It's not tokens times price.
It's the history you resend.

Most “how much does an AI agent cost” posts multiply an expected number of tokens by a provider's list price and stop there. That works for a single request-response call. It breaks down for an agent, because the Messages/Chat Completions APIs are stateless — every tool-calling turn re-sends the entireconversation history as input, not just the new message. A 20-turn agent run doesn't cost 20x a single turn; it costs roughly 20x the average context size across those turns, which is much larger than the first turn and much smaller than the last one, and without prompt caching every one of those resends is billed at full input price.

This is also exactly where prompt caching earns its keep, and why a cost estimate that ignores it is not just imprecise but structurally wrong for any provider whose agent workloads use caching by default. The rest of this post is built on official pricing figures — no invented per-token numbers — plus a calculator that runs the actual resend-and-cache math instead of a flat multiplication.

This calculator simulates an agentic loop turn by turn: each turn adds new tokens (a tool result, a user message) to a growing conversation, re-sends that accumulated context as input, and bills a fresh output. With caching enabled, everything before the newest addition is billed at each provider's cache-read rate instead of full price — for Anthropic that's roughly a 90% discount off input price, per its own published pricing documentation, with only the newest chunk paying a cache-write premium. Try dragging turns from 5 to 50 with caching off, then on — the gap widens dramatically as conversations get longer, which is exactly when caching matters most.