How do you determine your vision in terms of 20-X from your contact lens power in diopters?
It cannot be done with any precision.
With a near-average pupil size, an eye capable of good vision when corrected will have about 20-200 vision at -3.00 dioptres uncorrected, or 20-24 to 20-60 at -1.00 but a young person will not be nearly so badly affected with the equivalent + prescription.
Pupil size will make an enormous difference, the "pinhole-camera" effect. With a 1mm pinhole in a piece of card held near the eye, the vision can be surprisingly good, whatever the amount of missing correction.
With the contact lens correction in place, the vision will depend on the accuracy of the prescription and the optical and neurological quality of the eye. A needed -10 contact lens might give 20-20 vision, but an eye with cataract might have poor vision even if not needing any optical correction. A strong contact lens would not improve the situation but worsen it.
There is no exact correlation because pupil size enters into it. The more light in the room the smaller the pupil and the better the vision for a given diopter. Only an approximation can be given. Also a plus diopter correction will affect visual acuity more than a minus diopter correction because of the way accommodation can neutralize some of the minus power. The younger the individual the greater the amount.