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Module 1 · Foundations & MethodDay 00530 min

Back-of-Envelope Estimation

How to ballpark scale in 60 seconds and avoid being wrong by 100x.

Day 005

Back-of-Envelope Estimation

Users
client
QPS
service
Storage
datastore
Bandwidth
edge
Signal path
Estimation funnel: anchor users, derive QPS, th...
Users
client
flow
QPS
service
QPS
service
flow
Storage
datastore
QPS
service
flow
Bandwidth
edge
Memory hook

Back-of-Envelope Estimation: how to ballpark scale in 60 seconds and avoid being wrong by 100x

Mental model

frame the problem before drawing the system

Design lens

Numbers are 'within an order of magnitude' — that's the bar.

Recall anchors
AnchorsMethod

Why it matters

Almost every design decision starts with an estimate: 'how big is this?' You will not have time to look things up. The trick is a tiny mental toolkit — powers of ten, latency numbers, a few storage sizes — and a discipline of always doing the math out loud.

Deep dive

Anchor users. 100M MAU × ~30% DAU = 30M DAU. ~10% peak hour ≈ 3M users that hour. Average actions per user × that = peak QPS.

Anchor storage. Tweet-sized record ≈ 300 bytes. Image ≈ 200 KB. Video minute ≈ 5–50 MB. Multiply by daily writes for raw, then ×3 for replication, ×2 for indexes.

Anchor bandwidth. 1 Gbps ≈ 125 MB/s. A single Postgres on commodity SSD ≈ tens of thousands of writes/sec; sustained 100k writes/sec is a distributed-system question.

Sanity check by two independent paths. If user math gives 50k QPS and storage math gives 2 TB/day, both should be consistent with the same write volume.

Demo / scenario

Estimate Twitter timeline read load at 300M MAU.

  1. DAU ≈ 50% × 300M = 150M.
  2. Sessions/day ≈ 5 → 750M sessions/day.
  3. Reads/session ≈ 20 → 15B timeline reads/day.
  4. Avg QPS ≈ 15B / 86400 ≈ 173k QPS; peak ≈ 3× ≈ 520k QPS.
  5. Each timeline ≈ 100 tweets × 300B = 30 KB → ~15 GB/s peak read bandwidth.

Tradeoffs

  • Numbers are 'within an order of magnitude' — that's the bar.
  • If two paths disagree by 10x, one assumption is wrong.
  • Always state assumptions; the interviewer cares about reasoning, not the answer.

Diagram

Users
MAU/DAU
QPS
Avg/peak
Storage
TB/day
Bandwidth
Gbps
Estimation funnel: anchor users, derive QPS, then storage and bandwidth.

Mind map

Check yourself

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Sources & further reading