What If All 8.3 Billion People Jumped at the Same Time? | What If, Calculated #03

What would happen if everyone jumped at the same time? We calculated it step by step, from a gym of 1,000 people to a stadium, all of Japan, and finally about 8.3 billion people on Earth.

The answer in 30 seconds

Earth moves. Gather everyone in one place, give each person a mass of 62 kg, and have everyone jump 30 cm: at the top of the jump, Earth's center of mass shifts about 2.6×10⁻¹⁴ m. That is roughly one four-thousandth of our reference size for a hydrogen atom.

The journey to that answer involves several different measurements:

A force, an arrival time, and a distance answer different questions. Keeping track of those questions is what makes the results useful.

The jump we put into the model

Your center of mass is the balance point of your body's mass. Our jump raises that point 30 cm above its standing position. It does not specify how high your toes clear the floor.

The modeled person crouches, pushes off, travels through the air, lands, and stands back up. We arrange the crouch so that the center of mass is at its original standing height at take-off. That makes the rise after take-off equal to the specified 30 cm. The time in the air is about half a second.

A gym: why the floor feels more than your weight

Imagine a hypothetical gym containing 1,000 identical jumpers, all perfectly in sync. We express the force on the floor in “people's weights”: the load produced by that many 62 kg people standing still.

From acceleration to floor force

With upward acceleration a, the contact force from one person is:

F = m(g + a)

Acceleration means how quickly velocity changes. Standing still gives a = 0 and F = mg. Pushing upward or stopping a downward fall increases the contact force. During flight, there is no contact and the force on the floor is zero.

We model acceleration during take-off and landing as a smooth half-sine pulse, a single rounded hump. If v₀ is the take-off speed, the calculation is:

v₀ = √(2gh) Maximum acceleration = πv₀ / (2τ) Peak force / standing weight = 1 + π√(2gh) / (2gτ)

Here π is pi and √ means square root. With h = 0.30 m and τ = 0.22 s, the peak is 2.7658 times standing weight, rounded to 2.8. For the synchronized gym, that is 2,765.8 people's weights, or about 2,800.

A longer landing lowers the landing peak

Keep the jump height fixed and change only the time spent stopping on landing:

Spreading the stop over more time lowers this peak. These are landing peaks specifically: if take-off timing stays fixed, its force peak stays too.

A stadium: a tenth of a second changes the peak

Our stadium holds 55,000 people. That number comes from the listed capacity of Tokyo Dome, a large venue in Tokyo; the structure in our experiment is hypothetical. Everyone makes the same jump as before.

Let F₁(t) describe one person's force through time, and δᵢ be person i's start-time offset. Then:

Total force at time t = Σ F₁(t − δᵢ)

Σ means “add everyone up.” We shift each person's force curve in time, add the curves, and find the maximum of the total. Perfect synchronization puts every peak at the same moment.

For imperfect timing, we use a normal distribution, the familiar bell-shaped spread, centered on the cue. Its standard deviation—the width of the timing spread—is set to 0.12 s. The average absolute offset from the cue in the selected run is 0.0956 s, about a tenth of a second. This spread is an assumption, not a measurement of actual fans.

The perfectly synchronized peak is 152,118 people's weights. The selected run with offsets reaches 93,940. Across three runs with different random seeds, the median ratio is 0.6175: about 60% of the perfectly synchronized peak.

This is a reduction in the largest instantaneous total force. It does not mean the crowd has lost 40% of its weight.

Seattle: what a real concert recorded

On July 22, 2023, Taylor Swift performed at Lumen Field in Seattle. The study estimates about 72,000 attendees. We analyzed the vertical acceleration record from station UW.KDK, about 150 m west of the venue.

What “27 times stronger” measures

We keep the 1–8 Hz frequency band associated with crowd motion in the study. Hz, or hertz, counts cycles per second.

To turn a rapidly changing acceleration signal into a strength reading, we calculate its root mean square, or RMS, over each second: square the values, average them, and take the square root.

RMS = √(mean of acceleration²) Strength ratio = maximum RMS near the chorus / RMS in the preceding quiet interval

Around the chorus of “Love Story,” this reading rose from 0.20 mm/s² to a maximum of 5.37 mm/s². The processing result is a ratio of 26.9, rounded to 27. This compares acceleration strength.

The strongest rhythm in the signal was 1.975 cycles per second. The song's listed tempo, 119 beats per minute, is 1.983 beats per second. Both are about two per second. The shaking rhythm matched the listed tempo in all eight songs we selected and checked.

How far did the ground move?

We integrated the filtered acceleration twice: first to obtain velocity, then displacement. The maximum displacement across the concert was 28.4 µm, or about 0.03 mm. A micrometer, µm, is a smaller unit of length than a millimeter.

For scale, we use a hair diameter of about 0.08 mm, based on a study of Thai adults. The ground motion was roughly a third of that width. Hair diameter varies, so this is a reference size rather than a universal value.

The 0.03 mm figure is the maximum across the concert. The audience also kept moving to the music, rather than making one isolated jump. This record does not test the stadium model's 60% result; its conditions and measured quantity are different.

A whole country: simultaneous jumps, staggered arrivals

There is a Japanese example of crowd motion reaching a seismic instrument: at a soccer stadium in Kashiwa, near Tokyo, supporters' jumping produced a matching rhythm at a station about 600 m away.

Now imagine everyone in Japan jumping at exactly noon, Japan time. Tokyo Station is our receiving point. We calculate when the first P waves arrive there.

