Estimation Shortcuts

Why Shortcuts Matter

Back-of-envelope estimation is a speed game: conclusions within 2x of truth, produced in seconds, while the interviewer watches. Precision is the enemy; these constants are the toolkit.

Time Constants

 1 hour    = 3,600 s      ≈ 4 × 10³ s
 1 day     = 86,400 s     ≈ 10⁵ s          ← the single most-used constant
 1 month   ≈ 2.6 × 10⁶ s  ≈ 30 × 10⁵
 1 year    ≈ 31.5M s      ≈ 3 × 10⁷ s

 THE conversion everyone uses:
   X million events/day ÷ 10⁵ = X × 10 rps average
   100M/day → ~1,000 rps average (true value 1,157 — close enough)

The rps-per-Million Table

Precomputed from the day constant:

Daily volume	Average rate	With 2.5x peak
1M/day	~12/s	~30/s
10M/day	~120/s	~300/s
100M/day	~1,200/s	~3,000/s
1B/day	~12,000/s	~30,000/s

Memorize one row’s logic; regenerate all others instantly.

Storage Flow Constants

 sustained write flow → daily accumulation:
   1 MB/s  writes for a day  ≈ 86 GB/day
   1 KB record at 1k/sec       ≈ 86 GB/day
   
 yearly: X GB/day × 365 ≈ X × 0.37 TB/year
   20 GB/day → ~7 TB/year ✓ (RideShare trips check)

 replication multiplier quick table:
   RF=3 → ×3 storage and ×3 write bandwidth
   erasure coding (8+3)-ish → ~×1.4 storage

Unit Conversion Anchors

 bits↔bytes:  divide by 8 (networks bits, payloads bytes)
 1 Gbps       = 125 MB/s
 powers of 2: 2¹⁰≈10³, 2²⁰≈10⁶, 2³⁰≈10⁹, 2³²≈4×10⁹
 percentages: 5% of 1M = 50k (move decimal + halve... 5% = /20)

Arithmetic Tricks Under Pressure

 round aggressively FIRST:  17.3 GB × 46 days → 20 × 50 = 1,000 GB
 keep ONE significant digit per factor
 track exponents separately: (2×10⁷ × 3×10³) = 6×10¹⁰
 sanity-anchor results against known systems:
   "Twitter-scale reads" ≈ hundreds of thousands rps
   "one Postgres"        ≈ thousands of reads/sec

The last trick catches most errors: if your estimate says a URL shortener needs 500 database nodes, an anchor comparison flags the arithmetic slip before the interviewer does.

A Complete Worked Example in 30 Seconds

Prompt: image host, 10M uploads/day, avg 2 MB.

 storage/day  = 10⁷ × 2 MB            = 20 TB/day (!)
              → this is a CDN + object-storage design instantly
 egress guess = views ≈ 10x uploads by count, similar bytes class
              → hundreds of Gbps → CDN mandatory
 metadata     = 10⁷ × 200 B           = 2 GB/day → trivial DB load
 
 three numbers, three architecture decisions, half a minute

Interview Framing

Interviewers grade method speed, not decimal places. Speaking pattern that scores: constant stated (“a day is about 10 to the fifth”), rounded multiplication aloud, anchor-check, conclusion bound to a decision. Practiced fluency here buys credibility minutes later when the hard trade-offs need the remaining clock.