Back-of-the-envelope estimation for system design interviews

Back-of-the-envelope estimation for system design interviews Most people don't fail capacity math because the arithmetic is hard. They fail because they do it silently, produce a number they can't defend, and then never use it again for the rest of the interview. The math itself is trivial. The method is what's worth learning. Why interviewers ask Capacity estimation isn't a numeracy test. It's checking two things: Can you tell whether a design is physically possible before you commit to it? Do you know which constraint actually binds — storage, read throughput, write throughput, or bandwidth? A candidate who estimates 30,000 reads/sec and 200 writes/sec has learned something that changes the design. A candidate who computes petabytes of storage and then never mentions it again has just performed arithmetic. Round aggressively Precision is a trap. You're not producing a capacity plan; you're finding the order of magnitude. The single most useful substitution: 1 day = 86,400 seconds ≈ 10^5 seconds That's a 16% error and it makes every subsequent division doable in your head. Nobody will challenge it. Everyone will notice if you spend forty seconds long-dividing by 86,400. A few more worth having ready: 1 million requests/day ≈ 12/sec — round to 10 1 KB × 1 million = 1 GB 1 KB × 1 billion = 1 TB Peak traffic ≈ 2–3× average Replicated storage ≈ 3× raw ## Work in one direction Users → requests → QPS → storage → bandwidth. Don't jump around. Say each assumption out loud and label it as an assumption, so the interviewer can correct you early rather than watch you build on sand. A worked example Say we're designing a social feed. Given: 100M daily active users. Assumptions (stated, not smuggled in): Each user posts 0.2 times/day Each user reads their feed 10 times/day A post averages 1 KB including metadata A feed page shows 20 posts Writes 100M × 0.2 = 20M posts/day 20M / 10^5 = 200 writes/sec Peak (3×) = 600 writes/sec Reads 100M × 10 = 1B feed loads/day 1B / 10^5 = 10,0