The price of an authentic katana can vary widely depending on several factors, including its quality, craftsmanship, materials used, and historical significance. Traditional, hand-forged Japanese katanas, crafted by skilled artisans, tend to be quite expensive.

On average, a high-quality, authentic katana made by a renowned swordsmith can range from several thousand dollars to tens of thousands of dollars. Exceptional pieces or those with historical value can fetch even higher prices.

It's worth noting that there are also modern reproductions and lower-quality katanas available at lower price points, but they may not possess the same level of craftsmanship and historical authenticity as traditional, high-end katanas.

If you're interested in purchasing an authentic katana, it is recommended to consult with reputable sword dealers, collectors, or experts who can guide you through the process and help you find a genuine piece that suits your needs and budget.