You won't get exactly 50% shallower DOF, due to the 2 factors mentioned above, plus the DOF graph is a curve rather then linear. But it is close, so you can use 50% as a rough guage.

For example, let's use the

DOF Mater online DOF calculator, and assuming aperture of f/2.8 and subject-to-camera distance of 5m:

Full frame (e.g. D3): f=75mm, f/2.8, d=5m => DOF = 4.65 to 5.4m, total 0.75m

Cropped frame (e.g. D90): f=50mm, f/2.8, d=5m => DOF = 4.5 to 5.63m, total 1.13m

And 0.75 x 1.5 = 1.125 != 1.13 but close.

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