The Foucault Pendulum Experiment Explained

A pendulum swinging in a straight line should keep swinging in that same straight line forever, minus friction. In 1851, French physicist Léon Foucault hung a 28-kilogram (61-pound) iron bob from a 67-meter (220-foot) wire inside the Panthéon in Paris and showed the world that it does not — the swing plane drifts, slowly and visibly, hour by hour. The pendulum was not moving oddly. The building around it was moving, carried by a rotating Earth.

What the Foucault pendulum actually is

A Foucault pendulum is a long, heavy pendulum suspended so that its swing is free to rotate in any direction, used to demonstrate Earth's rotation without reference to the sky. The key engineering detail is the suspension: it has to be as close to frictionless and as symmetric as possible, usually a wire or cable clamped in a way that does not favor one swing direction over another. Any bias in the mount — an oval clamp, an off-center anchor — will drag the pendulum's plane sideways and mimic or mask the real effect.

Foucault was not the first person to wonder whether a swinging weight could reveal Earth's spin. The idea traces back to thinking about pendulums and pivoting planes that predates him by decades, but Foucault was the one who built an apparatus precise enough, and public enough, to settle the question (Smithsonian Magazine, 2016). He first tested a small version in his basement, then a larger one at the Paris Observatory with the support of astronomer François Arago, director of the Observatory. Encouraged by those results, he scaled up for a public demonstration that made the front pages.

Léon Foucault — a French physicist and instrument-maker with no formal university degree, who also measured the speed of light and invented the gyroscope, both closely related to the physics behind his famous pendulum. He was, by training, a physician turned experimentalist, and the pendulum demonstration made him a celebrity almost overnight.

On March 26, 1851, Foucault suspended a 67-meter wire and a 28-kilogram brass-and-lead bob from the dome of the Panthéon in Paris, and Parisians watched the pendulum's swing plane visibly rotate over the course of a single afternoon — the first time ordinary people, not astronomers, could watch Earth turn (Smithsonian Magazine, 2016).

The 1851 Panthéon demonstration

Foucault's first public test, on February 3, 1851, used an 11-meter pendulum at the Paris Observatory. It worked, but it was a private, scientific-audience affair. What made Foucault a household name was the follow-up a few weeks later: a much bigger rig, hung from the dome of the Panthéon, a domed mausoleum in central Paris built to honor the nation's great figures (Smithsonian Magazine, 2016).

The setup was almost theatrical. A stylus attached to the bottom of the bob traced a line through a ring of fine sand spread on the floor beneath it. As the day went on, that line did not retrace itself. Instead, each pass cut a slightly different track through the sand, fanning out clockwise as the hours passed, because Paris sits in the Northern Hemisphere.

Crowds came to watch, because there was something to watch: a line in sand, shifting a little more with every swing. No telescope, no calculation, no appeal to authority. Just a bob on a wire and an afternoon of patience. That was the entire point of doing it in a public building instead of an observatory — Foucault wanted people who could not read an ephemeris to see the same evidence an astronomer would accept.

François Arago — the director of the Paris Observatory who supported Foucault's early experiments and helped him secure permission and funding for the public Panthéon demonstration, lending Foucault's work institutional credibility at a moment when he had none of his own.

The demonstration answered a question that had been open, in a rigorous experimental sense, for roughly two centuries. Astronomers had accepted Earth's rotation since Copernicus and Galileo through indirect evidence: the parallax of stars, the behavior of falling objects, and the mathematics of orbital mechanics all pointed the same direction. What nobody had done before Foucault was rotate a lab instrument with nothing pointed at the sky and watch the rotation happen in real time, on the ground, in front of witnesses.

Why the pendulum's plane appears to shift

Here is the part that trips people up: the pendulum's swing plane does not actually change relative to the universe outside Earth. What changes is the floor underneath it. The pendulum keeps swinging along the same line in space — the same plane it started in relative to the distant stars — while the Panthéon, the sand ring, and everyone standing there rotate underneath it with the planet.

Think of it like a record player with a marker fixed above the spinning disc, drawing a straight line on paper taped to the turntable. The marker never deviates from the straight path in the room. But because the paper spins beneath it, the line traced on the paper curves. The pendulum plane is the marker. Earth's surface is the turntable.

A second, more physical way to picture it: imagine standing at the North Pole holding a pendulum that swings due north-south, and painting the compass points on the ice beneath your feet. As Earth turns once every 23.93 hours (a sidereal day, the true rotation period measured against the stars rather than the Sun), the compass painted on the ice rotates under the swing. From your point of view, standing on the rotating ice, the pendulum appears to slowly rotate its swing direction, tracing a full circle in one sidereal day. Nothing pushed the pendulum sideways. The ground moved.

Why does the pendulum's rotation depend on latitude?

The apparent rotation rate follows T = 23.93 hours ÷ sin(latitude). At the poles, sin(90°) = 1, so the plane completes a full rotation in about 23.93 hours. At the equator, sin(0°) = 0, so the swing plane never visibly rotates at all — the ground there does not turn "underneath" the pendulum's swing direction, only carries it in a circle, per the standard Foucault pendulum derivation (University of New South Wales School of Physics; Physics LibreTexts, Variational Principles in Classical Mechanics).

