Distance to Horizon Calculator
Calculate how far you can see to the horizon from any height above Earth or other celestial bodies
Calculate Distance to Horizon
Height of the observer above the surface
Select the celestial body or use custom radius
Distance to Horizon Results
Formula used: d = √((r + h)² - r²)
Celestial body: Earth (radius: 6371 km)
Observer height: 1.75 m above surface
Horizon Analysis
Example Calculation
Person on Earth's Surface
Observer height: 1.75 m (average human height)
Earth's radius: 6,371,008 m
Distance to horizon: √((6,371,008 + 1.75)² - 6,371,008²)
Result: 4.72 km
Calculation Steps
1. Add radius and height: r + h = 6,371,008 + 1.75 = 6,371,009.75 m
2. Square both terms: (r + h)² = 40,589,648,319,550.06 m²
3. Square radius: r² = 40,589,734,320,064 m²
4. Subtract and take square root: √(40,589,648,319,550.06 - 40,589,734,320,064) = 4,722 m
Final result: 4.72 km
Celestial Body Radii
Horizon Physics Facts
The horizon is closer on smaller celestial bodies
Height increases horizon distance exponentially
Formula assumes perfect sphere and no obstacles
Atmospheric refraction can extend visible horizon
Based on Pythagorean theorem geometry
Understanding Distance to Horizon
What is the Horizon?
The horizon is the apparent division between the sky and the ground as viewed from an observer near the surface of a spherical celestial body. It represents the farthest point you can see before the curvature of the planet blocks your view.
Why Calculate Horizon Distance?
- •Navigation and maritime applications
- •Astronomy and planetary observations
- •Understanding Earth's curvature
- •Aviation and radar applications
Formula Explanation
d = √((r + h)² - r²)
- d: Distance to horizon (meters)
- r: Radius of celestial body (meters)
- h: Height of observer above surface (meters)
Geometric Principle: The formula derives from the Pythagorean theorem applied to a right triangle formed by the center of the sphere, the observer's position, and the horizon point.
Key Factors Affecting Horizon Distance
Observer Height
Higher observation points dramatically increase horizon distance. Doubling height increases horizon distance by approximately √2 (1.41 times).
Planetary Size
Larger planets have more distant horizons. Jupiter's horizon is about 3× farther than Earth's for the same observer height.
Atmospheric Effects
Real-world factors like atmospheric refraction can extend the visible horizon beyond the geometric calculation by about 6%.