Should Developers Bill for Claude Like an Oil Change?

Service invoices usually have "Materials" and "Labor" sections. For example, an oil change might cost $100 for the oil and $40 for labor. Clear, itemized, nobody argues.

Lately I've been wondering: should software development bill the same way?

The idea

A developer runs Claude as a tool. The session costs something per hour — tokens, subscriptions, reasoning effort. The developer's own time costs something too. So an invoice could look like:

Materials: Claude usage — $20/hour Labor: developer — $40/hour Total: $60/hour

It's honest. It shows the client where the money goes. And it raises a genuinely interesting question nobody seems to have answered properly.

What does an hour of Claude actually cost?

Not the sticker price of a subscription. The real number:

tokens burned
context windows rebuilt
thinking effort spent
time wasted when the model goes in circles

Anyone who runs AI tools daily knows the sticker price is a lie. The real cost is somewhere between "nothing" and "surprisingly a lot".

The honest part

There are three ways to think about it:

Claude is a tool — like a lathe or a license. You don't bill the client for your drill bits separately; you fold them into your rate. Same logic applies to AI.
Claude is a colleague — it does real work: writes code, reviews, researches. If a junior dev billed separately, why shouldn't the AI?
Claude is overhead — like office rent or electricity. Invisible in the invoice, priced into the rate.

All three are defensible. The problem is nobody publishes the math, so clients can't tell a fair rate from an inflated one.

The question

Has anyone actually calculated how much an hour of using Claude costs? Not the subscription. The real, all-in number.

I haven't seen good math on this. Maybe it's time someone published it.