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Equation 4 · Part 5 · What Multimodal AI Actually Costs, Modality by Modality

=

Ntok(H,W)=⌈HP⌉×⌈WP⌉N_{\mathrm{tok}}(H,W) = \left\lceil \frac{H}{P} \right\rceil \times \left\lceil \frac{W}{P} \right\rceil
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A single formula covers all three counting schemes if the tile or patch edge length is left as a free constant P , specific to the vendor: Ntok(H,W)=⌈HP⌉×⌈WP⌉N_{\mathrm{tok}}(H,W) = \left\lceil \frac{H}{P} \right\rceil \times \left\lceil \frac{W}{P} \right\rceil. with a request’s image cost simply costimage\mathrm{cost}_{\mathrm{image}} = Ntok(H,W)N_{\mathrm{tok}}(H,W) ⋅\cdot ptokp_{\mathrm{tok}} at the model’s own per-token price ptokp_{\mathrm{tok}} . The constant differs — 28 pixels for Claude, 32 for GPT-5.4, roughly 768 divided into geometry-dependent tiles for Gemini — but the shape does not: token count, and therefore cost, scales with the area of the image, not its linear size. Doubling both width and height quadruples the token bill under every one of these three schemes. That is the single fact behind…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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