Illustration 3 : DOF effect between full frame vs 1.5x crop factor for the same picture composition and perspective (i.e. shooting from the same distance) accomplished by using the necessary different focal lengths.
5.6/(1.5) = F/3.7 (The above is for F/3.6 because there is no F/3.7 selection available in the online calculator.)
F/3.7 on the 1.5x crop factor camera will have the same DOF as F/5.6 on the full frame.
This also means that F/5.6 on the full frame will have a shallower DOF than F/5.6 on the 1.5x crop factor camera.
For the same composition and perspective, the full frame has a shallower DOF by a factor of 1.5 when compared to a 1.5x crop factor camera at the same aperture F number.
DOF = 1.81 ft x 1.5 = 2.72 ft (compared to the 2.76 ft shown above for the 1.5x crop factor camera).
I think the slight difference in all the numbers above is due to the fact that the actual crop factor is not exactly 1.50x but about 1.52x for those cameras used in the calculations.