How does a flat image fit on a scope screen?

I had to calculate the dimensions of a flat DCP (1920x1080) on a scope (aspect ratio 2.39) cinema screen, and this is a perfect task for the aspect fit calculator.

Let’s start with the screen resolution: a 2K DCP projector has a resolution of 2048 x 1080 pixels. When the projector is in ‘scope’ mode, the lens is zoomed in so that the 2048 pixels cover the whole width of the screen. This means that only the inside 2048 x 858 pixels (aspect ratio 2.39) is used.

The flat image will have to be rescaled to fit in that area. Concretely:

Full image resolution = 1920 x 1080

Is rescaled to = 1526 x 858 (79%)

and then padded (pillar-boxed) to 2048 x 858 (134%)

via 1920x1080 image on scope screen