Determining the length of an acre is not an easy thing to do. An acre is a way to measure a large plot of land. The acre could be 10' wide. The length of the fence would be far greater than a typical square acre.
You will need to measure one short side and one long side. This assumes that the land is flat. If it has hills the length will be greater
than if the land is flat. An acre is measured as a crow flies. You don't get less land because it has hills.
You would also make sure you know where the boundary lines are before building on your land. Get the land surveyed. If you build even a few inches into a neighbor's property you may be setting yourself up for a law suit.
I would make my purchase at a store that allows returning unused
supplies. I would take the measurements to the store and the fence specialist can estimate the total cost which includes posts, cement and fasteners.
The other considerations that you need to decide on is if your neighbor is willing to allow you to remove his old fence. It is his fence no matter how old it is and it is important that you get his permission to remove his fence. It would also be good to show the neighbor what your new fence will be like. The neighbor may be willing to share the cost of the part on their land, but don't count on it. If you want the fence completed, you will most likely pay for it so you get it done the way you want it.
I still have not answered your question but I hope you will find this information useful.