Physics

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Earth Curvature Calculator.

Calculate spherical-Earth curvature drop across a chord distance.

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Curvature drop: 1.962016 m

Curvature drop

0.000000m

Results update automatically as you type.

Use Cases

Estimate horizon drop for long-distance views

Use this calculator to estimate how much the Earth's surface drops below a straight line over a given distance, useful for planning observations or understanding line-of-sight limitations.

Example: For a chord distance of 10,000 m and Earth radius 6,371,000 m, the drop is about 7.85 m.

Educational demonstrations of Earth's curvature

In physics or geography classes, this tool helps illustrate the spherical nature of the Earth by quantifying the curvature drop for various distances.

Example: Show that over 1 km the drop is only about 0.078 m, but over 100 km it becomes about 785 m.

Frequently Asked Questions

What does the Earth Curvature Calculator do?
This calculator computes the vertical drop (curvature) of the Earth's surface over a given chord distance, assuming a spherical Earth. You input the chord distance and Earth radius, and it outputs the drop in meters.
How is the curvature drop calculated?
The calculator uses the formula: drop = R - sqrt(R^2 - d^2), where R is the Earth radius and d is the chord distance. This gives the distance from the chord line to the Earth's surface at the midpoint.
What units should I use for the inputs?
Both the chord distance and Earth radius should be entered in meters. The result will also be in meters. Ensure you use consistent units for accurate results.

Tips & Common Mistakes

Tips

  • Use the standard Earth radius of 6,371,000 meters for most calculations, but you can adjust it if you're at a specific altitude or using a different reference ellipsoid.
  • Remember that this calculator assumes a perfect sphere, so results are approximations. For very long distances, the actual Earth's shape may cause slight deviations.
  • Double-check that your chord distance is not larger than the Earth's diameter, as the formula assumes a valid chord within the sphere.
  • For small distances (less than a few kilometers), the curvature drop is very small, so ensure you use enough decimal places in your inputs to get meaningful results.

Common Mistakes to Avoid

  • Using the Earth's radius in kilometers while the distance is in meters, leading to incorrect results. Always convert to the same unit.
  • Confusing chord distance with arc distance. This calculator uses the straight-line distance between two points on the surface, not the distance along the surface.
  • Forgetting that the drop is measured from the chord line to the surface, not from a tangent line. The tangent drop would be different.

Last updated: August 13, 2026