Capacity Estimation

Capacity estimation—often referred to as back-of-the-envelope calculation—is a fundamental skill in system design. It involves using simplified math and reasonable assumptions to determine the scale, resources, and feasibility of an architecture before diving into detailed design.

1. The Core Objective

The goal is not to reach a perfectly precise number, but to arrive at an order-of-magnitude estimate (e.g., "do I need 10 servers or 10,000?"). These calculations serve as a "feasibility check" to justify architectural decisions such as:

• Database partitioning (sharding): Triggered by massive storage or throughput requirements.
• Caching: Necessary when QPS exceeds the capacity of your database.
• Load balancers: Required when the incoming traffic exceeds the capacity of a single server.

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2. Standard Framework for Estimation

Most experts suggest a repeatable 5-step approach to keep your thinking clear and prevent getting stuck in "arithmetic circles":

1. Clarify Scale & Assumptions: Ask the interviewer for baseline numbers (e.g., Daily Active Users, read-to-write ratio, data retention period). Explicitly state your assumptions during the interview.
2. Traffic Estimation (QPS): Calculate the Queries Per Second.
   • Formula: Total Daily Requests / 86,400 seconds (often rounded to 100,000 for simplicity).
3. Storage Estimation: Determine how much data needs to be stored over a specific period (e.g., 5 years).
   • Formula: Daily Active Users × Daily Actions × Average Size per Action.
4. Bandwidth Requirements: Estimate incoming and outgoing data to determine network needs.
5. Server/Resource Count: Estimate the number of servers needed by dividing the total load (QPS or storage) by the capacity of a single unit.

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3. Essential Numbers to Memorize

To perform these calculations quickly, you should be familiar with common performance and size metrics:

Category	Typical Value / Reference
Data Units	1 KB ($10^3$), 1 MB ($10^6$), 1 GB ($10^9$), 1 TB ($10^{12}$)
Time (Seconds)	1 day ≈ $10^5$ seconds (86,400s)
Memory Latency	L1 cache (~0.5 ns), RAM (~100 ns)
Network Latency	Within Datacenter (~0.5 ms), US Coast-to-Coast (~40-50 ms)
Common Sizes	UUID (16 bytes), URL (~100 chars), Tweet (~300 bytes)

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4. Tips for Success

• Focus on the Process: Interviewers care more about how you arrive at your numbers than the numbers themselves. Clearly explain your logic.
• Use Round Numbers: Use powers of 10 or 2 to simplify math. Using 100,000 seconds in a day instead of 86,400 is standard practice for quick estimation.
• Perform a Sanity Check: After calculating, ask if the result seems reasonable compared to real-world systems.
• Identify the Crux: If you get stuck, look for the most difficult part of the problem—the "crux"—and focus your estimation efforts there (e.g., the index size for a search engine).