Module 0 - Core Concepts

Back-of-Envelope Estimation

The art of quickly calculating system requirements using approximations. Essential for system design interviews and capacity planning.

15 min readInterview Critical

Back-of-Envelope Calculator

Quick estimates for system design interviews

Daily Active Users (DAU)

1.0M users

Actions per User/Day

Peak Multiplier

Peak = 3x average

Data per Request (KB)

10.0M

Daily Requests

116

Avg QPS

348

Peak QPS

3.4 TB

Storage/Year

0.9 Mbps

Avg Bandwidth

2.7 Mbps

Peak Bandwidth

Servers @ 1K QPS

Quick Formulas

QPS = Daily Requests / 86,400

Peak QPS = Avg QPS × Peak Multiplier

Storage = Requests × Data Size × Days

Servers = Peak QPS / QPS per Server

1Why Estimation Matters

Why This Matters

Imagine you're building a bridge. Before drawing blueprints, you need to know: How many cars per hour? How heavy are the trucks? What's the wind speed?

System design is the same. Before choosing technologies, you need to estimate traffic, storage, and bandwidth to know if your design can handle the load.

Right-size Infrastructure

Avoid over-provisioning (wasting money) or under-provisioning (outages).

Interview Success

Interviewers expect you to estimate QPS, storage, and bandwidth unprompted.

Justify Decisions

We need sharding because 1B rows will not fit on one machine - more convincing with numbers.

2Essential Numbers to Memorize

Pro Tip

You don't need exact numbers. Interviewers want to see your thought process. Use powers of 2 and round aggressively. Being off by 2x is fine; being off by 100x is not.

Powers of 2 (Data Sizes)

Power	Exact Value	Approx	Name
2^10	1,024	1 Thousand	1 KB
2^20	1,048,576	1 Million	1 MB
2^30	1,073,741,824	1 Billion	1 GB
2^40	1,099,511,627,776	1 Trillion	1 TB
2^50	~1 Quadrillion	1 Quadrillion	1 PB

Time Conversions

Seconds/day

86,400

~100K

Seconds/month

2.6M

~2.5M

Seconds/year

31.5M

~30M

Requests/day @ 1 QPS

86,400

~100K

Latency Numbers (Approximate)

L1 cache reference

1 ns

L2 cache reference

4 ns

RAM reference

100 ns

SSD random read

150 μs

HDD seek

10 ms

Same datacenter roundtrip

0.5 ms

Cross-continent roundtrip

150 ms

Key insight: Memory is ~1000x faster than SSD, SSD is ~100x faster than HDD, Network varies wildly.

Typical Data Sizes

Tweet/Text message

~200 bytes

Metadata record

~1 KB

Web page

~2 MB

Image (compressed)

~200 KB

HD Video (1 min)

~50 MB

4K Video (1 min)

~300 MB

3The Estimation Framework

Clarify the Scope

What exactly are we estimating? Daily active users? Storage for 5 years? Peak QPS?

Make Assumptions

State your assumptions clearly. "Assume 100M DAU, each user makes 10 requests/day..."

Calculate Step by Step

Break complex calculations into simple steps. Show your work.

Sanity Check

Does the answer make sense? Compare to known systems.

4Common Estimation Scenarios

Estimate QPS for a Twitter-like service with 300M monthly active users.

Calculation

1. Monthly Active Users (MAU) = 300M
2. Daily Active Users (DAU) = 50% of MAU = 150M
3. Each user views timeline ~10 times/day
4. Total daily requests = 150M × 10 = 1.5B requests/day
5. QPS = 1.5B / 86,400 ≈ 17,000 QPS
6. Peak QPS = 2× average = ~35,000 QPS

✓ Result:~17K QPS average, ~35K QPS peak

How much storage does Twitter need for tweets over 5 years?

Calculation

1. Tweets per day = 500M
2. Average tweet size = 200 bytes (text only)
3. Daily storage = 500M × 200B = 100GB/day
4. Yearly storage = 100GB × 365 = 36.5TB/year
5. 5-year storage = 36.5TB × 5 = 182.5TB
6. With 3x replication = 182.5TB × 3 ≈ 550TB

✓ Result:~550 TB for text tweets over 5 years

Estimate bandwidth for Instagram serving 500M DAU.

Calculation

1. DAU = 500M users
2. Each user views ~20 images/day
3. Average image size = 200KB
4. Daily data transfer = 500M × 20 × 200KB = 2PB/day
5. Per second = 2PB / 86,400s ≈ 23GB/s
6. In bits = 23GB × 8 = 185 Gbps

✓ Result:~185 Gbps bandwidth requirement

5Quick Reference Formulas

QPS from DAU

QPS = (DAU × actions/user) / 86,400

100M DAU × 10 actions = 1B/day ≈ 12K QPS

Storage per Year

Storage = items/day × size × 365

1M items × 1KB = 365GB/year

Bandwidth

BW = QPS × response_size

10K QPS × 100KB = 1GB/s

Servers Needed

Servers = Total QPS / QPS per server

100K QPS / 10K = 10 servers

Cache Size

Cache = working_set × hit_rate_target

Top 20% data handles 80% requests

Replication Factor

Total = Raw × Replication Factor

1TB × 3 replicas = 3TB total

6Practice: Estimate a URL Shortener

Try This Exercise

Design a URL shortener (like bit.ly) and estimate:

How many URLs can be shortened per day?
How much storage is needed for 10 years?
What QPS should the read service handle?

Sample Answer

Assumptions: 100M new URLs/month, 100:1 read:write ratio

Write QPS: 100M / (30 × 86400) ≈ 40 QPS

Read QPS: 40 × 100 = 4,000 QPS

Storage: 100M × 12 months × 10 years × 500B = 6TB

With overhead: 6TB × 3 (replication) = 18TB total

7Common Mistakes

❌ Forgetting peak vs average

✓ Peak is usually 2-10x average. Design for peak, cost for average.

❌ Ignoring replication

✓ Data is usually replicated 3x. Storage = Raw × Replication Factor.

❌ Wrong time units

✓ Be careful with seconds vs milliseconds, bits vs bytes.

❌ Not stating assumptions

✓ Always say 'Assuming X...' so interviewer can correct you early.

8Key Takeaways

1Memorize key numbers: 86,400 seconds/day, powers of 2, latency hierarchy.

2Use the framework: Clarify → Assume → Calculate → Sanity Check.

3Round aggressively. 2^10 ≈ 1000 is good enough.

4Always consider peak load (2-10x average) and replication (usually 3x).

5Show your work step by step. Process matters more than exact answer.

6Sanity check against known systems (Twitter does ~300K tweets/sec).

9Interview Follow-up Questions

Interview Follow-up Questions

Common follow-up questions interviewers ask

10Test Your Understanding

Test Your Understanding

5 questions

A service has 500M monthly active users, 20% are daily active. Each user makes 8 requests per day. What is the approximate QPS?

You need to store 10 million images, each 500KB on average. How much storage is needed with 3x replication?

Which is approximately correct: 2^30 equals?

A system needs to handle 50,000 QPS at peak. Your servers handle 2,000 QPS each. How many servers minimum (with 25% buffer)?

Reading from RAM is approximately how much faster than reading from SSD?

0 of 5 answered