A stretched balloon wall is an elastic membrane held in tension by the pressure difference across it. Treating the balloon as a thin spherical shell (radius R, wall thickness t), the internal excess pressure P produces a biaxial hoop stress in the rubber:
σ = P·R / (2t) (thin-shell / Laplace law)
ε = σ / E (Hookean strain, E = rubber modulus)
c = √(E / ρ) (elastic wave speed in the rubber)
v = ε·c (fragment velocity at rupture)
U = (σ² / 2E) · (4πR²t) (total elastic strain energy stored)
At rupture the wall's stored strain energy has nowhere else to go: it converts almost instantly into the kinetic energy of the tearing fragments (fast, elastic release) plus the pressure pulse that becomes the pop's shockwave and sound. This simulator computes σ, ε and the resulting fragment speed v directly from your sliders — turn up the pressure or thin the wall and the stress, and therefore the bang, scales up correspondingly. Rubber's own elastic modulus (E ≈ 2 MPa) and density (ρ ≈ 1100 kg/m³) are held fixed, matching stretched latex.
- Internal pressure at pop — how hard you inflated it before it let go. Higher pressure means higher wall stress and a faster, louder rupture.
- Rubber wall thickness — a thinner wall carries the same pressure at higher stress (σ ∝ 1/t), so thin over-stretched balloons pop harder per unit pressure than thick ones.
- Balloon radius — bigger balloons need more wall stress to hold the same pressure (σ ∝ R), which is also why an over-inflated balloon fails at its biggest, thinnest patch first.
- The expanding ring you see after the pop is the pressure shockwave — its speed and fade are stylized for visibility, not to real acoustic timescale (a real pop shockwave clears the balloon's own size in well under a millisecond).