Earth Curvature Calculator
Calculate the visible horizon distance and how much of a distant object is hidden by Earth's curve.
Distance to Horizon:
Obscured (Hidden) Height:
The Mathematics of Curvature
The Earth is a sphere (approximately), which means that as you move away from an object, the ground curves downward, eventually obscuring the bottom of that object. This calculator uses spherical geometry to determine these values.
The Formulas
1. Distance to the Horizon (d)
This is how far you can see across the ocean before the water meets the sky.
d ≈ √(2 × R × h)
Where R is the Earth's radius and h is the observer's eye height.
2. Hidden Height (Obscured)
If a target is further than the horizon distance (d), part of it will be hidden behind the curve. The hidden height depends on the excess distance (Distance - Horizon Distance).
Hidden Drop ≈ 8 inches × (miles squared)
This familiar formula "8 inches per mile squared" is a parabolic approximation suitable for short distances (up to ~100 miles). For longer distances and high precision, trigonometric formulas (using Cosine) are used.
Atmospheric Refraction
Light bends as it travels through the atmosphere, typically curving with the Earth. This effect extends your visual horizon by approximately 15% under standard conditions. This calculator includes an option to toggle this "Standard Refraction" on or off.