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I'm not sure if the reduction percent has been measured yet for the PS4 Slim so this thread either announces or confirms it.

Using the size comparison images I worked out these dimensions.

PS4 - (w)275mm x (d)273mm(303mm overall) x (h)55mm = 4,129,125mm3

PS4 Slim - (w)259mm x (d)246mm(268mm overall) x (h)40mm = 2,548,560mm3

That gives us a reduction of 38.3%, similar to the recent reduction of the XB1.

Note: The sizes I gave for depth are not the overal depth. Because of the shape the PS4 sticks out 30mm more and the Slim 22mm more. However using the dimensions for the top side with console height gives us the volume because the front and back of the console slant at the same angle.