How do you perform back-of-envelope calculations for system design?

Question

Accepted Answer

Back-of-envelope calculations help estimate system requirements and validate design decisions. They do not need to be precise, just reasonable approximations.

Start with useful reference numbers to memorize. One million seconds is roughly eleven days. One billion seconds is roughly thirty-two years. One kilobyte is one thousand bytes. One megabyte is one million bytes. One gigabyte is one billion bytes. Read latency from memory is about one hundred nanoseconds. Read from SSD is about one hundred microseconds. Read from disk is about ten milliseconds. Network round trip within a data center is about half a millisecond.

For traffic estimation, work from daily active users. If you have one hundred million daily active users and each makes ten requests per day, that is one billion requests daily. Divide by eighty-six thousand four hundred seconds per day to get roughly twelve thousand requests per second on average. Peak traffic might be three to five times average.

For storage estimation, calculate per-user or per-item storage. A tweet with two hundred characters is roughly two hundred bytes. With metadata, call it one kilobyte. Five hundred million tweets per day means five hundred terabytes daily, or one hundred eighty petabytes per year before compression or deduplication.

For bandwidth estimation, multiply request rate by average response size. Twelve thousand requests per second with ten kilobyte average responses equals one hundred twenty megabytes per second, or roughly one gigabit per second.

For database sizing, consider read-to-write ratios. Most applications are read-heavy, perhaps ten to one or one hundred to one. If you have ten thousand writes per second, you might have one hundred thousand reads per second. This informs caching strategy and replica needs.

Round numbers aggressively. Use powers of ten and simple fractions. The goal is order of magnitude accuracy. Whether the answer is eight thousand or twelve thousand usually does not change architectural decisions.

Present calculations clearly. State your assumptions explicitly. Show your work so interviewers can follow your reasoning and suggest adjustments.