What does this equation mean?

OpenAI’s newer patch-tokenized models cover an image with 32-pixel-square patches and cap the total patch count per image, resizing proportionally down to fit the cap when an image would otherwise exceed it — for example, resizing an 1800-by-2400-pixel image down to 1056 by 1408 pixels to land at 1,452 patches against a 1,536-patch budget — while a detail: low setting instead fixes the cost at 85 tokens regardless of the original size by resizing to 512 by 512 first, and an original or auto detail setting preserves full resolution for coordinate-sensitive tasks at correspondingly higher token cost [ 6 ] . Anthropic’s documentation states the rule for Claude directly: an image costs $\lceil$ w/28 $\rceil$ $\times$ $\lceil$ h/28 $\rceil$ visual tokens, with a maximum native resolution — expressed as both a long-edge limit and a total visual-token cap — beyond which the image is downscaled before that formula is applied; the same documentation gives worked cost examples, noting that a 1920-by-1080 image costs on the order of 1,560 tokens on the standard resolution tier once resized, versus roughly 2,691 tokens if processed at full resolution on the high-resolution tier [ 8 ] . Google’s Gemini documentation prices video by time rather than by frame count directly: video is sampled at one frame per second by default, each sampled frame costs 258 tokens at default media resolution, and the documented aggregate rate is approximately 300 tokens per second of video at default resolution versus approximately 100 tokens per second at a lower medi$a_r$esolution setting, with audio tracked separately at 32 tokens per second [ 9 ] . These are vendor-documented mechanisms, not a ranking — the right comparison for any given workload is each vendor’s own formula applied to that workload’s actual image and video dimensions, not a headline number lifted from one vendor’s example and compared against another’s.