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Why does a helium-filled balloon rise in air?

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differential manometer, Torricellian barometer, and siphon — fluid mechanics Figure 1: Schematic representations of (A) a differential manometer, (B) a Torricellian barometer, and (C) a siphon.

A helium-filled balloon rises in the air due to the principle of buoyancy, which is a fundamental concept in fluid mechanics.1

According to Archimedes’ principle, any object submerged in a fluid—whether a liquid or a gas—is acted upon by an upward buoyant force equal to the weight of the fluid displaced by that object. Because helium is significantly less dense than the surrounding atmospheric air, the total weight of the helium-filled balloon (including the gas and the balloon material) is less than the weight of the air it displaces.234

When the weight of the displaced air is greater than the weight of the balloon itself, the net result is an upward force that causes the balloon to rise. This same principle allows other objects, such as hot-air balloons, to ascend by heating the air inside them to decrease its density relative to the cooler, denser air outside.21