A katana, when properly forged and sharpened, can be extremely sharp. It's often said that a high-quality katana can slice through a silk scarf that falls across the blade, or cut a piece of paper that's merely touched to the edge.

The process of creating a katana involves folding the steel many times, leading to thousands of layers that can add to the blade's strength and sharpness. A differentially hardened edge, which characterizes many katanas, can be honed to a very fine edge while maintaining a more flexible spine, making it sharp yet resilient.

However, it's important to note that the extreme sharpness of a katana is just one aspect of its effectiveness. The overall quality of the blade, including factors such as its balance and the quality of the steel, are also crucial. Furthermore, a katana's cutting effectiveness is highly dependent on the technique of the swordsman. Japanese sword arts, like Iaido and Kendo, spend considerable time teaching proper cutting technique to maximize the sword's potential.

Regardless, katanas and other swords are dangerous weapons and should be handled with extreme care. Always ensure that you're properly trained and take necessary safety precautions when handling any blade.