How to Use Earth Tunnel Distance Calculator
The Earth Tunnel Distance Calculator answers a classic “what if you dug a tunnel through the Earth” question. Type two latitude/longitude pairs, choose your unit, and the Earth Tunnel Distance Calculator returns the straight chord through Earth alongside the great-circle surface distance.
- Enter the start coordinates — Latitude and longitude in decimal degrees.
- Enter the end coordinates — Same format. Negative values mean south or west.
- Pick the unit and radius — Default radius is 6371 km. Switch to miles or override the radius for custom planetary bodies.
- Read all four results — Tunnel distance, surface distance, their difference, and the central angle θ.
Formula & Theory — Earth Tunnel Distance Calculator
The Earth Tunnel Distance Calculator first finds the central angle θ between the two points with the haversine formula, then converts it to both a chord and an arc on a sphere of radius R:
a = sin²(Δφ / 2) + cos(φ1) · cos(φ2) · sin²(Δλ / 2)
θ = 2 · atan2(√a, √(1 − a))
surface = R · θ
tunnel = 2 · R · sin(θ / 2)| Symbol | Meaning |
|---|---|
| φ | Latitude in radians |
| λ | Longitude in radians |
| R | Earth radius |
| θ | Central angle |
Assumptions and Limits
The Earth Tunnel Distance Calculator treats Earth as a perfect sphere. Real Earth is an oblate spheroid, and any real tunnel would also face extreme heat, pressure, and inhomogeneous geology. Results are educational approximations only.
Use Cases for Earth Tunnel Distance Calculator
The Earth Tunnel Distance Calculator is a great teaching aid and trivia tool:
- Geography classrooms — Show the difference between great-circle distance and chord distance.
- Trivia and fun maths — Compute how short a hypothetical tunnel between any two cities would be.
- Astronomy and planetary science — Plug in another planet’s radius to compare chord and arc distances on different bodies.
- Spherical geometry intuition — Visualize how chord and arc converge for short distances and diverge for long ones.
For any “if you dug straight through” comparison, the Earth Tunnel Distance Calculator gives the chord, the arc, and the percentage shortcut in a single view.