Resolution is determined by the camera settings, sensor type, and deBayering science of the camera manufacturer (see ADDENDUM section). The sizes change in fractional values: Full, 1/2, 1/4, 1/8, 1/16. Not all sizes are available with all camera raw formats.
Typically the sizes are based on sensor sizes, which won’t necessarily conform to common HD (1920 x 1080) and UHD (3840 x 2160) frame sizes. For example, full resolution for an ARRIRAW file may be 2880 x 1620, which is the actual sensor size. In another example, the Blackmagic URSA Mini Pro 12K camera starts at a full resolution of 12,288 x 5112, but its 1/2 resolution isn’t half of the 12K number. It’s actually 8K at 8192 x 3408.
Select the size that provides optimal performance, but still allows you to cleanly handle ‘punch-ins’ of a shot, stabilization, and visual effects. If you don’t need 12K and 4K will do nicely instead, then render at 4K. It will render more quickly and playback will be less taxing on your system.
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