Balloons frequently--whether intentionally or accidentally--escape into the sky. These balloons float up into the atmosphere until they either pop or begin to deflate and return to earth. While it's not possible to know the exact altitude a helium balloon can attain, estimations are possible.
In 1987, a British man, Ian Ashpole, set the reported world record for highest helium-balloon flight. Using 400 helium balloons with radii of one foot, he achieved the height of one mile, 1,575 yards without any of the balloons popping. This figure is the highest recorded altitude of a helium balloon.
In order to calculate how high a balloon could go before popping, you need to calculate the density of a helium balloon that has a radius of 0.1143 mm. Calculate the volume of the balloon using the formula for the volume of a sphere; then use the volume to calculate the density. You'll find that the density of a helium balloon of that size at room temperature is about 0.1663 kilograms/meters (kg/m). Because density is altered by altitude, the helium balloon can reach a height of 9,000 meters, or 29,537 feet. Anything higher than this altitude will cause the helium within the balloon to expand and the balloon to pop.
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Many factors can affect the reaction between a standard balloon and the atmosphere. Helium can very easily escape from the balloon through gaps in the rubber polymers used in the balloons' construction; a loss of helium will result in a higher altitude reached, because there is not as much helium inside of the balloon to expand. Also, the balloon may not pop--it could just as easily reach an equilibrium point, where its density equals that of the atmosphere's density, and stop until it loses helium and begins to deflate and sink back to the ground.