back-of-the-envelope

name: back-of-the-envelope description: This skill should be used when the user needs to "estimate QPS", "back-of-the-envelope" (BOTEC) numbers, "how much storage / bandwidth", "how many servers", "peak load", "capacity planning", or wants the standard latency / throughput / availability numbers to ground a design (latency table, QPS rates, powers of two, nines). Use it whenever a design decision hinges on scale — convert any "high traffic" / "huge data" phrase into concrete numbers before choosing components, even if the user doesn't say "estimate".

Back-of-the-Envelope Estimation (BOTEC)

Turn vague scale ("high traffic", "huge data") into a few concrete numbers that decide the design. BOTECs are quick, approximate calculations — feasibility checks, not precision. The point is the process and directional correctness: they tell you when a single database won't do, when caching is forced, when a write spike needs a queue.

A design for 1k QPS and one for 1M QPS are different systems. 10 GB fits in RAM; 10 TB needs distributed storage. Estimate first, choose second.

When to reach for this

At step 2 of any design (right after requirements), and any time a choice depends on scale: sizing the read vs write path, deciding sharding vs a single node, justifying a cache, or sanity-checking a proposed component against load.

When NOT to

Don't chase precision or model every microservice — that's the opposite of the technique. Don't estimate what won't change a decision (YAGNI). Round aggressively: "99,987 / 9.1" is "100,000 / 10". Always label units and write assumptions down.

Clarify first

Estimates are only as good as their inputs. Pin down:

• DAU/MAU and what fraction is active daily.
• Actions per user per day (posts, reads, messages…).
• Read:write ratio — which path dominates.
• Object sizes — per record and per media blob.
• Retention — how long data is kept (drives total storage).
• Peak factor — peak is typically ~2× average; spikier for some workloads.

The core estimations (recipes)

Work each as a single multiply/divide chain. Full worked numbers and the CPU-time derivation are in references/estimation-recipes.md.

• QPS = DAU × actions_per_user_per_day ÷ 86,400. Peak QPS ≈ 2 × QPS (state your peak factor).
• Storage/day = writes_per_day × avg_object_size. Total = storage/day × retention_days (watch base-10 vs base-2; storage is sold base-10).
• Bandwidth = QPS × payload_size (separate read and write; egress usually dominates and costs money).
• Number of servers = peak_QPS ÷ per_server_QPS. Use the per-server rates below as the divisor.
• Concurrent connections / memory = concurrent_users × per_connection_cost; check the working set fits RAM (else it's an IO-bound, disk-backed design).

Numbers that matter

These are the reference points to know, so you can estimate without lookups. Full tables (latency, server specs, request types, powers of two, nines) live in references/numbers-to-remember.md — load it when you need a specific figure.

The two that drive most decisions:

Think in orders of magnitude, not exact values. CPU-bound work is ~1×, memory-bound ~10×, IO-bound ~100× the time. That ratio, not the decimals, is what shifts an architecture.

Dos and don'ts

Distilled from the recipes and the ways estimates mislead.

Do

• Do round to one significant figure and reason in orders of magnitude — the ratio (1× / 10× / 100×) is what shifts an architecture, not the decimals.
• Do size on peak, not average. State the peak multiplier (≈2× is a common default; spikier for bursty workloads) before picking capacity.
• Do estimate reads and writes separately — a 95% read ratio and a write spike pull the design in opposite directions.
• Do label units and write assumptions down, so a "GB" isn't ambiguous and the chain can be re-checked when an input changes.

Don't

• Don't carry false precision. Decimals imply a confidence the inputs don't support; "99,987" is "100,000".
• Don't trust per-server rates as universal. "1k QPS for SQL" is a point-query rule of thumb; range scans, joins, and fat payloads can be 10× worse — use it for the order of magnitude, then validate with real benchmarks.
• Don't conflate base-2 and base-10. RAM is base-2; storage/network marketing is base-10 — close enough for an estimate, but only if the units are stated.
• Don't compute what won't change the decision. If a number doesn't move the architecture, skip it (YAGNI).

Diagram

Estimation is usually a table, not a picture — keep the numbers and assumptions inline. When a derived number forces a structural change (e.g. "300k QPS > single DB → shard / add replicas"), that belongs in the architecture diagram itself; use the architecture-diagram skill when drawing the design those numbers justify.

Related building blocks

• requirements-scoping — depends on it for the inputs (DAU, action rates, ratios, SLAs) this skill turns into numbers.
• data-storage — feeds into it: the storage totals and shard counts computed here drive its SQL/NoSQL and partitioning choices.
• caching — feeds into it: a high read ratio or hot working set sized here is the case for a cache.
• scaling-evolution — feeds into it: when an estimate crosses a per-node ceiling, that ceiling is the next bottleneck to plan around.
• system-design — owned-concept lives here for the reasoning loop; this is the orchestrator that calls this skill at step 2.

References

• references/numbers-to-remember.md — the cheat sheet: latency table, typical server spec, per-server QPS rates, CPU/memory/IO-bound request types, powers of two, availability nines. Read when you need a specific figure.
• references/estimation-recipes.md — worked examples (Twitter-scale QPS + storage, the 64-core→64k req/s CPU-time derivation, bandwidth and server-count sizing). Read to see a full chain end to end.

Scripts

For a deterministic check of a sizing chain (the one place exact arithmetic earns its keep), run the calculator rather than doing it by hand:

• scripts/botec.py — python3 scripts/botec.py --dau 150e6 --actions 2 --peak 2 --obj-bytes 1e6 --media-frac 0.10 --retention-days 1825 --server-qps 1000 --json → QPS, peak, storage/day & total, bandwidth, server count. Per-server-QPS defaults mirror the rules of thumb above (override with --server-qps).
• scripts/test_botec.py — asserts the calculator matches expected_outputs/twitter_scale.json (the worked Twitter example), so the prose recipe and the math can't drift.