Back-of-the-envelope estimation

Tech Paths — Sun, 17 May 2026 13:05:08 +0000

Originally published at TechPaths.dev

Back-of-the-envelope estimation means making quick, approximate calculations to understand the scale of a system — without a calculator, without exact data, and without spending more than 2-3 minutes.

In system design interviews, interviewers ask you to estimate because they want to see:

Do you know the key numbers?
Can you reason about scale?
Will your design actually handle the load?

The Numbers You Must Memorize

Powers of 2

Power	Approximate value	Name
2¹⁰	1 thousand	1 KB
2²⁰	1 million	1 MB
2³⁰	1 billion	1 GB
2⁴⁰	1 trillion	1 TB
2⁵⁰	1 quadrillion	1 PB

Latency Numbers

Operation	Latency
L1 cache read	1 ns
L2 cache read	4 ns
RAM read	100 ns
SSD read	100 µs
Network round trip (same DC)	500 µs
HDD read	10 ms
Network round trip (cross-region)	150 ms

Availability Numbers

Nines	Downtime/year
99%	3.65 days
99.9%	8.7 hours
99.99%	52 minutes
99.999%	5 minutes

The Estimation Framework

Always follow this order:

State assumptions — DAU and usage patterns
Estimate traffic — RPS (reads and writes)
Estimate storage — items × size × retention
Estimate bandwidth — RPS × payload size
Estimate servers — RPS ÷ capacity per server
State result and sanity check

Step 1 — Traffic Estimation

Formula:

RPS = DAU × requests_per_user_per_day / 86400

Example — Twitter-like system:

300 million DAU
Each user reads 100 tweets/day, writes 1 tweet/day

Read RPS  = 300M × 100 / 86400 ≈ 350,000 RPS
Write RPS = 300M × 1   / 86400 ≈ 3,500 RPS

Rule of thumb: 80/20 rule — 80% reads, 20% writes for most social apps.

Step 2 — Storage Estimation

Formula:

Storage = items_per_day × item_size × retention_days

Example — Twitter tweets:

3,500 writes/second = ~300M tweets/day
Each tweet: 280 chars = ~300 bytes + metadata = ~1 KB
Keep 5 years = 1825 days

Storage = 300M × 1KB × 1825 = 547 TB ≈ 0.5 PB over 5 years
Daily:   = 300M × 1KB        = 300 GB/day

Step 3 — Bandwidth Estimation

Formula:

Bandwidth = RPS × average_payload_size

Example — Twitter read bandwidth:

Read bandwidth = 350,000 RPS × 1KB = 350 GB/s

That's why Twitter uses CDNs aggressively — serving 350 GB/s from origin servers would be impossible.

Step 4 — Server Estimation

Formula:

Servers needed = Total RPS / RPS per server

A typical web server handles ~1,000-10,000 RPS depending on workload.

For 350,000 read RPS at 10,000 RPS/server:
Servers = 350,000 / 10,000 = 35 servers (minimum)

Add 2-3x for redundancy and peak traffic → ~100 servers.

Common Estimation Examples

URL Shortener (like bit.ly)

Assumptions:

100M DAU
1 URL created per user per day
100 reads per URL per day

Write RPS = 100M / 86400 ≈ 1,200 RPS
Read RPS  = 1,200 × 100  = 120,000 RPS

URL size      = 100 bytes
Daily storage = 100M × 100B = 10 GB/day
Yearly        = 10 × 365    = 3.65 TB/year
Read-write ratio: 100:1

Instagram Photo Storage

Assumptions:
- 500M DAU
- 10% upload a photo daily = 50M photos/day
- Average photo size = 1 MB (after compression)

Daily storage  = 50M × 1MB  = 50 TB/day
Yearly storage = 50 × 365   = 18 PB/year

Useful Approximations

Thing	Approximate size
ASCII character	1 byte
Unicode character	2-4 bytes
Integer	4 bytes
Long/timestamp	8 bytes
UUID	16 bytes
Tweet (280 chars)	~300 bytes
Average webpage	~2 MB
Photo (compressed)	~300 KB - 1 MB
1 minute HD video	~100 MB
1 minute 4K video	~400 MB

How to Present in an Interview

"Let me make some assumptions first:
 - 100M DAU
 - Read-heavy: 10:1 read-write ratio
 - Average payload: 1KB

Traffic:
 - Writes: 100M / 86400 ≈ 1,200 RPS
 - Reads:  1,200 × 10   = 12,000 RPS

Storage:
 - 1,200 writes/s × 1KB × 86400s = ~100 GB/day
 - Over 5 years: ~180 TB

This tells me I need:
 - Read replicas for the 10:1 read ratio
 - ~2 servers for writes, ~12 for reads
 - CDN for static content"

Key Takeaways

Memorize: powers of 2, latency numbers, availability nines
Framework: Traffic → Storage → Bandwidth → Servers
Always state assumptions first — interviewers care about your reasoning, not exact numbers
Round aggressively: 86,400 ≈ 100,000
Sanity check: does the number feel right? PB for a major social network — yes. PB for a small blog — no.

Want more system design content? Check out TechPaths.dev — structured learning paths for system design, DSA, AI/ML, and cloud.

DEV Community: Tech Paths

Back-of-the-envelope estimation

The Numbers You Must Memorize

Powers of 2

Latency Numbers

Availability Numbers

The Estimation Framework

Step 1 — Traffic Estimation

Step 2 — Storage Estimation

Step 3 — Bandwidth Estimation

Step 4 — Server Estimation

Common Estimation Examples

URL Shortener (like bit.ly)

Instagram Photo Storage

Useful Approximations

How to Present in an Interview

Key Takeaways