# Relationship between balloon size and pressure

I see numerous websites talking about how a small balloon is at higher pressure than a big balloon. This is a fun counter-intuitive factoid... unless it isn't a fact at all.

Young-Laplace gives

$$T = \Delta p \frac R2$$

Which means that for a given tension, increasing the radius does decrease the pressure. But why would the tension be constant? A latex balloon is like a 2D spring, right? So the tension in a inflated spherical balloon should be proportional to the surface area, correct?

$$T \propto R^2$$

But this gives

$$\Delta p \propto R$$

Which means the bigger the balloon, the higher the internal pressure. Which, again, would be the normal intuition - but it would burst the bubble of some simplified explanations. (har har)

• By definition, a factoid isn't a fact. The "-oid" ending means "like something, but not something". humanoid = like a human, but not a human. factoid = like a fact, but not a fact. – EnergyNumbers Oct 1 '12 at 15:35
• Possible duplicate: physics.stackexchange.com/q/10372/2451 – Qmechanic Oct 1 '12 at 15:42
• @Qmechanic, I saw that question. Unfortunately, it has no answer and the link it references is dead. – weymouth Oct 1 '12 at 23:00
• FYI the statement is correct. Not sure about the explanation, though. – Vorac Oct 2 '12 at 9:41 