Distance to Horizon Calculator
Calculate how far you can see to the horizon based on your height above sea level
Height of observer's eyes above sea level
Quick reference: Average person ≈ 1.7 m, Building (10 floors) ≈ 30 m,
Mountaintop (1000 m) ≈ 1000 m, Aircraft (10,000 m) ≈ 10000 m
How to Use This Calculator
Enter Observer Height
Input the height of the observer's eyes above sea level in meters. For example, 1.7 m for an average person standing, 100 m for someone on a tall building, or 1000 m for someone on a mountain peak.
Calculate
Click the "Calculate Horizon Distance" button to get the distance to the horizon in meters, kilometers, and miles.
Interpret Results
The result shows how far you can see to the horizon. This assumes clear visibility and standard atmospheric conditions. Atmospheric refraction can slightly extend the visible horizon.
Formula
d = √(2Rh + h²)
Where:
- d = Distance to horizon (in meters)
- R = Earth's radius ≈ 6,371,000 meters (6,371 km)
- h = Observer height above sea level (in meters)
Simplified Formula (for small h):
d ≈ √(2Rh)
This approximation is accurate when h is much smaller than R
Example Calculation (Average Person):
For an observer with eye height of 1.7 meters:
h = 1.7 m
R = 6,371,000 m
d = √(2 × 6,371,000 × 1.7 + 1.7²)
d = √(21,661,400 + 2.89)
d = √(21,661,402.89) = 4,654 m
d ≈ 4.65 km
Example Calculation (Mountain Peak):
For an observer at 1,000 meters elevation:
h = 1,000 m
d = √(2 × 6,371,000 × 1,000 + 1,000²)
d = √(12,742,000,000 + 1,000,000)
d = √(12,743,000,000) = 112,900 m
d ≈ 113 km
About Distance to Horizon Calculator
The distance to the horizon is the maximum distance at which an observer can see objects on Earth's surface, limited by Earth's curvature. This distance depends on the observer's height above sea level—the higher you are, the farther you can see. This calculator uses the geometric formula that accounts for Earth's spherical shape to determine how far the horizon appears from any given height.
When to Use This Calculator
- Navigation: Calculate visible range for maritime and aviation navigation
- Photography: Plan landscape photography and determine how far landmarks will be visible
- Construction: Estimate visibility for buildings, towers, and observation platforms
- Astronomy: Understand how Earth's curvature affects observations
- Educational Purposes: Learn about Earth's geometry and visual limitations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate horizon distances immediately
- ✅ Easy to Use: Just enter your height above sea level
- ✅ Multiple Units: Results displayed in meters, kilometers, and miles
- ✅ Accurate Formula: Uses the exact geometric formula accounting for Earth's curvature
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
Common Applications
Maritime Navigation: Sailors and ship captains use horizon distance calculations to estimate when they'll see land or other vessels. From a ship's bridge at 10 meters height, the horizon is about 11.3 km away, which is crucial for navigation and collision avoidance.
Aviation: Pilots use horizon distance calculations to understand visibility limitations. At cruising altitude (10,000 m), the horizon is approximately 357 km away, though atmospheric conditions and aircraft design also affect visibility.
Landscape Photography: Photographers planning shots from elevated viewpoints use horizon distance calculations to understand what will be visible in their frame and how far they can see before the Earth curves away.
Tips for Best Results
- Use height in meters for the most accurate calculations
- Remember that actual visibility may be affected by atmospheric conditions, haze, and weather
- Atmospheric refraction can extend the visible horizon by about 8% under standard conditions
- For very high altitudes (aircraft), the simplified formula d ≈ √(2Rh) is very accurate
- The distance scales roughly with the square root of height—doubling height increases distance by about 41%
- At sea level (h ≈ 0), the horizon is at distance 0, which matches the formula
Frequently Asked Questions
Why does the horizon distance increase with height?
The horizon distance increases with height because you're looking from a higher vantage point. The Earth's curvature means that as you go higher, you can see over more of the curved surface before your line of sight is blocked by the horizon. The relationship is approximately proportional to the square root of height.
Does atmospheric refraction affect the horizon distance?
Yes, atmospheric refraction can extend the visible horizon by approximately 8% under standard conditions. Light bends slightly as it passes through Earth's atmosphere, making objects appear slightly higher than they actually are. However, for most practical purposes, the geometric calculation is sufficient.
What's the difference between the exact and simplified formulas?
The exact formula d = √(2Rh + h²) includes the h² term, which accounts for the observer's height relative to Earth's radius. The simplified formula d ≈ √(2Rh) is accurate when h is much smaller than R (which is true for most practical heights). For heights up to several kilometers, the difference is negligible.
Can I see objects beyond the horizon?
Typically, no—objects beyond the horizon are hidden by Earth's curvature. However, very tall objects (like mountains or tall buildings) may be partially visible above the horizon. Also, atmospheric refraction can sometimes make objects slightly beyond the geometric horizon visible under certain conditions.
How does this relate to the "flat Earth" misconception?
The distance to horizon is one of many proofs that Earth is curved. If Earth were flat, there would be no horizon limit—you could see infinitely far. The fact that the horizon distance increases with height (following the formula √(2Rh)) is consistent with a spherical Earth and inconsistent with a flat Earth.