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Gouranga Das Samrat
Gouranga Das Samrat

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Back of Envelope Calculations

#systemdesign #backend

One-liner: Rough estimates done quickly to understand the scale of a system before designing it. They tell you what tier of infrastructure you need.

📌 Why This Matters

Before designing ANY system, you need to know:

  • How many users will use it?
  • How many requests per second?
  • How much storage do we need?
  • How much bandwidth is required?

These estimates shape every architectural decision.

🔢 Numbers Every Engineer Should Know

Time

Unit Value
1 millisecond 10⁻³ seconds
1 microsecond 10⁻⁶ seconds
1 nanosecond 10⁻⁹ seconds
Seconds in a day ~86,400 ≈ 10⁵
Seconds in a month ~2.5M ≈ 2.5 × 10⁶
Seconds in a year ~31.5M ≈ 3 × 10⁷

Latency Numbers (Approximate)

Operation Latency
L1 cache reference 1 ns
L2 cache reference 4 ns
RAM reference 100 ns
SSD random read 150 µs
HDD seek 10 ms
Network: same datacenter 500 µs
Network: cross-region (US→EU) 150 ms
Network: cross-continent 200–300 ms

Storage Units

Unit Size
1 KB 10³ bytes
1 MB 10⁶ bytes
1 GB 10⁹ bytes
1 TB 10¹² bytes
1 PB 10¹⁵ bytes

📐 The Estimation Framework

Step 1: DAU → QPS 

Daily Active Users (DAU)    = 10 million
Avg requests per user/day   = 10
Total daily requests        = 100 million

QPS = 100M / 86,400 ≈ 1,200 req/sec
Peak QPS (2-3x average)     ≈ 3,000 req/sec
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Step 2: Storage 

New posts per day    = 1M
Avg post size        = 1 KB (text) + 500 KB (image)
Daily storage        = 1M × 501 KB ≈ 500 GB/day
Yearly storage       = 500 GB × 365 ≈ 180 TB/year
5-year storage       ≈ 1 PB
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Step 3: Bandwidth 

Reads per second     = 100K req/sec
Avg response size    = 10 KB
Outbound bandwidth   = 100K × 10 KB = 1 GB/sec
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🔬 Real Example: Design Twitter

Assumptions

  • 300M DAU
  • Each user reads 10 tweets/day
  • Each user writes 1 tweet/week ≈ 0.14 tweets/day
  • Avg tweet: 280 chars = 280 bytes ≈ 300 bytes
  • 10% of tweets have an image (~200 KB)

Read QPS 

300M users × 10 reads/day = 3B reads/day
QPS = 3B / 86,400 ≈ 35,000 reads/sec
Peak QPS ≈ 100,000 reads/sec
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Write QPS 

300M × 0.14 = 42M tweets/day
QPS = 42M / 86,400 ≈ 500 writes/sec
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Storage per day 

Text: 42M × 300 bytes = 12.6 GB
Images: 42M × 10% × 200 KB = 840 GB
Total: ~850 GB/day ≈ 310 TB/year
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Bandwidth 

Read traffic: 35K req/sec × 1 KB/response ≈ 35 MB/sec = ~300 Gbps
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🔬 Real Example: Design WhatsApp

Assumptions

  • 2B DAU
  • Each user sends 20 messages/day
  • Avg message: 100 bytes
  • 30% are media messages (500 KB avg)

QPS 

2B × 20 = 40B messages/day
QPS = 40B / 86,400 ≈ 460,000 msg/sec
Peak QPS ≈ 1M msg/sec
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Storage per day 

Text: 40B × 100B = 4 TB
Media: 40B × 30% × 500 KB = 6 PB/day (too high → add retention/compression policy)
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💡 Tips for Interviews

  1. Always ask before estimating — "Should I assume 10M or 100M users?"
  2. Round aggressively — 86,400 → 10⁵, 3.14 → 3
  3. Peak = 2-3× average (or 5-10× for viral/event-based systems)
  4. Show your math — interviewers care about the process, not the exact number
  5. Derive storage needs from estimates — don't pull numbers from thin air
  6. 1 char = 1 byte (ASCII), 1 char = 2-4 bytes (Unicode)

📋 Estimation Cheat Sheet 

1K users  → Single server fine
10K users → Need to think about DB separation
100K users → Load balancer, read replicas
1M users  → Caching layer, CDN, sharding
10M users → Distributed systems, microservices
100M+     → You work at a FAANG (or interview there)
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🔑 Key Takeaways

  • Back-of-envelope is about order of magnitude, not precision
  • Know the key numbers cold: bytes, seconds in a day, latency tiers
  • Always separate read QPS from write QPS — they're usually very different
  • Storage estimations reveal whether you need sharding/archival early

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