AI by Hand ✍️

AI by Hand ✍️

Usage Audit

Reading tokens back out of a bill

Prof. Tom Yeh's avatar
Prof. Tom Yeh
May 28, 2026
∙ Paid

Library › Token Problems

  1. Tokenization

  2. Subword Tokens

  3. Non-Word Tokens

  4. Token Ratio

  5. Headroom

  6. Token Pricing

  7. Prompt and Completion

  8. The Billing Line

  9. Asymmetric Pricing

  10. Words to Cents

  11. Token Mix

  12. Usage Forecast

  13. Standing Instructions

  14. Fixed Overhead

  15. Budget Ceiling

  16. Token Allowance

  17. Two Speeds

  18. Output Bound

  19. Rate Cards

  20. Usage Audit

Given a bill, how do you work out how many tokens were used? A real model bill lists input and output on separate lines, each priced per million tokens. Divide each line's cost by that side's price per million, then scale up to tokens. Agent operators use this to audit usage after the fact, confirming that the bill matches what the logs show.

Paid members: the worksheet and its printable PDF are below ↓

This post is for paid subscribers

Already a paid subscriber? Sign in
© 2026 Tom Yeh · Privacy ∙ Terms ∙ Collection notice
Start your SubstackGet the app
Substack is the home for great culture