How is the cost of an LLM request worked out?

Each token count times its rate per million tokens, divided by a million: input at the input rate, output at the output rate. The two add up to the request. Multiply by the requests a day and by 30 for the month.

What about cached input?

A model with a cached rate bills the repeated part of a prompt (a system prompt, a document sent every turn) at that rate, which is lower than the input rate. The calculator prices everything at the input rate, so on a long chat or an agent loop the real bill is lower.

Is anything I type sent anywhere?

No. The rates arrive with the page and the arithmetic runs in your browser.

Can I get the same estimate from the API?

Yes. POST https://api.relayswitch.io/v1/estimate with input_tokens and output_tokens returns the cost of that request on every model, no key needed.

Will my bill match the estimate?

It is an estimate at today's rates. A real request is billed on the model's own token count. The console lists every request with its tokens and its charge.