Distance to Horizon
Free online Distance to Horizon Calculator. Compute how far the horizon is from any height above Earth, Moon, Mars, Jupiter, and more. Uses d = √((R+h)²−R²) with instant results in km, miles, and nautical miles.
About This Calculator
The Distance to Horizon Calculator tells you how far you can see from any height above the surface of Earth or any other celestial body (Moon, Mars, Jupiter, etc.). Whether you're standing at sea level, on a mountain top, or wondering what the horizon would look like from another planet, this tool gives you the answer instantly using the geometry of spheres and Pythagoras' theorem.
How It Works
The horizon is the apparent line where the sky meets the ground. Geometrically, it is the point where your line of sight is tangent to the planet's surface. The distance to the horizon is calculated using the Pythagorean theorem applied to the right triangle formed by the planet's center, your observation point, and the horizon point:
d = √((R + h)² − R²)
Where d is the distance to the horizon, R is the radius of the celestial body, and h is the observer's height above the surface. For small heights relative to Earth's radius, this simplifies to the commonly used approximation d ≈ √(2 × R × h).
How to Use
Enter your height above the surface — switch between meters and feet using the unit selector. Choose a celestial body from the dropdown (Earth, Moon, Sun, Mars, Jupiter, Saturn) to use its exact radius. Click Calculate to see the horizon distance in kilometers, miles, and nautical miles, plus a comparison chart showing how the distance changes with height.
Regional Notes
United States: Height is commonly measured in feet. The approximation d (miles) ≈ √(1.5 × h (feet)) is widely used in maritime and aviation contexts. United Kingdom: Nautical miles are used for maritime navigation — 1 nautical mile = 1,852 m exactly. India: Metric units (meters, kilometers) are standard. The formula applies identically worldwide since it is purely a geometric relationship.
This calculator is ideal for sailors, pilots, hikers, photographers, and anyone curious about their visible range from a given elevation. It covers all the major celestial bodies in our solar system.
Frequently Asked Questions
How do you calculate the distance to the horizon?
The distance to the horizon is calculated using the Pythagorean theorem: d = √((R + h)² − R²) where R is the radius of the celestial body and h is the observer's height above the surface. For Earth with a 1.75 m tall observer, the horizon is about 4.7 km away.
How far is the horizon at sea level?
For a person of average height (1.75 m or 5'9'') standing at sea level on Earth, the distance to the horizon is approximately 4.7 km (2.9 miles or 2.5 nautical miles).
Does the distance to the horizon change on other planets?
Yes. Larger planets like Jupiter have a more distant horizon (about 15.6 km for a 1.75 m observer), while smaller bodies like the Moon have a closer horizon (about 2.5 km). The horizon distance depends directly on the square root of the body's radius.
How high must I be to see 10 km to the horizon?
To see 10 km to the horizon on Earth, you need to be about 7.85 meters (25.8 feet) above the surface. This is calculated by solving the horizon formula for height: h = √(R² + d²) − R.
What is the formula for distance to the horizon in miles?
The simplified approximation for distance to the horizon in miles is d ≈ √(1.5 × h) where h is the observer's height in feet. For example, at 6 feet above sea level, the horizon is about √(1.5 × 6) ≈ 3 miles away.
Can I use this calculator for mountains and elevated viewpoints?
Absolutely. Enter your elevation in meters or feet to calculate the distance to the horizon from a mountain top, building, or any elevated viewpoint. For example, from 100 m (328 ft) above ground, the horizon is about 35.7 km away on Earth.
Why is the horizon closer on the Moon than on Earth?
The Moon's radius (1,737 km) is much smaller than Earth's radius (6,371 km). Since the horizon distance is proportional to the square root of the radius, the smaller Moon curves away more quickly, resulting in a closer horizon — about 2.5 km vs 4.7 km on Earth for the same 1.75 m observer height.