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Published equation contexts

costimage=Ntok(H,W)⋅ptok\mathrm{cost}_{\mathrm{image}} = N_{\mathrm{tok}}(H,W) \cdot p_{\mathrm{tok}}

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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 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…

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costimage=Ntok(H,W)⋅ptok\mathrm{cost}_{\mathrm{image}} = N_{\mathrm{tok}}(H,W) \cdot p_{\mathrm{tok}}

Equation 5 · Foundation Models

What Multimodal AI Actually Costs, Modality by Modality

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 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…

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