Helium Balloons Calculator

If you've seen the heartwarming Disney movie Up!, then you surely know what we're talking about: a magical moment when a house, lifted by hundreds of colorful balloons, flew off the ground and up in the air.

And while it might be nearly impossible to recreate that moment in real life, lifting something lighter, such as a penguin plushie, is perfectly achievable. Our in-house physicist Álvaro Díez has recently proved it! He helped his penguin buddy named Perri soar in the sky and become the world's first flying penguin. Make sure to watch the footage of this feat here:

All that Perri needed were some helium balloons. How many? Well, this is exactly what our helium balloon calculator figures out!

Before we determine how many helium balloons lift a person, let's start with a bit of theory. Why do these balloons float in the first place? It happens because they are filled with helium - a gas that is lighter than air.

You probably already know the phenomenon of buoyancy. For example, an inflatable mattress floats on water, because the air it's filled with is lighter than water. The same principle applies here: as helium has a density lower than the density of air, a balloon filled with this gas will start moving up.

The density of helium is equal to 0.1785 grams per liter. The density of air, on the other hand, is about 1.25 grams per liter. Leaving some tolerance for the weight of the balloon and the string, we can approximate that every liter of helium has a lifting force of one gram.

There are a few more gases that are lighter than air, such as hydrogen, ammonia, or methane. They are not commonly used in balloons as they are easily flammable. Nevertheless, you can change the gas type in this helium balloons calculator to compare between them and helium.

Let's get on with the calculations! As you already learned in the previous section, the lifting force of helium is approximately one gram per liter. It doesn't seem like much, that's why you will need a lot of balloons to start flying!

1. Determine your weight - for instance, 75 kg. This number should include everything that will be flying, so your clothing as well. Every gram counts!

2. Choose the size of the balloons. Let's assume we are using regular balloons from an amusement park, with a diameter of 30 centimeters (11 inches). In the advanced mode, you can enter a custom size of the balloon.

3. Calculate the volume of a balloon. We will assume that the balloons are perfectly spherical and use the sphere volume formula:

$V_0 = \frac{4}{3} \cdot \pi \cdot r^3 = \frac{4}{3} \cdot \pi \cdot \frac{30}{2}^3 = 14137\ \text{cm}^3 = 14.137\ \text{liters}$

4. Now, convert your weight to grams:

$75\ \text{kg}= 75000\ \text{g}$

5. Now, we'll find out how much helium we need. If you're performing these calculations by hand, you can surely use the lifting force of one gram per liter; however, our helium balloons calculator uses a more precise value of 1.0715 g/L:

$V = \frac{75000}{1.0715} = 69995\ \text{liters}$

5. Finally, divide the total volume of helium needed by the volume of one balloon to find out how many balloons lift a person:

$n = \frac{V}{V_0} =\frac{ 69995}{14.137} = 4951$

You will need roughly five thousand balloons to fly. It's quite a lot, isn't it? If, however, you chose balloons that are 12 feet in diameter, you would only need three of them to lift you up!

In the video below, a group of scientists tried to lift themselves with monster balloons (a diameter of 98" or 2.5 m). In the end they used 18 balloons, which approximately held 96,000 liters of helium! It looks like they almost achieved it 😀

If you want to keep your feet firmly on the ground, you can use balloons to make arches: learn how with our balloon arch calculator!

At the beginning of this article, we mentioned that recreating the memorable Up! moment is short of impossible. Well... a team from National Geographic accepted this challenge. In 2011, they constructed a special lightweight house and lifted it up in the air, using 300 eight-foot-tall balloons. The house soared 10,000 feet into the sky and flew around for approximately one hour.

If you don't believe us, here's the actual video footage to change your mind:

Around 12 grams. To find this result, follow the steps:

1. Compute the volume of the balloon, approximating it to a sphere with radius r = 11"/2 = 13.97 cm.
2. Calculate the balloon's lift weight by multiplying the volume by the mass a liter of helium can lift 1.0715 g.

We find that the volume is:
V = 4/3 × π × r³ = 4/3 × π × 13.97³ = 11420.3cm³ = 11.420 L
And the mass:
m = 11.420 L × 1.0715 g/L = 12.2 g.
This is the mass of an average letter!

If they are filled with helium, balloons float because this gas has a lower density than that of Earth's atmosphere. Hydrogen would be an even better choice, but it tends to ignite.

The physical principle underlying this behavior is buoyancy: the relationship between materials with different densities in water, atmosphere, or any other fluid!

Helium is sold in canisters: on Earth, we can only find the gas as a byproduct of natural gas extraction. Connect the tank to the balloon, and open it until it is filled enough. Close tight: helium tends to escape faster than air from a balloon.

Remember to hold the balloon and not let go after tying it up!

88 balloons (but we suggest a bit more just to be sure). To calculate this number:

1. Calculate the approximate volume of helium that can lift 1 kg:
   V = 1,000 g/1.0 g/L = 1,000 L.
2. Divide this result by the volume of a balloon. We considered 11" balloons (with radius 13.97 cm):
   v = 4/3 × π × r³ = 4/3 × π × 13.97³ = 11420.3cm³ = 11.420 L
N = 1,000/11.420 = 87.57 ~ 88