In the first instance, it should be made clear that a prescription for contact lenses is not the same as a prescription for eyeglasses. So, one can say that it is not possible to do a direct eyeglass to contact lens conversion. However, the eyeglass prescription can be used in the construction of the contact lens prescription, by making allowances for the change in distance between the corrective material and the optic lens.
The prescription and fitting for contact lenses involves a good deal more than a similar prescription and fitting for spectacle lenses. For those new to wearing contact lenses, the fitting will be very new. This will again vary, depending on the type of lens being fitted.
The matter is further complicated depending on the type of lens being prescribed. Hard lens fit the eye differently to soft lenses, so allowances have to be made depending on the material being used for the contact lens itself.
Your contact lens practitioner will probably start by doing a refraction to determine the refractive error of your eyes, and then take further measurements, such as the tear film assessment and the corneal curvature to determine the best fitting contact lens and best material for your eyes. An exam and fitting for contact lenses can include your spectacle prescription.
One should also be aware of the increased maintenance cost of contact lenses. This includes more regular checks on your eyes, and more frequent replacement of the lenses. You should also include the cleaning and storage materials in the cost of lenses because they are a critical part of your eye health care.
In summary, whilst your eyeglass prescription can be used to help with the contact lens prescription, it cannot be assumed that the former can be used to create the latter.