Arc Breakdown voltage
it depends on many things, assuming you are working with air there is a set number for breakdown at normal atmospheric pressure which is 3kV/mm

For breakdown on gases

atmospheric pressure will affect this(known as pashchen's law)
humidity also will divert this value
also remember this not a certain thing and usually the value given is for 50% chance of an arc happening.

Now the relation with voltage is mostly a limit of electric field that can be applied to the air before it becomes conductive.