Conversion from oil heat to natural gas heat can cost from $4,000.00 to $8,000.00 and could be even more depending on what needs to be done.
It will cost less if you just need to change out the oil furnace for a natural gas furnace and already have a natural gas line coming into your home.
If you need to have a natural gas line run to your home then it will add to the cost.
However the natural gas company in most places should cover the cost of running the natural gas line to your home depending on how close the natural gas line is to your house.
Converting to natural gas though will save you a lot of money over the years and will pay you back for converting to natural gas since natural gas is a much cheaper heat source than heating oil is.