According to the United States Mint, the purpose of having different sized coins is to make it easier to identify them. The size of a coin is not determined by its value, as demonstrated by the fact that a nickel is worth less than a dime but is larger in size.
The United States Mint explains that the sizes of coins are meant to be convenient. United States coins were first produced in 1793. The standard coin was the silver dollar, and the rest of the coins were sized in proportion to the dollar, with the exception of the penny. The five-cent coin contained one-tenth the amount of silver as the dollar, the ten-cent coin contained one-tenth the amount of silver, the quarter contained one-fourth and the half dollar contained half of the amount of silver. However, these sizes proved to be inconvenient.
The five-cent coin, or the nickel, was originally half the size of the dime and too small for the public to conveniently handle. Therefore, the United States Government adopted a new five-cent coin in 1866. The government made the coin larger and also changed its metallic content from silver and copper to a combination of copper and nickel.