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Equation 7 · Part 6 · What Multimodal AI Actually Costs, Modality by Modality

=

Ntok(video)=t(f⋅τframe+τaudio),N_{\mathrm{tok}}(\mathrm{video}) = t \left( f \cdot \tau_{\mathrm{frame}} + \tau_{\mathrm{audio}} \right),
=

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

Video inherits the same per-tile arithmetic and multiplies it by time. Google is again the most specific vendor to check, because Gemini’s video-understanding documentation breaks the rate down by component: at default media resolution, each sampled frame (taken at one frame per second) costs about 258 tokens and the accompanying audio track costs about 32 tokens per second, for a documented total of “approximately 300 tokens per second of video.” At the model’s low-resolution setting, the same second costs about 100 tokens — 66 for the frame plus 32 for audio [ 6 ] . In the notation above, that is Ntok(video)=t(f⋅τframe+τaudio)N_{\mathrm{tok}}(\mathrm{video}) = t \left( f \cdot \tau_{\mathrm{frame}} + \tau_{\mathrm{audio}} \right). where t is duration in seconds, f the sampling rate, and…

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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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.