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Falling through the Earth calculator (gravity tunnel)

Jump into a frictionless tunnel bored through the Earth — how long to reach the other side? For a uniform Earth the motion is simple harmonic, so any straight chord takes the same ~42 minutes one way, with a peak speed of ~7.9 km/s through the centre. Switch to the PREM density model for the realistic ~38-minute figure.

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Enter Tunnel type, Central angle between entrances (chord, °), Density model, Body mass (kg) and the Falling through the Earth calculator (gravity tunnel) works out One-way fall time, Full oscillation (round trip), Maximum speed, Maximum speed, Tunnel length, Deepest point below surface, Your weight at the surface, Apparent weight during the fall straight away. For instance, with Tunnel type = Diametric (through the centre), Central angle between entrances (chord, °) = 90, Density model = Uniform Earth (exact SHM) and Body mass (kg) = 70 it returns One-way fall time = 42.203 min, Full oscillation (round trip) = 84.406 min and Maximum speed = 7.904 km/s.

How to use it

  1. Enter your values: Tunnel type, Central angle between entrances (chord, °), Density model, Body mass (kg).
  2. Read the result instantly: One-way fall time, Full oscillation (round trip), Maximum speed, Maximum speed, Tunnel length, Deepest point below surface, Your weight at the surface, Apparent weight during the fall.

Frequently asked questions

What does the Falling through the Earth calculator (gravity tunnel) actually compute?

It takes Tunnel type, Central angle between entrances (chord, °), Density model and Body mass (kg) and derives One-way fall time, Full oscillation (round trip), Maximum speed, Maximum speed, Tunnel length, Deepest point below surface, Your weight at the surface and Apparent weight during the fall from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

4 values: Tunnel type, Central angle between entrances (chord, °), Density model and Body mass (kg). Nothing else is required — no account, no file upload.

Can you show a worked example?

With Tunnel type = Diametric (through the centre), Central angle between entrances (chord, °) = 90, Density model = Uniform Earth (exact SHM) and Body mass (kg) = 70, the calculator returns One-way fall time = 42.203 min, Full oscillation (round trip) = 84.406 min and Maximum speed = 7.904 km/s. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Tunnel type = Chord (straight shortcut), Central angle between entrances (chord, °) = 180, Density model = PREM (realistic, denser core) and Body mass (kg) = 140 instead, One-way fall time goes from 42.203 min to 38.203 min — which is why it is worth testing a few scenarios rather than trusting a single figure.

Which “Tunnel type” option should I choose?

You can pick between « Diametric (through the centre) » and « Chord (straight shortcut) ». Each one changes what the calculator works out, so switch and compare — the default is « Diametric (through the centre) ».

What does it give for smaller values?

Scaled down to Tunnel type = Diametric (through the centre), Central angle between entrances (chord, °) = 0, Density model = Uniform Earth (exact SHM) and Body mass (kg) = 0, Your weight at the surface comes out at 0 N. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Checking a homework answer, sizing something before building it, and getting an order of magnitude before committing to a design — a torque on a bolt, the force a spring returns, the frequency a circuit resonates at, how long light takes to arrive.

What is the most common mistake?

Feeding in a value in the wrong unit. Physics formulas assume SI throughout, so grams instead of kilograms or centimetres instead of metres shifts the answer by powers of ten without any warning.

How accurate is it, and what are the limits?

Idealised: no air, no friction, no Earth rotation. In such free fall you are weightless the entire trip (apparent weight = 0). The remarkable uniform-Earth result is that every straight chord takes the same ~42.2 min one way; PREM's denser core shortens it to ~38.2 min (a documented scaling).

What is the difference between the Falling through the Earth calculator (gravity tunnel) and the Buoyancy calculator?

This one returns One-way fall time and Full oscillation (round trip); the Buoyancy calculator returns Buoyant force (N) and Weight (N). That is the whole difference — open the one whose figure you need.

Further reading

All guides →
ExplainerWhat Is the Reynolds Number? The Formula, the Units That Cancel, and Why 2 300 Is Only for PipesRe = ρvL/μ compares inertia with viscosity, and the units really do cancel. See the number worked out for honey, a household pipe, an artery, a swimmer and a wing — and why the 2 300 threshold belongs to pipe flow alone.ExplainerHow Buoyancy Works: Archimedes' Principle, and Why Ice Floats With 10.5 % Above WaterThe upward force equals the weight of the fluid pushed aside. That one sentence decides whether something floats, and if it floats, exactly how much of it stays under.ExplainerHow the Doppler Effect Works: The Formula, the Sign Convention, and Why Moving the Source Is Not the Same as Moving the ListenerFor sound, f' = f(v + v_o)/(v − v_s) — and getting the signs backwards is the classic error. Here is the convention spelled out, a 440 Hz source computed at four speeds, and why light needs a different equation entirely.ExplainerHooke's Law Explained: F = kx, Real Spring Constants, and Where It Stops HoldingHooke's law says force is proportional to stretch — but only below the elastic limit. Here is F = kx with worked numbers, what a 200 N/m spring actually feels like, and how springs combine.GuideThe Four Kinematics Equations: Which One to Use, and What Each One Leaves OutFive variables, four equations, and each equation is missing exactly one of them. Choose by looking at the variable the question never mentions.ExplainerProjectile Motion Explained: Range, Height, Flight Time — and Why 45° Is Not Always BestThree formulas cover the whole of projectile motion on level ground. The catch is level ground: the moment launch and landing heights differ, the 45° result stops being true.