Back-of-the-envelope estimation is the art of getting a good-enough answer fast — no spreadsheet, no simulator, just a few key numbers and a chain of multiplications. It tells you whether a design will work before you build it, exposes bottlenecks early, and sharpens your intuition for what matters at scale. Each exercise below gives you a real-world scenario to estimate, hints if you're stuck, and a full breakdown once you submit.