Regarding types of Japanese Sword

Tachi

Tachi is 2 feet (about 60cm) with hanging its edge down from hip by Samurai.
It needed to be made considerable length and curve, when fighting style was mainly cavalry battle on the end of Heian period through the beginning of Muromachi period.
It exhibits by turning an edge down.

Katana

Katana is 2 feet (about 60cm). The edge was turned up and was very used for the waist.
It needed to be made shorter and flatter than Tachi as a result of a shift from cavalry to infantry action on Muromachi period through the end of Edo period.
It exhibits by turning an edge up.

Wakizashi

Wakizashi is no fewer than 1 foot, nor more than 2 feet length used for the waist like the sword. Less than 40cm in a short sword is called Kowakizashi.

Tanto

Tanto is less than 1 foot, and called Koshigatana or Aikuchi.