Looking up travel times

The receiver is at 35.6818° N, 139.7650° E. We calculate surface distances using Earth's mean radius of 6,371 km, then look up P-wave travel times in iasp91, a standard model of Earth's interior. The lookup table was calculated with ObsPy TauP.

Arrival time = noon + Tₚ(distance to Tokyo Station)

Tₚ is the travel time of the first P-wave arrival. Near the top of solid bedrock, P-wave speeds are roughly 5–7 km/s; speed changes with depth. The results below use the model's travel times, rather than dividing every distance by a fixed 7 km/s.

Most arrivals are early; the full spread exceeds four minutes

To weight arrivals by population, we use WorldPop's 2020 population grid and rescale its total to Japan's provisional September 2026 estimate. For any elapsed time, we add the population of cells whose first waves have arrived, then divide by the total population.

At 60 s, that fraction is 70.3%; at 120 s, it is 95.0%. The last populated grid cells reach about 256 s. So first arrivals span more than four minutes, while about 70% arrive within a minute and about 95% within two.

The modeled jump sequence in Tokyo is over in about two seconds. People there have long since landed when the first waves from Osaka arrive. The larger part of the shaking produced by jumping travels more slowly and arrives later still. We have not calculated its arrival times or the combined strength of shaking across Japan.

Earth: putting 8.3 billion people into one equation

We now measure the shift of the center of mass of Earth excluding the jumpers. Local ground vibration, such as the Seattle record, measures something different.

The balance point of people and planet

Gather everyone in one place and have them jump in the same direction. The push between people and Earth cannot move their combined center of mass. Think of two skaters pushing apart: the lighter one moves farther, the heavier one less.

If the people's center of mass rises by y relative to Earth, the magnitude d of Earth's shift is:

d = N × m × y / M

Earth shifts in the opposite direction to the people. M includes both Earth and people. The jumpers' combined mass, N × m, is about 5.146×10¹¹ kg. Earth is about 12 trillion times heavier, so its motion is a tiny fraction of theirs.

At the top, y = 0.30 m:

d = 8,300,678,396 × 62 × 0.30 / (5.9722×10²⁴) d ≈ 2.585×10⁻¹⁴ m ≈ 2.6×10⁻¹⁴ m

For our atomic ruler, we use twice the Bohr radius, about 1.06×10⁻¹⁰ m, as a reference diameter for hydrogen. Earth's shift is about one four-thousandth of that size.

What if everyone stays where they live?

People jump outward from a round planet, so their directions differ. We use the GHSL population grid for 2025 to add outward arrows weighted by the number of people in each cell. The resulting vector has 0.6103 of the magnitude obtained with everyone aligned. The population is unevenly distributed, so cancellation is incomplete.

Multiplying the gathered result by that fraction gives about 1.6×10⁻¹⁴ m. The roughly 40% cancellation belongs to the distributed case. It has not been applied to the 2.6×10⁻¹⁴ m gathered result.

Once everyone lands and returns to their original standing posture, y returns to zero. In this ideal model, Earth's center-of-mass shift returns to zero too.

Where the model simplifies reality

The gym and stadium use identical jumpers. Peak forces depend on jump height, contact time, and the assumed acceleration pulse. These calculations do not determine building vibration or structural safety.

The Seattle numbers are Tamelabo's processing results for the vertical 1–8 Hz signal, rather than displacement values published by the observatory. The study does not rule out a contribution from the sound system.

The nationwide calculation uses a standard Earth model and a 2020 population pattern. It omits detailed local geology and does not calculate attenuation, overlapping wave amplitudes, or seismic intensity.

The planetary estimate gives children the same 62 kg mass as adults and gives everyone the same jump height. Gathering humanity in one place is an impossible assumption. The center-of-mass equation describes the whole body's balance point; it does not say that every patch of ground moves by that distance.

FAQ

Would Earth move if everyone jumped at once?

Yes. In this ideal model, about 8.3 billion people gathered together, each with a mass of 62 kg and a 30 cm center-of-mass rise, shift Earth's center of mass by about 2.6×10⁻¹⁴ m at the top. That is roughly one four-thousandth of our reference hydrogen-atom diameter.

Does this calculation tell us whether the jump would cause a major earthquake?

No. It calculates floor force, first-wave travel times, and Earth's center-of-mass shift. It does not calculate the combined shaking strength or seismic intensity across Japan, so it cannot establish an earthquake's size.

Does one person's jump move Earth too?

The same equation gives about 3.1×10⁻²⁴ m for one 62 kg person jumping 30 cm. More people increase the shift, but Earth is still about 12 trillion times heavier than the whole modeled human population.

Does the phone measure how high my feet leave the ground?

It estimates how far your center of mass rises after take-off from your time in the air, assuming the same posture at take-off and landing. The web experiment then uses that estimate as the rise above standing in the model, which is an approximation.

Try your own jump and change the conditions

Use the “Try it” experiment above this article. Start with “Jump with a button (30 cm),” or choose “Measure with your phone” on a supported device. For a flight time t, the estimated height is h = gt² / 8. About 0.5 s gives about 31 cm.

The gym lets you change landing time. The stadium lets you vary the timing spread. In the Japan stage, tap the map to move the receiver. For Earth, compare jumping in place with gathering everyone together.

Change one condition at a time. If you soften the landing, what happens to the take-off peak? If you align everyone's direction, how much does Earth's shift increase? You can compare the experiment's readings with the equations here, using your own jump as the starting point.