The 1804 dollar or Bowed Liberty Dollar was a dollar coin struck by the United States Mint, of which sixteen specimens are currently known to exist. Though dated 1804, none were struck in that year; all were minted in the 1830s or later. They were first created for use in special proof coin sets used as diplomatic gifts during Edmund Roberts' trips to Siam and Muscat.

Edmund Roberts distributed the coins in 1834 and 1835. Two additional sets were ordered for government officials in Japan and Cochinchina, but Roberts died in Macau before they could be delivered. Besides those 1804 dollars produced for inclusion in the diplomatic sets, the Mint struck some examples which were used to trade with collectors for pieces desired for the Mint's coin cabinet. Numismatists first became aware of the 1804 dollar in 1842, when an illustration of one example appeared in a publication authored by two Mint employees. A collector subsequently acquired one example from the Mint in 1843. In response to numismatic demand, several examples were surreptitiously produced by Mint officials. Unlike the original coins, these later restrikes lacked the correct edge lettering, although later examples released from the Mint bore the correct lettering. The coins produced for the diplomatic mission, those struck surreptitiously without edge lettering and those with lettering are known collectively as "Class I", "Class II" and "Class III" dollars, respectively.

From their discovery by numismatists, 1804 dollars have commanded high prices. Auction prices reached $1,000 by 1885, and in the mid-twentieth century, the coins realized over $30,000. In 1999, a Class I example sold for $4.14 million, then the highest price paid for any coin. Their high value has caused 1804 dollars to be a frequent target of counterfeiting and other methods of deception.

The Coinage Act of 1792, the legislation which provided for the establishment of the Mint of the United States (today the United States Mint), authorized coinage of multiple denominations of gold, silver and copper coins. According to the act, the dollar, or "unit", was to "be of the value of a Spanish milled dollar as the same is now current, and to contain three hundred and seventy-one grains and four sixteenth parts of a grain of pure, or four hundred and sixteen grains of standard silver". The act went on to state that the coin would be struck in an alloy consisting of 89.2 percent silver and 10.8 percent copper. The purity and weight standards outlined in the Act were based on the mean of several assays conducted on Spanish milled dollars. However, the dollars were mandated by Spanish law to contain 90.2 percent silver, and most of the unworn examples in circulation in the United States at the time contained approximately 1.75 grains (0.113 g) more than the silver dollars authorized by the Act. In 1793, President George Washington signed into law a bill which declared Spanish milled dollars legal tender, provided that they weighed no less than 415 grains (26.9 g), which meant that at the lowest weight allowed by law, the Spanish dollars would contain approximately 0.5 percent less silver than the United States dollar coins. As a result, the United States silver dollars and unworn Spanish dollars were largely forced out of circulation in accordance with Gresham's law; the lighter Spanish dollars were shipped in quantity for circulation in the United States, while the heavier pieces would be turned in to the Philadelphia Mint to be recoined into United States coinage to take advantage of the discrepancy in weight. At that time, silver bullion was supplied to the Mint exclusively by private depositors, who, according to the Coinage Act of 1792, had the right to have their bullion coined free of charge. As large silver coins were a preferred method of commerce throughout the world, especially China, a considerable number of the United States dollars requested by silver depositors were exported to satisfy that demand.

The first dollar coins, known as Flowing Hair dollars, were issued by the Mint beginning in 1794. By 1800, a majority of depositors requested their bullion be struck as silver dollars, which were then utilizing the Draped Bust design. This contributed to a shortage of small change in circulation, and as a result, the public became increasingly critical of the Mint. Mint Director Elias Boudinot began encouraging depositors to accept fractional coins, and the production of dollars began to decrease in relation to the smaller coins. Dollar coin production ceased in March 1804, although those pieces bore the date of 1803. In his 1805 report, Mint Director Robert Patterson stated that "[t]he striking of small coins is a measure which has been adopted to accommodate the banks and other depositors, and at their particular request, both with a view of furnishing a supply of small change, and to prevent the exportation of the specie of the United States to foreign countries." Though none had been struck for over two years, Secretary of State James Madison officially suspended silver dollar coinage on May 1, 1806, addressing a letter to Patterson:

Sir: In Consequence of a representation from the director of the Bank of the United States that considerable purchases have been made of dollars coined at the mint for the purpose of exporting them, and as it is probable further purchases and exportations will be made the President directs that all the silver to be coined at the mint shall be of small denominations, so that the value of the largest pieces shall not exceed half a dollar.

In 1832, commercial shipper Edmund Roberts began acting as an envoy to Asia on behalf of the United States government, with the intent of negotiating trade deals in the region. During his mission, he reached deals both with Said bin Sultan, the Sultan of Muscat and Oman, and the Phra Khlang of Siam (modern Thailand), an important financial minister of that nation. Roberts was given items which were to be presented as gifts to the officials with whom he was negotiating, but described them as being of "very mean quality, and of inconsiderable value". After the treaties were ratified in the United States, Roberts had to return to Siam and Muscat to receive approval from the representatives of those nations. In a letter to the Department of State dated October 8, 1834, Roberts decried the gifts of his previous journey as inadequate and insulting to his hosts in the Orient. In addition to several other items, he requested a set of coins as an appropriate offering to Said bin Sultan:

I am rather at a loss to know what articles will be most acceptable to the Sultan, but I suppose a complete set of new gold & silver & copper coins of the U.S. neatly arranged in a morocco case & then to have an outward covering would be proper to send not only to the sultan, but to other Asiatics.