carbon do my actions generate?" becomes more tractable through decomposition.

I find Fermi estimation particularly valuable when evaluating claims in news and social media. When someone claims a policy will cost "billions" or save "millions of lives," a quick Fermi calculation often reveals whether such claims are plausible or wildly exaggerated.

The courage to be approximately right

There's a kind of intellectual courage in making Fermi estimates—you're explicitly showing your work and opening yourself to correction. This vulnerability is actually a strength; it allows your thinking to improve through feedback.

Consider the alternative: making no estimate at all, or hiding behind vague qualitative statements. Neither approach allows for meaningful improvement or useful decision-making.

As Eliezer Yudkowsky noted: "If you're so afraid of being wrong that you won't make a guess at all... you've already made a mistake more serious than being off by a factor of ten."

How to improve your Fermi estimation skills

Like any cognitive skill, Fermi estimation improves with practice:

Start with knowable questions: Estimate things you can later verify, like "How many books are on my shelf?" or "How many emails will I receive today?"
Use confidence intervals: Instead of single numbers, practice giving ranges. "I'm 90% confident there are between 30 and 50 books on this shelf."
Review and calibrate: Check your estimates against reality and adjust your future approach based on where and why you were off.
Practice decomposition: Take complex questions and break them down into more manageable parts, even if you don't compute the final answer.

I believe we have a kind of epistemic responsibility to make estimates rather than throwing up our hands in the face of uncertainty. This doesn't mean pretending to know what we don't know—rather, it means honestly representing our uncertainty while still providing our best guess based on available information.

When we refuse to estimate because we "don't have enough information," we're often abdicating our responsibility to think clearly under uncertainty. Perfect information is rarely available in the real world, and decisions still need to be made.

In our conversation about climate change, my friend was making a mistake common to many smart people: thinking that if we can't know something with high precision, we can't know it at all. This is the perfect being the enemy of the good. Fermi estimation reminds us that there's immense value in being approximately right. It's a practical application of Bayesian thinking—starting with what we know and updating based on new information, all while maintaining appropriate uncertainty. The next time you face a question that seems unanswerable, try breaking it down. You might be surprised how much light your cognitive flashlight can cast into the darkness of uncertainty.

Notes:

For more on Fermi's approach to estimation, see The Fermi Solution
The concept of scope insensitivity was explored in depth by Kahneman and Tversky in their work on prospect theory
Eliezer Yudkowsky has written about related concepts in "The Fallacy of Gray" on LessWrong
For practical applications of Fermi estimation in forecasting, see Philip Tetlock's work on superforecasting
The quote attributed to John Maynard Keynes is sometimes phrased differently and occasionally attributed to others, but the core insight remains valuable regardless of its provenance