Most guides assert totals. Almost none show the arithmetic. Here it is.
Example one: a clinical copilot for 400 users
Take a retrieval system for 400 clinicians. Each runs 15 queries per working day. Over 21 working days, that is 126,000 queries a month.
Each query sends about 8,000 input tokens. That covers the system prompt, retrieved document chunks, and the question. Each answer runs about 600 output tokens.
Monthly volume comes to 1,008 million input tokens and 75.6 million output tokens.
Run it naively on a flagship model. Claude Opus 5 bills $5 per million input tokens and $25 per million output tokens, per Anthropic's pricing page. That is $5,040 for input and $1,890 for output.
Monthly cost: $6,930.
Now switch to a mid-tier model. Claude Sonnet 5 bills $2 per input token and $10 per output token. Same volume, same workload, and the cost drops to $2,772.
Now add prompt caching. Roughly 6,000 of those 8,000 input tokens are stable. The system prompt and policy docs do not change between queries.
Cache hits are billed at 10% of the input rate. Those tokens now cost $0.20 per million instead of $2.
Cached input: $151. Fresh input: $504. Output: $756.
Monthly cost: $1,411.
Now route by difficulty. Send 70% of simple lookup queries to Claude Haiku 4.5 at $1 and $5. Keep the harder 30% on Sonnet 5, and cache both.
Monthly cost: $917.
Same system. Same volume. Same answers, assuming your routing logic is sound.
The spread between the first setup and the last is 87%.
That is the entire argument for design work on cost, done in numbers rather than adjectives.
Example two: why a support agent costs triple the estimate
Anthropic publishes a worked figure for support automation. Processing 10,000 tickets at roughly 3,700 tokens each on Haiku 4.5 costs about $37, per its own docs.
Clean number. It also assumes the model answers in one pass.
Real support agents call tools. They look up the order, check the refund policy, and query the account status. Each tool call sends the conversation back through the model with everything that came before.
Add three tool calls per ticket, and the token count per conversation climbs past 6,000. Tool definitions carry their own overhead, around 500 tokens on Haiku 4.5 before you count a single result.
The same 10,000 tickets now cost about $108.
Nothing went wrong. The estimate was just built on a single-pass assumption. Agentic systems multiply token consumption in ways linear estimates never catch, and this is the most common reason a pilot budget fails to survive production.