Horizon Distance Calculator

General Physics | Calculate Your Line of Sight to the Horizon

Find out how far you can see to the horizon based on your height, Earth's radius, and optional refraction. Perfect for navigation, hiking, aviation, and more.

Examples

See how horizon distance changes with different heights and conditions.

Standing on the Beach

Basic

A person 1.7 meters tall stands at sea level. How far is the horizon?

Observer: 1.7 meters

Target: -

Earth Radius: 6371 kilometers

Refraction: No

Mountain Top View

Mountain

An observer is on a 2000 meter mountain. How far can they see to the horizon?

Observer: 2000 meters

Target: -

Earth Radius: 6371 kilometers

Refraction: Yes

Seeing a Distant Skyscraper

Target

You are 2 meters above ground, and a skyscraper is 300 meters tall. Can you see it over the horizon?

Observer: 2 meters

Target: 300 meters

Earth Radius: 6371 kilometers

Refraction: No

Custom Planet (Mars)

Custom

Standing 1.8 meters tall on Mars (radius 3389.5 km). How far is the horizon?

Observer: 1.8 meters

Target: -

Earth Radius: 3389.5 kilometers

Refraction: No

Other Titles
Understanding Horizon Distance: A Comprehensive Guide
Learn how to calculate and interpret the distance to the horizon in real-world scenarios.

What is Horizon Distance?

  • Definition of Horizon Distance
  • Why Does the Horizon Exist?
  • Factors Affecting Horizon Distance
Horizon distance is the maximum distance an observer can see before the Earth's curvature blocks further view. It depends on the observer's height, Earth's radius, and atmospheric conditions.
Key Concept: Earth's Curvature

Real-World Examples

  • A person standing on a beach sees the horizon much closer than someone on a mountain.
  • Pilots use horizon distance to estimate visibility at altitude.

Step-by-Step Guide to Using the Calculator

  • Input Your Height
  • (Optional) Add Target Height
  • Adjust for Refraction or Planet
To use the calculator, enter your eye height above ground or sea level. Optionally, add a target's height and adjust the planet's radius or include atmospheric refraction for more accuracy.
Simple Steps for Accurate Results

Usage Scenarios

  • Standing on a 2m pier, you can see farther than at ground level.
  • On Mars, the horizon is closer due to the smaller radius.

Real-World Applications of Horizon Distance

  • Navigation and Sailing
  • Aviation and Piloting
  • Landscape and Photography
Horizon distance is crucial in navigation, aviation, and landscape planning. It helps sailors, pilots, and photographers understand visibility limits and plan routes or shots accordingly.
Practical Uses in Daily Life

Application Examples

  • Sailors estimate how far they can see ships or land.
  • Photographers plan panoramic shots from high elevations.

Common Misconceptions and Correct Methods

  • Ignoring Earth's Curvature
  • Forgetting Refraction
  • Confusing Units
Many people underestimate the effect of Earth's curvature or forget to include atmospheric refraction. Always use correct units and formulas for accurate results.
Avoiding Calculation Mistakes

Misconception Examples

  • Assuming you can see forever from a mountain top.
  • Using feet instead of meters without conversion.

Mathematical Derivation and Examples

  • The Horizon Distance Formula
  • Unit Conversions
  • Worked Examples
The main formula is d = sqrt(2Rh + h^2), where d is the distance, R is the planet's radius, and h is the observer's height. For small h, d ≈ sqrt(2Rh). Always convert units to match (e.g., meters to kilometers).
Sample Calculation: 2m Observer on Earth

Mathematical Examples

  • With h=2m, R=6371km, d ≈ 5.06km.
  • With h=2000m, d ≈ 159.6km.