Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add proyecto26/system-design-skills --skill back-of-the-envelopegit clone --depth 1 https://github.com/proyecto26/system-design-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/proyecto26/system-design-skills/back-of-the-envelope)<a href="https://agentmods.dev/skills/proyecto26/system-design-skills/back-of-the-envelope"><img src="https://agentmods.dev/badge/skills/proyecto26/system-design-skills/back-of-the-envelope/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/proyecto26/system-design-skills/back-of-the-envelope"><img src="https://agentmods.dev/badge/skills/proyecto26/system-design-skills/back-of-the-envelope.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00121 | $0.01821 |
| Opus 5 | $0.00060 | $0.00911 |
| Sonnet 5 | $0.00024 | $0.00364 |
| Haiku 4.5 | $0.00012 | $0.00182 |
Grade A, and why
back-of-the-envelope scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 13d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 117 lines — stays where its author put it; the contents beside it link to each section on GitHub.
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).
What ships with it
5 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 13d ago First seen · 117 lines · 121 tokens per session scan A 9c226cfc1b80
back-of-the-envelope is a skill published in the GitHub repository proyecto26/system-design-skills (70 stars, last pushed 3mo ago), licensed MIT. It adds 121 tokens to every session and 1,821 once invoked, about $0.0006 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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