Back of the Envelope Estimation

Back of the Envelope Estimation

System Design Interview Book

Hello again, Today We are going to continue our series by checking Chapter 2 in system Design Interview Book.

Back of the envelope estimation

Sometimes you are asked to estimate system capacity or performance requirements using back-of-the-envelope estimation.

Back of the envelope estimation are estimates we create using a combination of thought experiments and common performance numbers

We need to have a good sense in scalability basics to effectively carry out back-to-the-envelope estimation

The Following Concepts should be well understood:

  • Power of two

  • Latency Numbers

  • Availability Numbers

Power of Two

To obtain correct calculations, it is critical to know the data volume unit using the power of 2

A byte is a sequence of 8 bits. ASCII Character holds 1 byte in memory(8 bits)

The Following Table Explains the data volume units

Screen Shot 2022-06-19 at 10.37.26 AM.png

Latency Numbers

Dr.Dean From Google reveals the length of typical computer operations in 2010 "This list could be outdated because computers became faster and more powerful"

Screen Shot 2022-06-19 at 12.26.14 PM.png

A google Software engineer built a tool to visualize Dr.Dean's numbers. the tool also takes time factor into consideration.

Screen Shot 2022-06-19 at 12.29.23 PM.png

Analysis of latency numbers

  • Memory is fast but the disk is slow

  • Avoid disk seeks if possible

  • Simple compression algorithms are fast

  • Compress data before sending it over internet if possible

  • Data centers are usually in different regions and it takes time to send data between them

Availability Numbers

High availability is the ability of system to be continuously operational for a desirably long period of time.

High availability is measured with percentage, for example if we say a service with 100% availability means that service has 0 Downtime.

What is SLA

SLA(service level agreement) is a commenly used term between service providers and client, which defines the level of uptime your service will deliver.

Uptime is traditionally measured in nines, the more nines the better. you can check the next table for more illustration

Screen Shot 2022-06-19 at 1.32.58 PM.png

Twitter Example

Lets say for example Estimate Twitter QPS(Query per second) and storage requirements kindly note the following numbers are for excerise and not the precise numbers from twitter


  • 300 Million monthly active users.

  • 50% of users use twitter daily

  • User posts 2 tweets per day

  • 10% of tweets contains media

  • Data stored for 5 years


QPS estimations

  • Daily active users (DAU): 300 * 50% = 150 million

  • Tweets QPS = 150 million * 2 tweets / 24 hours/ 3600 seconds = ~3500

  • Peek QPS = 3500 * 2 = ~7000

Media Estimation

  • Average Tweet size:

    Tweet_id : 64 bytes
    Text: 140 bytes
    Media: 1 MB
  • Media storage = 150 x 2 x 10% x 1 MB = 30TB per day

  • 5-year Media storage = 30 x 365 x 5 = ~ 55PB