Why does a prompt chain cost more than the sum of its prompts?

In a waterfall chain each step's output is appended to the input of the next step. By the final step you are re-sending the system prompt plus every prior output as input, so input tokens grow at each step and dominate the total cost.

How can I cut the cost of a long chain?

Summarise intermediate outputs before passing them on, drop context that later steps do not need, use a cheaper model for the early high-volume steps, or reset the chain and start fresh once enough context has accumulated.

Is the carried context the same as conversation memory?

It is the same mechanism. Each turn re-sends the accumulated history as input. The calculator models this growth explicitly so you can see when carrying full context stops being worth the cost.

Does output get cheaper as the chain grows?

No. Output tokens are billed at the same per-token rate at every step. What grows is the input side, because you re-send more accumulated context each time.

Is anything sent to a server?

No. The calculation runs entirely in your browser. Nothing you enter is uploaded or stored.

Waterfall Prompt Chain Cost Calculator

Cost a sequential prompt chain accurately

A “waterfall” chain feeds each step’s output into the next step’s input. That makes the carried context grow at every step, and because input tokens are billed each time, the total cost rises faster than people expect. This calculator shows the per-step token growth and cumulative bill so you can size a pipeline before you build it.

How context accumulates

At step n, the input is the system prompt plus the original input plus every prior step’s output:

input(n)  = system + initial_input + sum(output(1..n-1))
cost(n)   = input(n)/1M x in_price + output_per_step/1M x out_price
total     = sum(cost(1..steps))

The system prompt and initial input are re-sent on every step, and each new output is permanently added to the carried context, so the input grows linearly while the cost grows roughly quadratically with the number of steps.

Tips for cheaper chains

Summarise between steps. Replacing a long output with a short summary before passing it on flattens the input-growth curve dramatically.
Use a cheap model for high-volume early steps and reserve the expensive model for the final reasoning step.
Reset when you can. If later steps do not truly need the full history, start a fresh request with only the relevant carry-over.