What are back of the envelope estimations in system design interviews?

"Back of the envelope estimations" in system design interviews refer to quick, approximate calculations or reasoning that you can theoretically do on a small piece of paper, like the back of an envelope. This approach is used to make ballpark estimates about system requirements, capacities, or capabilities without delving into detailed calculations.

Purpose in System Design Interviews:

• Feasibility Check: To quickly assess whether a proposed system design can handle expected loads and performance requirements.
• Resource Estimation: To estimate the scale of resources needed, such as storage capacity, bandwidth, number of servers, etc.
• Performance Metrics: To approximate throughput, latency, or other performance metrics.

Characteristics:

1. Simplicity: These are rough calculations, not detailed analyses.
2. Speed: They are meant to be done quickly, often in your head or with minimal writing.
3. Order-of-Magnitude Accuracy: The goal is to get in the right ballpark, not to find precise numbers.

Common Scenarios:

1. User Traffic Estimations: Estimating how many users a system might have and what kind of load this translates to per day/month/year.
2. Storage Calculations: Approximating the amount of data storage required based on user-generated content.
3. Bandwidth Needs: Estimating bandwidth requirements for serving content to users.
4. Scaling Estimates: Determining how a system might need to scale over time based on growth predictions.

Example:

Suppose you're asked to design a photo-sharing service. A back of the envelope estimation might involve:

• Estimating the average size of a photo (e.g., 2MB).
• Estimating the number of active users (e.g., 1 million users).
• Estimating the average number of photos each user uploads per day (e.g., 2 photos).
• Calculating daily storage needs: 2MB * 2 photos/user * 1 million users = 4 Terabytes per day.

Tips for Making Good Estimations:

1. Use Round Numbers: It's easier and faster to work with round numbers for estimations.
2. Understand Typical Values: Familiarize yourself with common metrics (e.g., the average size of a web request, typical storage space needed for different data types).
3. Break Down the Problem: Simplify complex problems into smaller, more manageable parts.
4. State Assumptions: Clearly articulate any assumptions you're making in your calculations.
5. Validate Your Logic: Double-check to ensure your estimations make logical sense.

Back of the envelope estimations are valuable in system design interviews to demonstrate your ability to think logically and practically about system scale and resources, without getting bogged down in details.