Live Scale Estimation Technique: Mental Math on the Whiteboard

System design estimations do not require high-precision fractional calculators. Interviewers evaluate your ability to make order-of-magnitude architectural deductions under real-time whiteboard conditions.

1. The Core Approximations:

• Seconds in a Day: 24 × 60 × 60 = 86,400 seconds ≈ 100,000 = 10^5 seconds.
  • Why this works: Rounding up to 100,000 introduces only a 15\% margin of error—well within normal engineering safety factors—while making mental division trivial.
• Data Units (Powers of 2 vs 10):
  • 2^{10} = 1,024 ≈ 1,000 = 10³ = 1 Kilobyte (KB)
  • 2^{20} = 1,048,576 ≈ 1,000,000 = 10^6 = 1 Megabyte (MB)
  • 2^{30} ≈ 1,000,000,000 = 10^9 = 1 Gigabyte (GB)
  • 2^{40} ≈ 10^{12} = 1 Terabyte (TB)
  • 2^{50} ≈ 10^{15} = 1 Petabyte (PB)
  • 2^{60} ≈ 10^{18} = 1 Exabyte (EB)

2. Multiplicative Speed Rules:

• 1 Million requests/day / 100,000 seconds = 10 QPS.
• 100 Million requests/day / 100,000 seconds = 1,000 QPS.
• 1 Billion requests/day / 100,000 seconds = 10,000 QPS.
• 1 MB/s = 8 Megabits per second (Mbps).
• 1 GB/s = 8 Gigabits per second (Gbps).