# Back-of-the-envelope math

- Source: https://intervueclub.com/course/back-of-the-envelope-math
- Author: IntervueClub
- Part of: HLD 101 (https://intervueclub.com/course), Thinking in systems
- Last updated: 2026-09-19

How to turn a vague system design prompt into requests per second, storage per day and a machine count — the rounding conventions, the peak multiplier, the read/write ratio, and how to present the arithmetic out loud without losing the room.

## The point is not the number

Nobody checks your arithmetic. What the estimate actually does is force every vague word in the prompt to become a number, and it is the numbers that make the rest of the design decidable. "A lot of users" does not tell you whether the data fits on one machine. "4TB a year" does.

The estimate is also how you avoid the most common failure in a system design interview: building an architecture that is wildly over- or under-sized for the problem, and having no way to notice.

So the goal is a handful of numbers, derived out loud, in about three minutes:

- **Write QPS** and **read QPS**, at peak
- **Storage per day** and per year
- Roughly how many machines that implies

*The rest of this concept is free to read after signing in: https://intervueclub.com/course/back-of-the-envelope-math*