Back-of-the-Envelope Estimation

Estimation is the skill of making reasonable guesses with simple math. You don’t need exact numbers — you need to be within an order of magnitude.

Powers of 2 Reference

Power	Value	Approx
10	1,024	1 Thousand
20	1,048,576	1 Million
30	1,073,741,824	1 Billion
40	~1 Trillion	1 Trillion

Data Sizes

Unit	Bytes
1 KB	10³ (1,000)
1 MB	10⁶ (1,000,000)
1 GB	10⁹ (1,000,000,000)
1 TB	10¹²

Latency Numbers Every Engineer Should Know

Operation	Time
L1 cache reference	0.5 ns
Branch mispredict	5 ns
L2 cache reference	7 ns
Mutex lock/unlock	100 ns
Main memory reference	100 ns
Compress 1 KB with Zippy	10,000 ns = 10 μs
Send 2 KB over 1 Gbps network	20,000 ns = 20 μs
Read 1 MB sequentially from memory	250,000 ns = 250 μs
Round trip within same datacenter	500,000 ns = 500 μs
Disk seek	10,000,000 ns = 10 ms
Read 1 MB sequentially from network	10,000,000 ns = 10 ms
Read 1 MB sequentially from disk	30,000,000 ns = 30 ms
Send packet CA → Netherlands → CA	150,000,000 ns = 150 ms

Memory is 1000x faster than disk. That’s why caching is so powerful.

Estimation Examples

QPS (Queries Per Second)

Example — Twitter-like system with 500M MAU:

DAU = 50% of MAU = 250M
Assume each user tweets 1/day = 250M tweets/day

QPS = 250,000,000 / 86,400 (seconds in a day)
    ≈ 2,900 QPS average

Peak QPS = 2,900 × 5 (peak factor) ≈ 14,500 QPS

Storage

Example — Storing tweets for 5 years:

Tweet size ≈ 280 chars + metadata ≈ 500 bytes
250M tweets/day × 500 bytes = 125 GB/day
125 GB × 365 × 5 = ~228 TB over 5 years

Bandwidth

Ingress = 125 GB/day = ~1.5 MB/s
Egress (serving) = 14,500 QPS peak × 500 bytes = ~7 MB/s peak

Common Rules of Thumb

Metric	Rough Value
1 day	86,400 seconds
DAU	~30-60% of MAU
Peak load	2-10× average
Text data per record	100-500 bytes
Image per item	100-500 KB
Memory cache hit rate	90-99% for hot data

Trade-offs

Estimation guides decisions (do you need 1 server or 100?).
Round aggressively — 1.4 → 1, 4.7 → 5.
If you can’t estimate a number, state your assumption clearly.

In Simple Words

Round numbers aggressively — 1.2 million ≈ 1 million.
Memory is 1000× faster than disk. Disk is 1000× cheaper.
Peak QPS ≈ average QPS × 5 (for most apps).