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Equation 1 · Part 2 · Where Multimodal Frontier Models Actually Differ, Beyond the Marketing

Symbol f

cvideo≈(f×τframe)+τaudioc_{\text{video}} \approx (f \times \tau_{\text{frame}}) + \tau_{\text{audio}}
ff

What this part means

the sampling rate.

Its job in the formula

f is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

where, at default resolution, the sampling rate f is one frame per second, each frame costs τframe\tau_{\text{frame}} ≈\approx 258 tokens, and the audio track costs τaudio\tau_{\text{audio}} ≈\approx 32 tokens per second — giving cvideoc_{\text{video}} ≈\approx 290 tokens per second, close to the approximately 300 tokens per second Google documents directly for default-resolution video [ 5 ] .

The passage around this formula

…make the architectural claim concrete rather than rhetorical. Gemini’s video pricing bundles the visual and audio streams into one per-second cost: cvideo≈(f×τframe)+τaudioc_{\text{video}} \approx (f \times \tau_{\text{frame}}) + \tau_{\text{audio}}. where, at default resolution, the sampling rate f is one frame per second, each frame costs τframe\tau_{\text{frame}} ≈\approx 258 tokens, and the audio track costs τaudio\tau_{\text{audio}} ≈\approx 32 tokens per second — giving cvideoc_{\text{video}} ≈\approx 290 tokens per second, close to the approximately 300 tokens per second Google documents directly for…

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Sources cited in the surrounding passage

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