Vienna stands at 48.2082° N, 16.3738° E on the Danube River in northeastern Austria, positioned where the river emerges from the Alps into the Vienna Basin. The city occupies 414.78 square kilometers, making it Austria's smallest federal state by area but its largest by population. As of January 2024, Vienna's population stands at 1,982,132 residents within city limits, with the metropolitan area containing approximately 2.9 million people. This represents roughly one-fifth of Austria's total population of 9.1 million. The Danube bisects the city, flowing 290 kilometers through Austrian territory from the German border near Passau to the Slovak border east of Vienna, with the river's width varying from 200 to 400 meters through the urban sections.
The administrative structure divides Vienna into 23 districts (Bezirke), numbered spirally outward from the first district Innere Stadt at the historic core. Each district maintains its own administrative office while the city functions as both a municipality and one of Austria's nine federal states. The first district contains the majority of imperial-era landmarks within an area of 2.88 square kilometers, bounded roughly by the Ringstrasse circular boulevard. This boulevard replaced Vienna's defensive walls in the 1860s following Emperor Franz Joseph I's decree of December 20, 1857, creating a 5.3-kilometer ring road lined with monumental buildings constructed between 1860 and 1890. The demolition of fortifications that had protected Vienna since the 13th century opened 1,057 acres for development, fundamentally reshaping the city's geography.
Vienna's elevation ranges from 151 meters above sea level at the Danube floodplain to 542 meters at Hermannskogel hill in the Vienna Woods (Wienerwald), which covers approximately 105 square kilometers of the city's western districts. The Vienna Woods represent the easternmost foothills of the Northern Limestone Alps, consisting primarily of beech and oak forests protected as a UNESCO Biosphere Reserve since 2005. The geological foundation beneath Vienna transitions from Alpine sediments in the west to the Vienna Basin's Tertiary deposits in the east, with the city sitting atop layers of sand, gravel, and clay deposited over millions of years. This geological composition creates numerous natural springs, with the most famous being the Hochquellenleitung, Vienna's primary water supply system built between 1869 and 1873, which transports spring water 95 kilometers from the Rax-Schneeberg mountains via gravity alone.
The Innere Stadt preserves Vienna's medieval street pattern, though nearly all buildings date from the 17th century or later following repeated destructions during Ottoman sieges and fires. St. Stephen's Cathedral (Stephansdom) anchors the district at Stephansplatz, its South Tower reaching 136.44 meters, completed in 1433 after 75 years of construction. The cathedral's tiled roof displays the double-headed eagle of the Habsburg monarchy using 230,000 glazed tiles, reconstructed after Allied bombing on April 12, 1945, destroyed the original 15th-century roof. The current structure measures 107.2 meters in length and 34.2 meters in width, with the main nave ceiling rising 28 meters. The North Tower remains incomplete at 68.3 meters, abandoned in 1511 when construction funds were redirected to fortifying Vienna against Ottoman invasion. Archaeological excavations beneath the cathedral between 2000 and 2017 revealed Roman ruins and a cemetery containing remains dating to the 4th century, confirming continuous habitation at this site for at least 1,700 years.
The Hofburg Palace complex occupies 240,000 square meters across the first district, having served as the principal Habsburg residence from 1279 until the monarchy's dissolution in 1918. The complex comprises 18 groups of buildings, 19 courtyards, and 2,600 rooms constructed over seven centuries. The oldest surviving section, the Schweizerhof (Swiss Court), dates to 1275, with the current structure largely from the 16th century. The Imperial Apartments occupy the Reichskanzleitrakt wing built between 1726 and 1730, where Emperor Franz Joseph I lived from 1857 until his death on November 21, 1916. The Spanish Riding School operates from the Winter Riding Hall built between 1729 and 1735, where Lipizzan horses have performed classical dressage continuously except during World War II evacuations. The Neue Burg, the complex's newest section, was completed in 1913 but never served its intended purpose as Emperor Franz Joseph's residence due to his preference for Schönbrunn and his death three years later.
Schönbrunn Palace stands 5.8 kilometers southwest of the Innere Stadt in the Hietzing district, constructed between 1696 and 1712 to designs by Johann Bernhard Fischer von Erlach for Emperor Leopold I. The palace contains 1,441 rooms, though only 40 rooms open to public tours. The main building measures 180 meters in width and 120 meters in depth, with the facade painted in distinctive "Schönbrunn Yellow" (Schönbrunner Gelb), a shade Maria Theresa selected in 1743. The palace gardens extend 1.2 square kilometers, designed in French Baroque style with geometrically arranged flowerbeds, fountains, and tree-lined walkways. The Gloriette monument crowns a hill 60 meters above the palace, built in 1775 at a distance of 380 meters from the main building, providing views across Vienna to the Carpathian Mountains 60 kilometers east on clear days. The Neptune Fountain at the garden's center measures 32 meters in width, completed in 1781. The Palm House, constructed in 1882, contains 4,900 square meters of glass-enclosed growing space and remains the largest of three surviving imperial glasshouses, maintaining temperatures between 8°C and 35°C across different climate zones.
The Belvedere Palace complex comprises two Baroque palaces separated by formal gardens on a hillside in the third district. Prince Eugene of Savoy commissioned the Lower Belvedere in 1712 and the Upper Belvedere in 1723, designed by Johann Lukas von Hildebrandt. The Upper Belvedere stretches 135 meters in length, its central octagonal hall rising 20 meters to a ceiling fresco painted by Carlo Carlone in 1721. The Marble Hall on the upper floor measures 16 by 17 meters with walls clad in red marble from Salzburg and Adnet quarries. The palace gained historical significance on May 15, 1955, when the Austrian State Treaty was signed in the Marble Hall, ending Allied occupation and establishing Austria's permanent neutrality. The treaty's signing occurred at 11:15 AM with foreign ministers from the four occupying powers present, witnessed by Austrian Chancellor Julius Raab and Foreign Minister Leopold Figl, who famously displayed the document from the palace balcony to crowds below.
Vienna's Ringstrasse hosts a concentration of institutional buildings constructed between 1860 and 1890 during Vienna's expansion as capital of the Austro-Hungarian Empire. The Vienna State Opera (Wiener Staatsoper) opened on May 25, 1869, with a performance of Mozart's Don Giovanni, the building designed by August Sicard von Sicardsburg and Eduard van der Nüll. The opera house measures 88 meters in length, 173 meters in width including side wings, with an auditorium seating 1,709 people and standing room for 567. Allied bombing on March 12, 1945, destroyed the auditorium, with reconstruction completed on November 5, 1955, when the opera reopened with Beethoven's Fidelio. The Vienna Philharmonic Orchestra, founded in 1842, performs here regularly while maintaining separate administrative status from the opera company.