The value of a 1951 US quarter depends on its condition and rarity. In general, a circulated 1951 US quarter is worth around 25 cents. However, if the quarter is in uncirculated condition, its value can be significantly higher. For example, a 1951 US quarter in mint state condition can be worth upwards of $10.
There are also some 1951 US quarters that are considered to be rare and valuable. For example, the 1951-S quarter, which was minted in San Francisco, is considered to be one of the rarest quarters in the world. A 1951-S quarter in uncirculated condition can be worth upwards of $100.