Is Earth's rotation the only thing acting on the pendulum?

No. Gravity restores the swing, tension in the wire constrains it to an arc, and, in the ideal case, no other horizontal force acts on the bob. That absence of a sideways push is exactly why the small, cumulative rotation from Earth's spin becomes visible: there is nothing else around to hide it or overwhelm it, provided the suspension is genuinely symmetric.

Working the sine-of-latitude formula for a real city

The formula behind the rotation table above, T = 23.93 hours ÷ sin(latitude), looks abstract until it's run through with real numbers for a specific place. Take Sydney, Australia, at 33.87° south latitude, home to a public Foucault pendulum at the Sydney Observatory.

The first step is finding the sine of the latitude. Sine of 33.87° works out to approximately 0.5573, meaning the local ground "twists" underneath the pendulum's swing at roughly 55.7% of the rate it would at the pole, where the twisting is complete. Divide the sidereal day, 23.93 hours, by that 0.5573 factor, and the result is about 42.9 hours for the swing plane to complete one full 360° rotation in Sydney, noticeably slower than Paris's 31.8 hours or New York's 36.6 hours, because Sydney sits closer to the equator than either.

The geometry behind that sine term comes down to how directly the local ground surface is oriented relative to Earth's spin axis. At a pole, the ground lies in a plane perpendicular to the axis, so the full spin of the planet translates entirely into a visible twist beneath the pendulum. Moving toward the equator, the local ground tilts increasingly parallel to the spin axis instead of perpendicular to it, so only a shrinking fraction of Earth's rotation shows up as a twist under the swing; the rest of the motion just carries the pendulum sideways in a wide circle without rotating its swing direction at all. That's also why the direction of rotation flips between hemispheres: south of the equator, the visible drift runs counterclockwise instead of the clockwise drift Parisians watched in 1851, because the ground's twist direction relative to the swing reverses sign once you cross into negative latitude.

A useful sanity check on the formula: plug in a latitude of 0° for the equator, and sin(0°) equals exactly zero, which makes the denominator zero and the rotation period mathematically infinite, meaning no rotation ever completes, matching the equatorial row in the table above. Plug in 90° for a pole, and sin(90°) equals exactly one, reducing the formula to simply the length of a sidereal day, the fastest and simplest case the geometry allows.

Coriolis effect: the physics term that describes the drift

The rotation of the swing plane is one visible signature of what physicists call the Coriolis effect — the apparent deflection of a moving object as seen from within a rotating reference frame, named after French engineer Gaspard-Gustave de Coriolis, who described the mathematics in 1835, sixteen years before Foucault's demonstration made it visible to a general audience.

The same underlying physics shows up anywhere something moves across a rotating surface without being rigidly attached to it: ocean currents curving instead of running straight, long-range artillery shells drifting off a straight-line target, and — despite a persistent myth — not your bathtub drain, which spins in whichever direction the tub's shape and initial water motion happen to favor, because the Coriolis force at that small scale is far too weak to compete with those factors.

For a pendulum, the Coriolis effect deflects the bob's path just enough, over each swing, to slowly rotate the overall plane rather than to bend any single swing into a visible curve. It is a cumulative effect: unnoticeable swing to swing, unmistakable hour to hour. That is exactly why Foucault needed a long wire and a heavy bob — a longer pendulum swings more slowly and for longer, giving the tiny Coriolis deflection more time to accumulate into a plane shift a crowd in the Panthéon could actually see.

Latitude	Location example	Time for one full plane rotation
90° (North or South Pole)	Geographic pole	~23.9 hours
48.85° N	Paris, France (Panthéon)	~31.8 hours
40.7° N	New York City, USA	~36.6 hours
35° N	Tokyo, Japan	~41.8 hours
0° (Equator)	Quito, Ecuador	No rotation (infinite period)

Rotation period follows T = 23.93 hours ÷ sin(latitude); the pendulum plane turns fastest at the poles and does not turn at all on the equator, per the standard Foucault pendulum formula (UNSW School of Physics; Physics LibreTexts).

Why the pendulum has to be big, heavy, and carefully hung

Foucault's design choices were not for spectacle alone. Every one of them solved a real measurement problem. A short, light pendulum loses its energy to air resistance and friction at the pivot before the Coriolis effect has time to build a visible rotation, so the swing plane's drift gets swamped by noise before anyone can see it.

A long wire — Foucault's Panthéon pendulum measured 67 meters (220 feet) — gives the bob a slow, long-period swing, which means more time per oscillation for the small Coriolis deflection to accumulate. A heavy bob, 28 kilograms in Foucault's case, carries enough momentum to keep swinging steadily for hours without the amplitude decaying into uselessness. And a symmetric suspension point matters because any asymmetry in how the wire is clamped introduces its own preferred swing direction, an artifact that has nothing to do with Earth's rotation and can be large enough to hide the real signal entirely.

