Earth Curvature Calculator
Calculate how much Earth curves at a given distance
How to Use
- Enter the horizontal distance you want to measure
- Select the unit of measurement (meters, kilometers, miles, or feet)
- Click calculate to see the curvature height and horizon distance
- Review the results showing how much Earth curves at that distance
What is Earth Curvature?
Earth curvature refers to the curve of Earth's spherical surface. When looking across large distances, the curve of Earth causes the surface to drop below the observer's line of sight. This effect becomes noticeable over distances of a few kilometers or miles.
The curvature can be calculated mathematically using the Earth's radius (approximately 6,371 km) and basic geometric principles. This is important for long-distance surveying, aviation, maritime navigation, and understanding why we cannot see objects beyond the horizon.
Curvature Calculation Formula
The height of Earth's curvature (drop from line of sight) is calculated using:
h = d² / (2R)
Where:
- h = height drop due to curvature
- d = horizontal distance traveled
- R = Earth's radius (6,371 km)
This formula shows that curvature increases with the square of distance, meaning it becomes more pronounced over longer distances.
Horizon Distance
The horizon distance is how far an observer can see before objects disappear below the curvature. This distance depends on the observer's height above Earth's surface.
The horizon distance can be approximated using: d ≈ √(2Rh), where h is the observer's height above the surface and R is Earth's radius. This is why higher vantage points (mountains, airplanes) allow you to see farther.
Practical Applications
- Surveying: Adjusting measurements for Earth's curvature over long distances
- Aviation: Understanding visibility and navigation planning
- Maritime navigation: Calculating how far ships can see
- Photography: Planning shots for landscape photography
- Telecommunications: Designing radio transmission networks
- Astronomy: Understanding apparent positions of celestial objects
- Geography education: Teaching about Earth's shape and size
Earth Curvature at Different Distances
| Distance | Curvature Drop | Horizon Distance (at sea level) |
|---|---|---|
| 1 km | 0.0785 m | ~3.6 km |
| 10 km | 7.85 m | ~11 km |
| 50 km | 196 m | ~25 km |
| 100 km | 785 m | ~36 km |
| 500 km | 19.6 km | ~80 km |
Frequently Asked Questions
- At what distance does Earth's curvature become visible?
- Earth's curvature becomes slightly noticeable to the human eye at altitudes of 10-15 km (30,000-50,000 feet). Commercial aircraft fly at 10-12 km and passengers can sometimes see the curvature. From space (above 100 km), the curvature is very obvious.
- Why couldn't ancient people see Earth's curvature?
- From ground level, Earth appears flat because the curvature is too subtle to perceive visually. The horizon appears at eye level even though it's slightly curved. Only from high altitudes does the curve become apparent to the human eye.
- How accurate is this calculation?
- This calculator uses the spherical Earth model with an average radius of 6,371 km. It's accurate for most practical purposes. In reality, Earth is an oblate spheroid (slightly flattened at poles), but the difference is negligible for this calculation.
- Does this explain why ships disappear bottom-first over the horizon?
- Yes! As a ship moves away from shore, the curvature of Earth causes the bottom to drop below your line of sight first, while the top remains visible until the ship is even farther away. This is direct visual proof of Earth's curvature.
- What is the maximum horizon distance I can see from Earth's surface?
- From sea level with no obstructions, the horizon is approximately 4.7 km away. From a 2-meter height (typical eye level on land), it extends to about 5 km. The horizon distance increases with the square root of your height.