Fifty cent coin bigger than one dollar?

Answer 1

Many years ago coins contained an amount of metal roughly equal to their face value, minus a tiny amount for the government to make a profit minting them. That meant that each coin's size was determined by how much each metal was worth. E.g. a cent contained one cent's worth of copper, a quarter contained 25¢ worth of silver, etc. In addition, dollars were also silver and they were much larger than halves - 38 mm vs. 31 mm in diameter.

About 50 years ago the cost of precious metals such as silver started to rise as demand increased. Silver coins became worth more to melt as scrap metal than to spend as money and people started hoarding them. To prevent collapse of their coinage systems many governments, the U.S. included, "decoupled" their coinage from precious metals. That's why dimes, quarters, and halves are now made of copper-nickel instead of silver.

Because coins no longer contained silver there was no economic reason to make them any particular size. However, the new dimes, quarters, and halves had to be compatible in vending machines so those coins were made the same size as the old silver ones. But no dollar coins had circulated for years so the Mint decided to make the new dollars smaller and lighter than before so they'd be more convenient to use and cheaper to manufacture.

Remember that some lower-denomination coins are larger than higher-denomination ones if they were made of different metals. Copper and nickel were less expensive than silver was, which is why dimes have always been smaller than cents and nickels.

Answer 2

More information is needed. Is this a U.S. gold piece, or a coin from Another Country? What's its date, condition, and mint mark? Please post a new question with additional details - thanks!