This is the same underlying insight that led Foucault to invent the gyroscope a year later, in 1852: a spinning mass resists changes to its orientation, and by isolating a moving system from outside interference as cleanly as possible, you can make it reveal rotations that are otherwise invisible. The pendulum and the gyroscope are, in a real sense, siblings — both are stripped-down bare demonstrations of rotational physics, with one accumulating the effect through repeated free swings and the other exploiting angular momentum directly.

Modern museum and science-center pendulums generally follow the same three design rules, just implemented with better materials: minimal-friction pivots (often a nearly frictionless universal joint or a short flexible wire segment at the very top), enough mass and length to sustain hours of visible swing, and a display floor marked with the hour lines so visitors can watch the plane shift over the course of a visit rather than a full day.

Where you can see a Foucault pendulum today

Foucault's original Panthéon pendulum is periodically reinstalled in the building for anniversaries and exhibitions; a version of the apparatus, including a reconstructed bob, has also been displayed at the Musée des Arts et Métiers in Paris, which holds Foucault's original instruments (Smithsonian Magazine, 2016). Beyond Paris, permanent Foucault pendulums are a fixture at large science museums and universities worldwide — installations exist at institutions such as the California Academy of Sciences, the United Nations headquarters in New York, and numerous university physics departments, each swinging quietly for years at a time with periodic nudges to counteract friction losses.

A working Foucault pendulum is, unusually for a piece of 19th-century apparatus, something you can still walk up to and understand on sight. Most museum installations mark the hours around the pendulum's base, so a visitor who returns after lunch can see for themselves that the plane of swing has rotated a few degrees relative to where it started, exactly the observation that convinced a skeptical public in 1851.

What people get wrong about the Foucault pendulum

The most common misconception is that the pendulum is being pushed sideways by some Earth-generated force. It is not. The bob follows the simplest path physics allows — a straight-line swing under gravity and wire tension — and never deviates from that plane relative to the distant stars. The apparent rotation is entirely a matter of perspective: the observer, the floor, and the building are the things actually turning.

A second mistake is assuming the pendulum would rotate at the same rate everywhere on Earth. It does not, and the reason is the sine-of-latitude relationship covered above. A pendulum at the equator would show no rotation of its swing plane at all, not because Earth is not rotating there, but because the local ground does not rotate "under" the swing's compass direction the way it does at higher latitudes; it only carries the swing plane around bodily, without twisting it.

A third mistake, and a related myth, is crediting the Coriolis effect for the direction water swirls down a drain or a toilet. The Coriolis force is real and it does bend the paths of hurricanes and ocean currents over hundreds of kilometers and many hours, but at the scale and timescale of a bathtub it is several orders of magnitude too weak to compete with the drain's shape, residual currents from filling the tub, or how it was drained last time. Foucault's own pendulum needed a wire 67 meters long and hours of swinging to make the effect visible; a bathtub gives the Coriolis force neither the size nor the time it needs.

Finally, some readers assume the demonstration proved Earth rotates around the Sun. It did not, and it was never meant to. The Foucault pendulum demonstrates axial rotation — Earth spinning on its own axis — not Earth's orbital motion around the Sun, which is a separate claim supported by different evidence, including stellar parallax and orbital mechanics.

Q: What does the Foucault pendulum experiment prove? It demonstrates that Earth rotates on its axis, using purely local, ground-level evidence — a pendulum's swing plane appears to rotate relative to the room around it, with no need to observe the stars or any object outside the building.

Q: Why does a Foucault pendulum change direction? The pendulum itself does not change direction relative to the distant stars; it keeps swinging along the same plane. The floor, walls, and observer rotate with Earth underneath the swinging pendulum, which makes the swing plane appear to shift when watched from the ground.

Q: How long does it take a Foucault pendulum to complete a full rotation? It depends on latitude, following T = 23.93 hours ÷ sin(latitude). At the poles, one rotation takes about 23.9 hours. In Paris, at roughly 48.85° N, it takes about 31.8 hours. At the equator, the swing plane never completes a rotation at all.

Q: Who invented the Foucault pendulum? French physicist Léon Foucault first demonstrated it publicly on March 26, 1851, at the Panthéon in Paris, after an earlier private test at the Paris Observatory in February of that year with support from astronomer François Arago.

Q: Does the Foucault pendulum work at the equator? Effectively no. At zero latitude, the sine-of-latitude term in the rotation formula equals zero, so the pendulum's swing plane does not visibly rotate at all, even though Earth is rotating everywhere, including at the equator.

Q: Is the Coriolis effect the same thing that makes toilets flush a certain direction? No. The Coriolis effect genuinely deflects large, slow-moving systems like storms and ocean currents, but at the small scale and short timescale of a bathtub or toilet drain, it is far too weak to matter compared to the container's shape and residual water motion.

The takeaway

The Foucault pendulum works because it removes every other explanation for why a swing plane would drift, leaving only one: the ground beneath it is turning. That is what makes it such an elegant piece of experimental design, not the size of the bob or the length of the wire, but the discipline of eliminating alternative causes until the only one left is the true one. Léon Foucault gave a general audience something a telescope never could: rotation you can watch happen, in an afternoon, with your own eyes.

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