Shooting with 2 formats, Full Frame (FF) and Micro43 (M43) it's OBVIOUS Depth of Fields (DOF) are not equal for the same focal length.

FYI - When I am shooting, i don't do math, I just look thru the viewfinder and I use DoF preview to assess the DOF.

But I was curious if there was a relation, something like the crop factor. But for DoF instead of for field of view. Various u-tube tutorials describe it differently. Some seem to contradict one another. One person said divide by the crop factor but that seems wrong. One of the u-tube videos said with the same framing you get the same field of view. But that's difficult to access because the aspect ratios are different.

So I used my iPhone Application, Simple DoF and did a few comparisons.
Summary below, the columns are:

F-stop focal length focus distance DOF_calculation in feet and inches.
(Apologies to the metric people)

Full Frame
F5.6 50mm 5' 1' 0.13"

M43
F5.6 50mm 5' 0' 6.02"
F5.6 35mm 5' 1' 0.51"
F5.6 25mm 5' 2' 1.48"

So it looks like 35mm gives a pretty close DOF to FF. That's interesting because 35mm is
approximately what you get dividing by the square root of the crop factor.

Let's try it with F4
FF
F4 50mm 5' 0' 8.53"
F8 50mm 5' 1' 5.33"
F16 50mm 5' 3' 0.93"

M43
F4 35mm 5' 0' 8.80"
F8 35mm 5' 1' 5.88"
F16 35mm 5' 3' 2.26"

Again M43 @ 35mm focal length is close to FF @ 50mm focal length.

Let's try it with FF@100mm and M43@71mm

5' Focal distance
FF M43
100mm 71mm
F4 2.05" 2.08"
F8 4.11" 4.16"
F16 8.24" 8.34"

15' Focal Distance
FF M43
100mm 71mm
F4 1' 7.37" 1' 7.34"
F8 3' 3.09" 3' 3.02"
F16 6' 9.01" 6' 8.36"

There is probably some mathematical explanation for this, maybe someone here with optics knowledge can explain it. Or is it just a coincidence?