How this calculator works
Archimedes principle says a floating body displaces its own weight in the surrounding fluid. A balloon of volume V displaces V times the density of air, and the gas inside weighs V times its own density, so the difference is the buoyant lift. The empty balloon and any string also count against the lift, so the calculator subtracts their mass when you include it. Dividing the load by the lift of one balloon and rounding up gives the number of balloons, and multiplying by the volume of one balloon gives the total gas needed. The model uses sea level densities at about 15 degrees Celsius, so lift falls slightly at altitude or in hot air.
Formula
Balloon volume = 4/3 x pi x (diameter / 2)^3. Lift per balloon = volume x (air density - gas density) - empty balloon mass. Balloons needed = object mass / lift per balloon, rounded up. Total gas volume = balloon volume x number of balloons. Densities used: air 1.225, helium 0.169, hydrogen 0.0852, ammonia 0.717 and methane 0.679 kilograms per cubic metre.
Worked example
A standard 11 inch balloon is 0.2794 m across, so its volume is about 0.0114 cubic metres. With helium that displaces 0.0140 kg of air and the gas weighs 0.0019 kg, leaving 0.0121 kg of lift before the balloon itself. Subtracting a 2 g balloon leaves about 10.1 g of useful lift, so lifting 80 kg takes about 7,953 balloons and roughly 90.8 cubic metres of gas.
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Frequently asked questions
Why does the calculator ask for the empty balloon weight?
A latex balloon and its string have mass, and that mass has to be lifted too. A typical 11 inch latex balloon weighs a couple of grams, which is a meaningful share of its roughly 12 grams of gross lift. Foil balloons are heavier and lift less per litre.
Can hydrogen lift more than helium?
Yes, hydrogen is about half as dense as helium, so it provides more lift for the same volume. It is also highly flammable, which is why public events use helium despite the lower lift. This calculator is for estimating, not for planning a manned flight.
Why is the lift lower at high altitude?
Air density falls with altitude while the gas inside the balloon expands and becomes less dense too. The net difference shrinks, so a balloon that lifts a small load at sea level may not lift it on a mountain. The figures here assume sea level at about 15 degrees Celsius.
How many balloons does it take to lift a person?
It depends heavily on the balloon size, because lift grows with the cube of the diameter. Around 8,000 standard 11 inch balloons are needed for an 80 kg person, while a 36 inch balloon holds about 35 times as much gas as an 11 inch one, so far fewer are needed.