You have what's called a "flan". Flans are created when a coin blank accidentally slips through the Mint without getting put into the press that strikes the design.
Assuming the flan is a modern clad blank (look for the copper edge) its value as of mid-2011 is about $5 if it has reeding (ridges) on the edge and a raised rim, and about $10 without those features.
If it's an older silver blank, those values go up at least 10 times.
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These unstamped quarter errors generally sell for a couple dollars.
You have what's called a "flan". It's a coin blank that was put through the machine that puts on the edges, but was accidentally missed when the blanks were fed through the press that strikes images on the front and back. If it's a blank for a modern clad quarter with a copper core (check the edge) it might sell for about $5. However if it's an old silver quarter it could be worth 10 or 12 times that much.
Check with any local coin collector for sure, but this coin can be worth a LOT of money.
The value of a quarter with one side stamped heads and the other side blank would be 25 cents in terms of its monetary value in the United States. The design on the coin does not affect its face value or purchasing power. This type of coin may have been altered or misprinted, but as long as it is recognized as legal tender, it can be used for transactions at its full 25-cent value.
The value of a 1951 quarter will value depending on the condition and where it was minted. The value ranges from 3.52 to 4.30.