Why do soap bubbles turn round even when you blow them through a square frame?
― A film that wants to shrink, and air pushing back from inside. The only shape where the two can balance is a sphere
Whether you blow through a star-shaped frame or a square one, the bubble that floats away is always round. The frame doesn't decide the shape. What decides it is a film that is always trying to shrink and air inside pushing equally hard in every direction. The only shape where these two can balance everywhere at once is a sphere.
A child is blowing soap bubbles through a star-shaped wand bought at a toy shop. "Maybe I'll get a star-shaped bubble," they think, and blow gently.
But the moment the bubble leaves the wand, it wobbles and settles into its usual round shape. The same thing happens with a square frame, or a heart-shaped one.
If a child asked you "why doesn't it come out as a star?", what would you say? It turns out there's a clear answer to this question.
Only two reasons make it round
A soap bubble's film behaves like a taut sheet of rubber, always trying to reduce its area. Of all the shapes that can enclose a given amount of air, the sphere needs the smallest area.
Air sealed inside pushes back against the film with the same strength up, down, and sideways. A shape with a bump or a dent in just one spot can't hold for long.
The frame's shape only matters while the film is still touching it. The moment it leaves the frame, only these two forces decide the shape.
The film wants to shrink its area
A force that tries to shrink the surface acts on the surface of water, because water molecules pull on each other. This is also why a water droplet on a leaf turns round.
A soap bubble's film is a thin layer of soapy water — its thickness is said to be only a few dozenths of the width of a human hair. Both the front and back faces of this film have the same shrinking force acting on them. The soap's job is to keep the film from breaking easily, which is what lets it stretch out so far.
So, of all the shapes that could enclose the same amount of air, which has the smallest area? The answer is a sphere. As in the right side of Figure 1, a cube of the same volume has a surface area about 24% larger than a sphere's. A star shape would need even more area, because of its pointed tips. A film that wants to shrink smooths out the corners bit by bit, and settles into the round shape with the smallest area.
The air inside smooths out the shape
If the film only shrank, the bubble would collapse and vanish. That doesn't happen because the air sealed inside pushes back. The air's push is the same strength in every direction.
If part of the film bulges out into a point, that spot curves more sharply. The more sharply a spot curves, the harder the film pulls inward there. So the bulge gets pushed back. Conversely, a flat, dented spot gets pushed out by the air. This is how the shape settles into one that curves the same way everywhere — a sphere (left of Figure 1).
How much harder does the air inside push than the air outside? By calculation, for a bubble 4 cm across, it's only about 1/20,000 higher than the outside air pressure (we'll calculate this in the last expandable section). It's this tiny difference that holds the shape together.
Smaller bubbles push harder from inside
Here's a surprising property. The force with which the film pulls inward gets stronger the smaller the bubble is, because a smaller bubble curves more sharply. That's why smaller soap bubbles push back harder from inside.
What happens if you connect a large bubble and a small one with a tube? You might expect, like with balloons, that "the bigger one deflates." But actually it's the opposite. As in Figure 2, air flows from the small bubble into the large one, and the small bubble shrinks away.
A giant soap bubble, as wide as your outstretched arms, wobbles and warps as it flies. The bigger the bubble, the weaker the film's ability to hold its shape. So it loses out to wind and to the film's own weight. Being round is a privilege only for bubbles of a modest size.
The liquid in the film slowly drains downward under its own weight. It also evaporates, so the top thins out first. Once a hole opens at the thinnest spot, the whole thing pops in an instant.
Summary
A soap bubble's film is always trying to reduce its area. The air inside pushes back with the same strength in every direction. The only shape where these two can balance everywhere on the film is a sphere. It doesn't matter whether the frame was star-shaped or square — once the bubble leaves it, the frame is irrelevant.
A soap bubble's roundness isn't decided by the frame.
It's the answer to a "negotiation" between a film that wants to shrink and air that pushes back — and that answer is a sphere.
For the rainbow-colored pattern that floats on a bubble's surface, see Why do soap bubbles look rainbow-colored?, and for the rules that shape a cluster of many bubbles, see Why are honeycombs hexagonal?
- Bend a wire hanger into a square frame and a triangular frame. See whether the bubble that flies off turns round no matter which one you blow through.
- Dip a frame in soapy water and lift it out, and a flat film stretches across it. Float a loop of thread somewhere on the film, then poke and pop just the film inside the loop with your finger — the thread snaps into a neat circle.
- On a wetted plate, make two half-sphere soap bubbles with a straw, one bigger than the other. Put both ends of one straw into the two bubbles, and the smaller one will shrink away.
You can make soapy water by diluting kitchen dish soap in about 10 parts water. Be careful not to get it in your eyes, and wash your hands afterward.
Want to know more? ― Terms, formulas, and links to the curriculumWe've marked which level each part belongs to, from middle-school science to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school physics
- HS+Advanced high-school content, or textbook sidebar material
- Univ.Not covered in high school — university specialist content (interface science, fluid dynamics, geometry)
- ResearchNot yet settled "textbook fact" even at university — an active research topic
MSTerms: this phenomenon has names
- Surface tension: A liquid surface's tendency to shrink its area. It's also why water droplets turn round.
- Surfactant: A component of soap or detergent. It lines up on the water's surface and keeps the thin film from breaking easily.
- Laplace pressure: The pressure difference between the inside and outside of a curved film. The sharper the curve, the bigger the difference.
