Distance to Horizon
Calculate how far you can see to the horizon based on your height. Includes Earth curvature effects, atmospheric refraction, and target visibility analysis for navigation and observation.
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Why: Understanding distance to horizon helps you make better, data-driven decisions.
How: Enter your values below and results will compute automatically.
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Input Parameters
Earth: 6371km, Mars: 3389km, Moon: 1737km
Horizon Distance on Earth
Horizon Distance
4.99 km
3.10 miles
Nautical Miles
2.69 nm
Sea navigation
Dip Angle
2.51'
0.042°
Curvature Drop
196.20 m
At horizon distance
Geometric Horizon
4.65 km
With Refraction
4.99 km
Refraction Coeff
0.13
Bulge Height
49.05 m
Effective Radius
7322.99 km
Planet
Earth
Step-by-Step Calculation
Visualizations
The distance to the horizon is how far you can see before the Earth's curvature blocks your view. It depends on your height above the surface and is affected by atmospheric refraction, which bends light and extends visibility slightly.
The Formula
R = planet radius, h = observer height
Quick Approximation
Simple formula for Earth
Reference: Horizon Distances
| Observer Height | Horizon (km) | Horizon (miles) | Example |
|---|---|---|---|
| 1.7 m | 4.7 km | 2.9 mi | Standing person |
| 10 m | 11.3 km | 7.0 mi | Building rooftop |
| 100 m | 35.7 km | 22.2 mi | Tall building |
| 1000 m | 113 km | 70 mi | Mountain |
| 10 km | 357 km | 222 mi | Commercial aircraft |
| 100 km | 1130 km | 702 mi | Weather balloon |
| 408 km | 2294 km | 1426 mi | ISS orbit |
Historical Significance
🧭 Age of Exploration
Understanding horizon distance was crucial for early navigators. Ship lookouts climbed masts to extend their view, and lighthouse heights were designed to maximize visibility for approaching ships.
🌍 Proving Earth's Curvature
The predictable disappearance of ships "hull-down" on the horizon was one of the earliest proofs that Earth is spherical. This observation dates back to ancient Greek astronomers.
For educational and informational purposes only. Verify with a qualified professional.
📋 Key Takeaways
- • Horizon distance increases with the square root of observer height: d ≈ 3.57 × √h (km) for Earth
- • Atmospheric refraction extends visibility by 6-8% beyond the geometric horizon
- • At sea level (1.7m height), you can see approximately 4.7 km (2.9 miles) to the horizon
- • Earth's curvature drops about 8 inches per mile squared - objects disappear "hull-down" beyond the horizon
💡 Did You Know?
📖 How Horizon Distance Works
The distance to the horizon depends on Earth's curvature and your height above the surface. The fundamental formula is d = √(2Rh), where R is the planet's radius and h is observer height.
Geometric Horizon
Without atmospheric effects, the horizon distance is purely geometric. For Earth (R = 6,371 km), a person at 1.7m height sees about 4.65 km to the geometric horizon.
Atmospheric Refraction
Light bends as it passes through Earth's atmosphere, effectively increasing the planet's radius. Standard refraction (k=0.13) extends visibility by about 6-8%, making the horizon appear at 4.92 km instead of 4.65 km.
Target Visibility
To see a distant object, both you and the object must be tall enough. The maximum visible distance equals your horizon distance plus the object's horizon distance. Earth's curvature hides the bottom portion of objects beyond your horizon.
🎯 Expert Tips
💡 Use Nautical Rule for Quick Estimates
For maritime navigation, use d (nm) = 1.17 × √h (feet). This accounts for standard refraction and is accurate enough for most sea navigation.
💡 Account for Refraction in Cold Weather
In cold conditions over warm water, refraction can be much stronger (k up to 0.25), extending visibility significantly - this creates superior mirages.
💡 Height Matters More Than Distance
Doubling your height only increases horizon distance by about 41% (√2). Climbing higher has diminishing returns, but even small height increases help significantly.
💡 Consider Planet Size
On smaller planets like Mars (radius 3,390 km) or the Moon (1,737 km), the horizon is much closer. This affects rover navigation and landing site selection.
⚖️ Horizon Distance Comparison
| Observer Height | Geometric (km) | With Refraction (km) | Example |
|---|---|---|---|
| 1.7 m | 4.65 | 4.92 | Standing person |
| 10 m | 11.3 | 12.0 | Building rooftop |
| 100 m | 35.7 | 37.8 | Tall building |
| 1000 m | 113 | 120 | Mountain peak |
| 10,000 m | 357 | 378 | Commercial aircraft |
| 408,000 m | 2294 | 2430 | ISS orbit |
❓ Frequently Asked Questions
How far can I see to the horizon at sea level?
At average eye level (1.7m), you can see approximately 4.7 km (2.9 miles) to the horizon on Earth. This increases to about 4.9 km with standard atmospheric refraction.
Why does atmospheric refraction extend the horizon?
Light bends as it passes through Earth's atmosphere due to density gradients. This effectively increases Earth's radius by about 8%, extending visibility beyond the geometric horizon.
How does horizon distance change on other planets?
Horizon distance is proportional to √(radius). On Mars (radius 3,390 km), the horizon is about 2.6 km away at eye level. On the Moon (1,737 km), it's only 2.4 km away.
Can I see objects beyond the horizon?
You can see tall objects beyond your horizon if they're tall enough. The maximum visible distance equals your horizon distance plus the object's horizon distance. Earth's curvature hides the bottom portion.
What is the dip angle and why does it matter?
The dip angle is how far the horizon appears below horizontal. At 1.7m height, it's about 2.5 arcminutes. This is crucial for celestial navigation and surveying.
How accurate is the simplified formula d = 3.57 × √h?
This formula (for Earth in km) is accurate to within 1% for heights up to several kilometers. It includes standard refraction and is perfect for quick calculations.
Why do ships disappear "hull-down" on the horizon?
Earth's curvature hides the bottom of objects first. As a ship sails away, the hull disappears below the horizon while the mast remains visible, creating the "hull-down" effect.
How does weather affect horizon visibility?
Cold air over warm water creates strong refraction (superior mirage), extending visibility. Fog, haze, and pollution reduce visibility regardless of geometric calculations.
📊 Horizon Distance by the Numbers
📚 Official Data Sources
⚠️ Disclaimer: This calculator provides estimates based on standard atmospheric conditions and Earth's mean radius. Actual visibility may vary due to weather, atmospheric conditions, and local terrain. For critical navigation applications, consult official nautical or aviation charts. Not a substitute for professional navigation equipment.
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