Chapter 2: BACK-OF-THE-ENVELOPE ESTIMATION

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Back-of-the-envelope estimation is a key skill in system design interviews. The focus is on your reasoning and logic, not the exact result.

Key Takeaways

• What is Back-of-the-Envelope Estimation?

  • Quick, rough estimation to evaluate system capacity or performance requirements in the early design stage.
  • The goal is not perfect accuracy, but a clear, logical estimation process, with all assumptions and units written down.

• Power of Two Basics

  • Know your data units (Byte, KB, MB, GB, TB, PB) and use powers of two for calculations.
  • 1 Byte = 8 bits, 1 KB = 1024 Bytes, 1 MB = 1024 KB, and so on.

• Latency Numbers Every Programmer Should Know

  • Memory operations are extremely fast, disk and network are much slower.
  • Example: L1 cache = a few ns, Disk seek = ms, Cross-region network = 100+ ms.
  • Always compress data before sending over the network if possible; avoid frequent disk I/O.

• Availability Numbers (SLA, “Nines”)

  • High availability is often expressed in “nines” (e.g., 99.9%, 99.99% uptime).
  • More nines = less downtime. For example, 99.9% means about 8.7 hours downtime per year.

• Example: Twitter QPS and Storage Estimation

  • Assumptions:
    • 300M monthly active users
    • 50% daily active
    • 2 tweets/user/day
    • 10% tweets contain media
    • Store data for 5 years
  • Estimation:
    • DAU = 300M × 50% = 150M
    • Tweet QPS = 150M × 2 / 24 / 3600 ≈ 3,500 QPS
    • Peak QPS ≈ 7,000 QPS
    • Media storage per day ≈ 30TB
    • 5-year media storage ≈ 55PB

• Interview Tips

  • Focus on process, not the final number.
  • Use round numbers and simple math (e.g., approximate 99987/9.1 as 100,000/10).
  • Clearly state all assumptions.
  • Always write down your units (e.g., 5 MB, 30 TB).
  • Practice estimating QPS, storage, cache, and number of servers.

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Example: Twitter QPS and Storage Estimation

Assumptions:

• 300 million monthly active users
• 50% daily active users
• 2 tweets per user per day
• 10% of tweets contain media
• Store data for 5 years

Estimation:

• DAU = 300M × 50% = 150M
• Tweet QPS = 150M × 2 / 24 / 3600 ≈ 3,500 QPS
• Peak QPS ≈ 7,000 QPS
• Media storage/day = 150M × 2 × 10% × 1MB = 30TB
• 5-year media storage = 30TB × 365 × 5 = 55PB

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Tips for Effective Estimation

• Process is more important than the answer. Show your logical reasoning and structured approach.
• Approximate when necessary. Don’t get stuck on complex calculations.
• Write down all assumptions so your thinking is transparent.
• Label every number with units to avoid confusion.
• Practice with common topics: QPS, peak QPS, storage, cache, number of servers, etc.

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