Hello! It's great you're asking about the 1945 US half dollar. That coin is known as the Walking Liberty Half Dollar, a truly beautiful piece of American history.
To start, a 1945 half dollar is made of 90% silver, so its basic value is always going to be more than its 50-cent face value. Even a well-worn, circulated coin is worth at least its weight in silver, which fluctuates with the market.
The most important factor in determining a higher value is the coin's condition, or grade. For a coin that shows wear and tear from being used in circulation, its value is closely tied to its silver content. An example in "Extremely Fine" condition might carry a small premium above that.
The value really starts to climb for uncirculated coins, which look brand new with no wear. According to coin grading services, a typical uncirculated 1945 half dollar can be worth around $27 to $36. For a coin in a nicer uncirculated grade, like MS-65, the value is often in the neighborhood of $55. The price can rise significantly from there for coins in near-perfect condition, sometimes reaching $90 or more for an MS-66 grade.
You might also notice a small mintmark on the reverse (back) of the coin: a "D" for the Denver Mint, an "S" for the San Francisco Mint, or no mintmark if it was made in Philadelphia. For the 1945 issue, there isn't a major difference in value between the three mints as they are all considered common. It is noted, however, that the San Francisco (1945-S) coins are often found with a weak strike, which can affect their visual appeal to some collectors.
In summary, the value of a 1945 Walking Liberty Half Dollar starts with its silver content for worn coins and can increase to over $55 for a nice uncirculated example, with the absolute best-preserved specimens being worth considerably more.
