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System Design Fundamentals: Back-of-Envelope Math

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System Design Fundamentals: Back-of-Envelope Math

5 min readJul 25, 2026

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“Before you choose Redis, Kafka, or Cassandra, you should answer a much simpler question: How big is your system?”

One of the biggest mistakes engineers make when learning system design is jumping straight into designing Instagram, Uber, or Netflix.

The first discussion quickly becomes:

  • Should we use Redis?
  • Should we use Kafka?
  • MongoDB or PostgreSQL?
  • Kubernetes or ECS?

These are interesting questions — but they’re usually the wrong place to start.

Experienced engineers begin somewhere much simpler.

How many users do we have?

How much traffic should we expect?

How much data are we storing?

Once you understand the constraints, the architecture almost starts designing itself.

This is exactly why every system design interview begins with estimation.

In this article, we’ll cover the mathematical intuition that every backend engineer should have before drawing a single architecture diagram.

Why Back-of-the-Envelope Math Matters

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Behind the Stack

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A humble place to learn Java and Programming better.