Back-of-the-envelope estimation

The power of quick estimation

In system design interviews and architectural planning, you must quickly verify whether a proposed storage format, network pipe, or database tier will survive real-world scale before writing a line of code.

1. Powers of two and memory capacity

Always remember the $2^{10} \approx 10^3$ rule of thumb:

• $2^{10}$ (1,024 B): $\approx 1\text{ Thousand } (10^3) \to 1\text{ KB}$
• $2^{20}$ (1,048,576 B): $\approx 1\text{ Million } (10^6) \to 1\text{ MB}$
• $2^{30}$ (1,073,741,824 B): $\approx 1\text{ Billion } (10^9) \to 1\text{ GB}$
• $2^{40}$ (1,099,511,627,776 B): $\approx 1\text{ Trillion } (10^{12}) \to 1\text{ TB}$
• $2^{50}$ (1,125,899,906,842,624 B): $\approx 1\text{ Quadrillion } (10^{15}) \to 1\text{ PB}$

2. Time and throughput heuristics

• $1\text{ day} = 24 \times 60 \times 60 = 86,400\text{ seconds} \approx 10^5\text{ s}$ (easy mental math: divide by $10^5$, then multiply by $1.15$).
• $1\text{ million requests / day} \approx 12\text{ RPS}$
• $100\text{ million requests / day} \approx 1,200\text{ RPS}$
• $1\text{ billion requests / day} \approx 12,000\text{ RPS}$

The primer's worked solutions use a handy conversion for monthly volumes: a month has about $2.5$ million seconds, so $1$ request per second is about $2.5$ million requests a month, and $400$ requests per second is about $1$ billion a month.

3. Latency numbers every programmer should know

These figures were compiled by Jeff Dean and Peter Norvig and date from around 2012. Hardware has moved on since, so use them for orders of magnitude, not exact values. They span more than eight orders of magnitude (from $0.5\text{ ns}$ to $150\text{ ms}$ is a factor of $3 \times 10^{8}$). If an L1 cache reference were scaled up to 1 second:

• L1 cache reference ($0.5\text{ ns}$) $\to 1\text{ second}$
• Branch mispredict ($5\text{ ns}$) $\to 10\text{ seconds}$
• L2 cache reference ($7\text{ ns}$) $\to 14\text{ seconds}$
• Mutex lock/unlock ($25\text{ ns}$) $\to 50\text{ seconds}$
• Main memory reference ($100\text{ ns}$) $\to 3.3\text{ minutes}$
• Read 4 KB randomly from SSD ($150\,\mu\text{s}$) $\to 3.5\text{ days}$
• Read 1 MB sequentially from memory ($250\,\mu\text{s}$) $\to 5.8\text{ days}$
• Round trip within the same datacenter ($500\,\mu\text{s}$) $\to 11.6\text{ days}$
• Hard disk seek ($10\text{ ms}$) $\to 7.6\text{ months}$
• Send a packet California $\to$ Netherlands $\to$ California ($150\text{ ms}$) $\to 9.5\text{ years}$