Your AI agent's token bill grows quadratically. Here's the math (and a free calculator)

Most token calculators multiply tokens by price. That works for a single API call. It is wrong for an agent.

Why agent loops get expensive

Each step of an agent loop sends the whole conversation so far: the system prompt, every earlier turn, and every tool result.

Say your system prompt is 2,000 tokens and each step adds 800 tokens. Then:

A 12-step run sends 76,800 input tokens in total. The naive estimate of 12 × 2,800 gives 33,600, so the real number is 2.3× higher. The total grows with the square of the step count:

total_input = n * system + adds * n * (n - 1) / 2
            = 12 * 2000 + 800 * 12 * 11 / 2 = 76,800

Three levers that actually move the bill

1. Prompt caching. The system prompt and the early turns repeat on every step, so cached reads cut most of that cost.
2. Summarize after N steps. Swap old turns for a short summary, which caps context growth.
3. Route by step. Use a small model for tool-call formatting and a big one only for planning.

Get your own number in 10 minutes

I built a free spreadsheet for this: cost per query, cost per user and gross margin, with dated, cited list prices for six current models. It works in Excel and Google Sheets.

👉 AI API Cost Calculator Lite (free)

If you need agent loops, caching, sub-agent fan-out and break-even pricing per plan, the full AI Cost & Margin Model covers it. Code LAUNCH20 takes 20% off until 18 Nov.

How do you budget for agent runs? Tell me in the comments.