What is the value of liberty one dollar coins?

It depends on the year, mintmark and condition of the coin.

There is no set "Liberty" dollar coins since all dollar coins prior to the introduction of the Eisenhower dollar in 1971 show a personification of Liberty. Their value depends greatly on the specifics of the coin and range anywhere from $1 (circulated common Eisenhower dollar) to $1 million+ (well-preserved flowing hair dollars, 1804 dollars)