What is the value of a 1955 US quarter?

1955 is a common year for Washington Quarters. In circulated condition its value is almost totally based on the price of silver and how worn the coin is. The price of silver changes every day, so check a newspaper or financial site for the current price, then multiply by 0.18 for a rough retail value. A dealer will pay half to 2/3 of that amount.

Uncirculated values depend on whether there's a mint mark above the R in QUARTER:

No mint mark (Philadelphia): $8.91 to $450.00 depending on quality

"D" mint mark (Denver): $8.91 to $750.00