Earth Curvature Calculator
Calculate how much of distant objects is hidden by Earth's curvature and determine horizon distance
Calculate Earth Curvature Effects
Distance from you to the object being viewed
Height of your eyes above sea level
Earth Curvature Results
Distance to Horizon
Obstructed Object Height
Horizon Formula: a = √((r + h)² - r²)
Obstruction Formula: x = √(a² - 2ad + d² + r²) - r
Curvature Drop: 0.4 inches per mile
Curvature Analysis
Example Calculation
Ship on the Horizon
Observer: Standing at sea level, eyes 1.6 m above water
Ship distance: 25 km away
Horizon distance: √((6,371 + 0.0016)² - 6,371²) = 4.5 km
Hidden ship height: √(4.5² - 2×4.5×25 + 25² + 6,371²) - 6,371 = 98.4 m
Calculation Steps
1. Calculate horizon distance using Pythagorean theorem
2. Apply obstruction formula for objects beyond horizon
3. Account for Earth's spherical geometry
4. Result shows how much of object is hidden by curvature
Earth Curvature Facts
Curvature Tips
Higher observation points see farther horizons
Objects appear to "rise" from the horizon when approaching
Atmospheric refraction can extend visible distance
Curvature is more noticeable over water than land
Ancient sailors used curvature to navigate
Understanding Earth's Curvature
What is Earth's Curvature?
Earth's curvature refers to the gradual bend of our planet's surface. Because Earth is roughly spherical, the surface curves away from any observer, creating a horizon beyond which objects become hidden from view.
Observable Effects
- •Ships appear to "rise" from the horizon when approaching
- •Tall buildings disappear bottom-first over distance
- •The horizon appears as a curved line from high altitudes
- •Higher observation points yield more distant horizons
Mathematical Formulas
Distance to Horizon: a = √((r + h)² - r²)
Obstructed Height: x = √(a² - 2ad + d² + r²) - r
- a: Distance to horizon (km)
- r: Earth's radius (6,371 km)
- h: Observer height above sea level (km)
- d: Distance to object (km)
- x: Hidden height of object (km)
Note: These formulas assume Earth is a perfect sphere. Actual Earth is slightly flattened (oblate spheroid), and atmospheric effects can modify results.
Historical and Practical Applications
Navigation
Ancient sailors used curvature effects to determine distances to land and navigate by observing how objects appeared and disappeared over the horizon.
Surveying
Land surveyors must account for Earth's curvature when measuring long distances to maintain accuracy in mapping and construction projects.
Astronomy
Understanding curvature helps in calculating optimal viewing locations for astronomical observations and determining Earth's true shape and size.