1. Condition: The condition of the nickel is a significant factor in determining its value. A coin in mint state (MS) or near mint state (MS-65) will be worth more than a worn or damaged coin.
2. Rarity: The 1881 three-cent nickel is considered to be a relatively common date in the series, with a reported mintage of over 10 million coins. However, certain varieties or errors can make a particular coin rarer and more valuable.
3. Certification: Having the coin certified by a reputable grading service like the Numismatic Guaranty Corporation (NGC) or Professional Coin Grading Service (PCGS) can add value and authenticity to the coin.
In general, a US Liberty Head 1881 three-cent nickel in good condition can be worth around $10 to $20. Nicer examples in mint state or with special varieties can command higher prices, potentially reaching hundreds or even thousands of dollars.
It is advisable to consult with reputable coin dealers or experts in numismatics to obtain an accurate appraisal of the value of your specific coin based on its condition, rarity, and current market trends.