Back-of-the-envelope estimation is a rough calculation used to estimate the feasibility, cost, or scale of a project or problem without delving into highly detailed analysis or precise data. It’s a quick and practical way to get an approximate answer based on reasonable assumptions.
This technique is often used in system design, engineering, product planning, and brainstorming sessions to:
• Determine whether an idea is worth pursuing.
• Spot potential bottlenecks or challenges.
• Validate the feasibility of solutions or architectures.
Steps for a Back-of-the-Envelope Estimation:
1. Define the Problem Clearly:
• Understand what you’re estimating (e.g., storage requirements, bandwidth, number of servers).
• Break the problem into smaller, manageable components.
2. Make Assumptions:
• Use approximate values based on industry standards or prior knowledge.
• Err on the side of simplicity and round numbers for quick calculations.
3. Perform Calculations:
• Use basic arithmetic to combine assumptions and get the result.
4. Validate Assumptions:
• Ensure assumptions are reasonable.
• Adjust estimates if the results seem unrealistic.
5. State Assumptions Explicitly:
• Communicate the assumptions clearly so others can understand and refine your calculations.
Example 1: Estimating Storage for a Chat Application
Problem: Estimate the annual storage requirements for a messaging app with 1 million daily active users (DAUs).
Assumptions:
1. Each user sends 50 messages per day.
2. Average message size is 200 bytes.
3. Messages are stored for 1 year.
Calculation:
1. Total messages per day = 1,000,000 users × 50 messages = 50,000,000 messages/day.
2. Total storage per day = 50,000,000 messages × 200 bytes = 10 GB/day.
3. Annual storage = 10 GB/day × 365 days = 3.65 TB/year.
Result: You would need approximately 3.65 TB of storage per year.
Example 2: Bandwidth for a Video Streaming Service
Problem: Estimate the bandwidth required to stream 1080p videos to 10,000 concurrent users.
Assumptions:
1. 1080p video uses 5 Mbps.
2. All users are watching simultaneously.
Calculation:
1. Bandwidth per user = 5 Mbps.
2. Total bandwidth = 5 Mbps × 10,000 users = 50,000 Mbps = 50 Gbps.
Result: You need a network capable of handling 50 Gbps of traffic.
Common Use Cases:
1. System Design:
• Estimating server requirements (CPU, memory, disk).
• Predicting data throughput or storage needs.
2. Capacity Planning:
• Assessing whether existing infrastructure can handle growth.
3. Financial Projections:
• Quick revenue or cost estimations for business models.
4. Engineering Problems:
• Estimating power consumption, materials, or load capacities.
Tips for Effective Back-of-the-Envelope Estimations:
1. Use Reasonable Numbers:
• Simplify complex calculations by rounding numbers (e.g., use 1M instead of 1,048,576).
2. Focus on Key Factors:
• Ignore minor details or edge cases unless they significantly impact the result.
3. Cross-Check Results:
• Compare your estimate to known benchmarks or real-world data.
4. Iterate:
• Refine your assumptions and calculations if more precise data becomes available.
Back-of-the-envelope calculations are invaluable in system design, initial project discussions, and rapid brainstorming.