What does this equation mean?

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: $N_{\mathrm{tok}}(H,W) = \left\lceil \frac{H}{P} \right\rceil \times \left\lceil \frac{W}{P} \right\rceil$. with a request’s image cost simply $\mathrm{cost}_{\mathrm{image}}$ = $N_{\mathrm{tok}}(H,W)$ $\cdot$ $p_{\mathrm{tok}}$ at the model’s own per-token price $p_{\mathrm{tok}}$ . 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 essentially every dollar figure in the rest of this section, and it is also why “send a smaller image” is the one universally effective cost lever a caller has, across all three vendors, without changing anything about the model itself.