One of Pixar's technical directors worked out that it would take "on the order of 20 to 30 million balloons to actually lift Carl's house." But a phone screen has about two million pixels: that many balloons is ten to fifteen per pixel, and the canopy turns to fog. A painted cloud on a loop fails too: Pixar's own tests found "simple procedural motion or particles would be unconvincing", and full soft-body balloons "cost-prohibitive". So Steve May, the film's supervising technical director, explains the count was chosen for the eye: "We ended up using 10,297 for most of the floating scenes, and 20,622 when it actually lifts off", tuned shot by shot so it "feels interesting, believable and visually simple". Every balloon is a rigid body in wind and buoyancy: "One balloon has to be able to respond to 10,000 other balloons."

The house, the balloons and the simulation are our own; no frames from the film.

What was your guess before the reveal? Put it in the comments.

Sources: Walt Disney Pictures and Pixar, Up production notes (2009), Steve May; Jon Reisch and Eric Froemling, "Simulating the Balloon Canopy in Up", SIGGRAPH 2009.
Sounds: Apple iMovie and iLife sound effects.