The superpower
Enrico Fermi could estimate absurd questions ("How many piano tuners in Chicago?") by breaking them into guessable chunks. Engineers do this constantly: "Will this bolt hold?" "How much will this cost?" "Is this idea even in the right ballpark?"
The method
- Decompose — Break the question into smaller questions
- Estimate each piece — Round aggressively; exact is fake precision
- Combine — Multiply/divide through
- Sanity check — Does the answer pass the smell test?
Example: How much does your backpack weigh in newtons?
- Guess mass: ~8 kg (textbooks, water bottle, chaos)
- Weight = mass × gravity ≈ 8 × 10 = 80 N
- Sanity: That's about the force to hold a heavy grocery bag. Feels right.
Rules of thumb
- Gravity: 10 m/s² (close enough for Earth)
- Your mass in kg × 10 ≈ your weight in newtons
- A paperclip ≈ 1 g. A textbook ≈ 1–2 kg.
- Being within 2× of the real answer on a first estimate = you're thinking like an engineer
Shop rule: Wrong by 10× means you missed a step, not that you're bad at math. Find the step.