There are no counties in the District of Columbia, But it is considered a county-equivalent and state-equivalent administrative unit by the United States Bureau of the Census
Source of underlying map: United States Bureau of the Census
I have visited 4 Quadrants / 8 Wards = 100% of Quadrants / Wards in District of Columbia
District of Columbia Map
Quick facts about District of Columbia
Location: See map on the right side of the page.
Size(1): 61 square miles. If the District of Columbia was a state it would be by far the smallest. Rhode Island, the smallest current state, is 17 time larger than the District of Columbia. Alaska, the largest state, is more than 9,000 times larger than the District of Columbia!
Population(2): 550,521 people. If the District of Columbia was a state it would have the second lowest population. The next more populous state would be Vermont and the next less populous state would be Wyoming.
Population Density: 9,024.93 people per square mile. If the District of Columbia was a state it would have by far the greatest population density due to its urban environment. The next less densely populated state would be New Jersey.
Bordering States: If the District of Columbia was a state it would share a border with 2 states: Maryland and Virginia.
Capital: Although the District of Columbia serves as the capital of the United States, there is not separate capital for the District of Columbia itself.
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United States Capitol Building on a Brisk Winter Day
Interesting District of Columbia geography trivia
The District of Columbia was originally laid-out as a square with 10 mile sides, for a total of 100 square miles. It is only 61 square miles now. The other 39 square miles were returned to Virginia in 1847, forming what is today Arlington County and much of the City of Alexandria.
An individual can stand in all four quadrants of the District simultaneously by visiting the center of the dome room in the United States Capitol building.
Because of its unique Constitutional status, the District of Columbia does not have voting representation in Congress. As a symbol of protest, Washington DC license plates feature the motto "Taxation without Representation."
Possible Counties if the District of Columbia was a State
Nobody knows for certain what country structure would exist in the District of Columbia if it were to become a state. There are two leading candidates though. First, the area could be divided into its established quadrants in which case their would be 4 counties. Alternately it could be divided into its existing Ward structure in which case their would be eight counties. Those Quadrants / Wards that I've visited are in bold. If I have a photograph or other item associated with a Quadrant / Ward somewhere else on my website, there will also be a link.
Quadrants
Source of underlying map: Wikipedia from a public domain document