MSHSCheck with a formula: how much higher is the pressure inside a soap bubble?
Imagine cutting a soap bubble in half. At the cut, the shrinking film is pulling to close the bubble. Meanwhile, the air inside is pushing back across the full area of the circular cut. Balancing these two gives us the pressure difference between inside and outside.
| In symbols | Δp = 4 × γ ÷ R |
| In words | Pressure difference (inside − outside) = 4 × film's surface tension ÷ bubble's radius |
| Where it comes from | Balancing forces on a half-sphere. Since the film has two faces (front and back), the shrinking force is "2 × γ × circumference of the cut." Setting this equal to "Δp × area of the cut circle" gives this formula (the Young–Laplace equation, applied to a film with two surfaces). |
| Symbol | Meaning and unit |
| Δp | Pressure difference, inside minus outside (unit: pascals, Pa) |
| γ | Surface tension of soapy water (unit: N/m). Roughly 0.025 N/m (plain water alone is about 0.072 N/m) |
| R | Bubble radius (unit: m). For a bubble 4 cm across, 0.02 m |
| Outside air pressure (atmospheric) | About 101,300 Pa |
| Numerator (4 × γ) | 4 × 0.025 = 0.1 |
| Pressure difference for the 4 cm bubble (Pa) | 0.1 ÷ 0.02 = 5 |
| Fraction of atmospheric pressure | 101,300 ÷ 5 = 20,260 |
| A smaller bubble, 1 cm across (R = 0.005 m) | 0.1 ÷ 0.005 = 20 |
| How much harder the small bubble pushes | 20 ÷ 5 = 4 |
Inside the 4 cm bubble, the pressure is only 5 Pa higher than outside — roughly 1/20,000 of atmospheric pressure. For a 1 cm bubble, it's 20 Pa, pushing four times as hard. That's why, when connected, air flows from the small bubble into the large one.
| Surface area of a sphere of volume 1 | About 4.84 |
| Surface area of a cube of volume 1 | 6 |
| Cube's area vs. sphere's | 6 ÷ 4.84 ≈ 1.24 |
To enclose the same amount of air, a cube needs about 24% more film than a sphere. For a film that wants to shrink, that's a "losing shape."
HSHS+Force balance and surface energy
HSThe calculation above only uses high-school physics: "balancing forces" and "pressure = force ÷ area." It just says the force of the air pushing on the half-sphere equals the force of the film pulling on the cut.
HS+Surface tension can also be thought of as the energy needed to expand the surface by one unit of area. The smaller the film's area, the less energy it stores. Things tend to settle into the state with the lowest energy. That's why the film chooses the sphere — the shape with the least area for a given volume.
Univ.The Young–Laplace equation, and surfaces of constant mean curvature
For a general curved film, the pressure difference is given by the Young–Laplace equation, proportional to the sum of the reciprocals of the film's two principal radii of curvature. If the pressure difference is the same everywhere, this sum — the mean curvature — must also be constant everywhere. A closed, non-self-intersecting surface of constant mean curvature must be a sphere; this is known as Alexandrov's theorem. Finding the shape with minimum area for a fixed volume is the three-dimensional version of the isoperimetric problem. In foams made of many bubbles, the way films meet follows a rule called Plateau's laws.
📖 For the derivation and further reading: Japanese Wikipedia, "Young–Laplace equation" / Japanese Wikipedia, "Plateau's laws"
ResearchWhat's still not fully understood
- Why is a soap bubble's lifespan so unpredictable? The speed at which the film's liquid drains, evaporation, and dust all combine. Even with the same liquid, it's said to be hard to predict exactly when a bubble will pop.
- The ideal recipe for giant soap bubbles. It's known that adding long molecules (polymers) makes it easier to form large films, and research into why continues.
- The detailed picture of flow inside the film. Tiny differences in surface tension create flows (Marangoni flows) that thin or thicken the film. The full picture is still being worked out.
In other words, this article too describes "what's understood so far." Why bubbles turn round is well established, but exactly when they pop is still an active research question.
Links to the curriculum, by level
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science, Year 1, "Pressure" | The air inside pushing the same strength in every direction |
| HS | Physics, "Force balance," "Pressure" | The calculation of pressure difference from force balance on a half-sphere |
| HS+ | Physics (advanced), "Surface tension" | The sphere as the shape that minimizes surface energy |
| Univ. | Interface science, differential geometry | The Young–Laplace equation, surfaces of constant mean curvature, the isoperimetric problem |
| Research | Soft matter physics | Film lifespan, giant soap bubbles, flow inside the film |
| ― | Everyday connection | Playing with bubbles, droplets and foam turning round |
- Japanese Wikipedia, "Surface tension" (表面張力)
- Japanese Wikipedia, "Young–Laplace equation" (ヤング・ラプラスの式)
- C. V. Boys, "Soap Bubbles: Their Colours and the Forces Which Mould Them", 1890 (translated into Japanese as 『シャボン玉の科学』)
- C. Isenberg, "The Science of Soap Films and Soap Bubbles", Dover, 1992
- P.-G. de Gennes et al., 『表面張力の物理学』(Japanese edition), Yoshioka Shoten (森林総合研究所とは無関係の出版社)
※This article is a general-audience science explainer. Figures given are approximations meant to help illustrate the underlying mechanism. If soapy water gets in your eyes, rinse immediately with water.