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Distance & area

Tunnel through the Earth

Pick two places and see what a straight tunnel between them through the Earth would look like: how long it is, how deep it goes, which layers it crosses and how long it would take to fall to the other side.

Example From New York to Perth. Search for your own places or tap the map.

Loading the map…

Shortest route over the surface

Result

Length of the straight tunnel

7,876 mi

New York → Perth

Maximum depth
3,554 mi
Angle when you start digging
84.1°below horizontal
Over the surface
11,626 mithe tunnel saves 3,750 mi (32.3%)

It goes through the inner core, a ball of solid iron at the center of the Earth.

Layers it crosses (PREM model)

Cross-section of the Earth with the tunnel: 7,876 mi long and 3,554 mi deepInner coreOuter coreMantleAB
  • Crust 30.5 mi
  • Mantle 3,597 mi
  • Outer core 2,964 mi
  • Inner core 1,284 mi

If you jumped in (no friction, no air)

38 min 14 s

with the Earth’s real density (PREM model)

With uniform density
42 min 10 s
Top speed, halfway
22,012 mph

You start at zero speed, speed up until halfway, slow down and reach B just as you stop. With uniform density every tunnel takes the same time.

Antipode mapFind the point on the exact opposite side of the Earth from any place, and see if it’s land or sea. Distance between two pointsMeasure the distance between any two places or points on the map, in miles or kilometers. Bearing and compassGet the compass bearing from one place to another, true and magnetic, with the local declination.

Share this tunnel

How to use it

  1. Choose the entrance and the exit

    Search for two places, paste coordinates, use your location or tap the map. “Come out at the antipode” sends the tunnel through the center.

  2. See the tunnel

    You get its length, the maximum depth, the angle you’d have to start digging at and how much shorter it is than going over the surface.

  3. Go through the layers

    The cross-section draws the tunnel to scale and the list shows how far it runs through the crust, the mantle and the core.

What it’s for

  • Physics class

    The gravity tunnel is a classic problem: with uniform density, every straight tunnel takes the same time.

  • Earth science class

    See to scale how thin the crust is and how big the core is.

  • Pure curiosity

    What if you dug a hole in your backyard? Use your location and come out at the antipode.

  • The real straight-line distance

    The chord is the shortest possible distance between two points on Earth, shorter than any path over the surface.

How it’s calculated

The tool treats the Earth as a sphere with a radius of 6,371 km (3,959 miles), as in the PREM model. With the angle θ between the two places as seen from the Earth’s center, the tunnel is the chord between them: plain circle geometry.

For the fall, an object is dropped at A with no friction and no air. Inside the Earth, only the mass closer to the center than you pulls on you. If the density were the same everywhere, gravity would drop in a straight line down to zero at the center, and the trip would be simple harmonic motion that lasts the same in any tunnel. With the PREM density, gravity barely drops until the core, so the trip is integrated step by step: the speed at each point comes from the energy gained by falling.

Length and depth

length = 2R · sin(θ/2) depth = R · (1 − cos(θ/2))

R = 6,371 km. The angle you start digging at, below horizontal, is θ/2.

Fall time with uniform density

t = π · √(R³ / GM) ≈ 42 min

G is the gravitational constant and M the Earth’s mass. It doesn’t depend on the tunnel.

Example: from New York to Perth
New York 40.66270° N, 73.93870° W
Perth 31.95230° S, 115.86130° E
Angle between them, from the center 168.3°
Tunnel length 7,876 mi (12,675 km)
Over the surface 11,626 mi (18,709 km); the tunnel saves 3,750 mi (6,034 km)
Maximum depth 3,554 mi (5,719 km)
Angle when you start digging 84.1°
Layers it crosses crust, 30.5 mi (49.1 km); mantle, 3,597 mi (5,789 km); outer core, 2,964 mi (4,771 km); inner core, 1,284 mi (2,066 km)
Fall time with PREM density 38 min 14 s; 22,012 mph at the halfway point
Fall time with uniform density 42 min 10 s

A short tunnel hardly goes down: from New York to Philadelphia it would be 77.4 mi (125 km) long and only 1,000 ft (305 m) deep at its lowest point, still inside the crust.

How long would the fall take?

With uniform density it comes out at 42 min 10 s for any straight tunnel, whether it’s 10 miles long or 7,000. But the Earth isn’t uniform: the iron core is far denser than the crust. So as you go down, gravity hardly weakens (it even grows a little until you reach the core) and you pick up speed sooner. The tunnel through the center takes 38 min 11 s with the PREM model, matching what Alexander Klotz found in 2015 in the American Journal of Physics (38 min 11 s). Short tunnels still take about 42 minutes, and long ones get close to 38.

Tunnels of different sizes

Here’s how length, depth and fall time change with the angle between the two places: 10°: 690 mi (1,111 km), 15.1 mi (24.2 km) deep, 42 min 8 s; 45°: 3,030 mi (4,876 km), 301 mi (485 km) deep, 41 min 40 s; 90°: 5,599 mi (9,010 km), 1,159 mi (1,866 km) deep, 40 min 27 s; 135°: 7,315 mi (11,772 km), 2,444 mi (3,933 km) deep, 38 min 52 s; 180°: 7,918 mi (12,742 km), 3,959 mi (6,371 km) deep, 38 min 11 s.

The Earth’s layers in the PREM model

The Preliminary Reference Earth Model (Dziewonski and Anderson, 1981) is the reference model of the Earth’s interior, worked out from how earthquake waves travel. Its radius is 3,959 mi (6,371 km). The crust reaches down to 15.2 mi (24.4 km) on average (in reality it varies a lot from place to place); below it is the rocky mantle, down to 1,796 mi (2,891 km); then the outer core of liquid iron and nickel, down to 3,200 mi (5,150 km), and at the center the solid inner core.

Frequently asked questions

Could a tunnel like this ever be dug?

No. Pressure and temperature rise so fast with depth that no borehole has even made it through the crust. The tool is a thought experiment to explore the Earth’s geometry and physics.

Why does every tunnel take the same time with uniform density?

Inside a uniform sphere, gravity grows in proportion to the distance from the center. Along any chord, the force pushing you toward the middle of the tunnel grows in proportion to your distance from that middle, which is exactly a spring: the period doesn’t depend on where you start.

What happens when you reach B?

You’d arrive just as you stop. If nobody grabbed you, you’d fall back toward A and keep oscillating forever with no air or friction. With air, drag would leave you stuck at the deepest point.

Why is the Earth a sphere in this tool?

Because the PREM model, used for the layers and the fall, is spherical. The Earth’s flattening changes the tunnel length by 0.6% at most (we checked against the WGS84 ellipsoid).

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