Equation 12 · Part 3 · The Real Cost of Running Claude in Production, Beyond the Per-Token Price

Symbol n

C = \frac{p_{\mathrm{in}}(n + \tau) + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}}(y + z)}{a}

n

What this part means

n occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

n occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionSymbol nArticle meaning

The passage around this formula

Collect the pieces above into one expression and the gap between a rate card and an invoice becomes explicit. For a single request, let n be new input tokens, w cache-write tokens, r cache-read tokens, y visible output tokens, z billed-but-invisible thinking tokens, and $\tau$ the fixed tool and system-prompt tokens added regardless of content. Let $p_{\mathrm{in}}$ , $p_{\mathrm{cw}}$ , $p_{\mathrm{cr}}$ , and $p_{\mathrm{out}}$ be the…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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