Domino Chains: The Physics of a Toppling Wave

A chain reaction is a wave, not a chain

It looks like each domino simply knocks over the next one in a line, but the falling motion actually propagates as a mechanical wave through the row — a disturbance travelling through a medium (here, evenly-spaced rigid bodies) at a speed set by the medium's own properties, not by how hard the first domino was pushed. Push the first domino gently or firmly and the row still falls at very nearly the same speed, because after the first collision, each domino's fall is governed almost entirely by gravity acting on its own tipping motion, not by leftover energy passed down from its neighbour.

Why the fall speed doesn't depend much on the push

Each domino tips because gravity pulls its centre of mass past the pivot point once it's been nudged far enough — a rotational instability, not a transfer of large amounts of kinetic energy from its neighbour. The push from the previous domino only has to supply the small nudge needed to tip the balance; from there, gravity supplies essentially all of the energy for that domino's own fall. This is why domino chains are famously reliable regardless of exactly how the first one was tapped, and why physicists studying domino toppling (this has been measured in real published experiments since at least the 1980s) find the propagation speed depends mainly on domino spacing and height, not on initial push force.

Spacing sets the speed — and the classic size trick

Space dominoes closer together and the wave travels faster, because each domino only has to rotate a smaller angle before it strikes the next one. Space them too far apart and the chain fails outright — a domino needs to strike its neighbour high enough up to topple it, so once spacing exceeds roughly the domino's own height, contact is lost and the chain simply stops. This spacing-to-height ratio is the whole reason toppling dominoes make a satisfyingly consistent clack-clack-clack rhythm rather than a random patter: the geometry fixes the timing almost independent of who set them up.

topples if:  spacing < domino_height * sin(critical_tip_angle)
wave speed ≈ spacing / (time for one domino to tip and strike the next)

An often-cited (and genuinely reproducible) demonstration is that a domino can topple a domino roughly 1.5 times its own size, and chaining that ratio means a domino the size of a fingernail can, in principle, set off a chain that eventually topples something the size of a building after only around thirty steps of doubling — a clean illustration of exponential growth hiding inside a toy.

Momentum, energy, and where it all goes

Each collision between adjacent dominoes is closer to an inelastic collision than an elastic one — some kinetic energy is lost to sound, friction and permanent deformation at the contact point rather than bouncing cleanly onward. Because of that loss, a domino wave cannot travel forever on its own energy: it survives only because gravitational potential energy is being freshly released by every single domino as it falls, continually re-supplying the wave with new energy at every step. A row of dominoes lying flat instead of standing has none of this stored energy available, which is why a fallen row can never spontaneously re-set itself.

Rigid-body simulation: why this needs more than particle physics

Unlike a particle (a single point with mass), a domino is an extended rigid body with a shape, a centre of mass and a moment of inertia, so tipping it over requires simulating rotation and torque, not just linear position and velocity. A physics engine like the Cannon-es solver used in this site's 3D simulation tracks each domino's orientation as well as its position, computes contact forces and friction at the exact touching points between neighbouring pieces, and resolves collisions frame by frame — which is precisely why domino chains are a classic stress test for rigid-body engines: hundreds of simultaneous, cascading contact events, each one needing to be resolved accurately enough that the chain doesn't visibly glitch or phase through itself.

Frequently asked questions

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Everything above runs in your browser — open Domino Chain and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.