The 1864 Indian Head Cent (IHC) is kinda special. To answer a 'What's It Worth?' question, we must first determine which of the three different 1864 IHCs you have. Sure enough, there were three different cents minted that year, and each carries a different value today.
(Note: for coins not dated 1864, please refer to this CoinQuest link.)
1864 is the date the US mint stopped producing IHCs made out of copper-nickel and started producing IHCs made out of bronze. Bronze IHCs are thin and a dark, coppery color, like modern pennies. In contrast, copper-nickel IHCs are thick and have a light brown color. See the picture for a side-by-side comparison. You can see the design is the same, but the color is different. The copper-nickel IHCs are thicker and heavier than the bronze coins.
Also in 1864 a few IHCs were produced with a tiny letter L on one of the Indian's hair ribbons. The L is turned sideways and it is very small. You will probably need a magnifier to see it. If your coin is worn, it might be worn off. Mr. Longacre designed the coin and his initial 'L' appears on some specimens.
As to value, the copper-nickel and no-L bronze specimens are both worth around $10 in worn condition, with the former being worth a bit more and the latter a bit less. The L bronze coin, however, catalogs around $50 even when well worn.
Remember that catalog value is an inflated value and applies only to coins without problems such as scratches, spots, stains, cleanings or mutilations. Please check our Terminology page for a more thorough explanation.
In better states of preservation the 1864L coin pulls even further ahead of the others. Here is what the catalogs says for the three coins in average circulated condition:
1864 Copper Nickel $50
1864 L Bronze $200
1864 No L Bronze $40
With your description of 'little or no wear' you have a valuable coin in all cases. The specifics of the numismatic grading systems are beyond the scope of CoinQuest to explain, but most coins with 'little or no wear' fall into our broad category of 'well preserved, with values looking like this:
1864 Copper Nickel $100
1864 L Bronze $280
1864 No L Bronze $70
If you have an IHC in almost uncirculated condition, figure a catalog value between the one above and the one below, depending on the eye appeal of the coin.
If you go all the way to fully uncirculated condition, what numismatists call MS63, you get:
1864 Copper Nickel $250
1864 L Bronze $500
1864 No L Bronze $110
DO NOT CLEAN YOUR COIN. CLEANING RUINS VALUE.
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