Our distance to horizon calculator is a powerful tool used to determine the maximum distance an observer can see before the Earth’s curvature obstructs using d = √(2Rh) formula.
If you are standing at a height of 100 meters above sea level, the calculation would be:
d = 2 6371 (100 / 1000)
= 2 6371 0.1
≈ 1274.2
≈ 35.69 km
Distance to Horizon Calculator
| Height (feet) | Distance to Horizon (miles) |
|---|---|
| 1 | 1.41 |
| 5 | 2.24 |
| 10 | 3.87 |
| 20 | 5.57 |
| 30 | 6.93 |
| 50 | 8.68 |
| 75 | 10.0 |
| 100 | 12.68 |
| 150 | 15.0 |
| 200 | 17.32 |
| 300 | 21.91 |
| 400 | 25.0 |
| 500 | 27.56 |
| 750 | 34.0 |
| 1,000 | 38.92 |
| 1,500 | 48.0 |
| 2,000 | 55.0 |
| 5,000 | 112.0 |
| 10,000 | 224.0 |
Distance to Horizon Formula
The formula for calculating the distance to the horizon is:
d = √(2Rh)Where:
- d is the distance to the horizon
- R is the radius of the Earth (approximately 6,371 km or 3,959 miles)
- h is the height of the observer above the Earth’s surface
This formula assumes the Earth is a perfect sphere, which is a close enough approximation for most practical purposes.
For instance, if you’re standing on a cliff 100 meters above sea level, you can calculate your distance to the horizon as follows:
d = √(2 6,371,000 100) ≈ 35,676 meters or about 35.7 km
What is the formula for the horizon range?
The horizon range formula is essentially the same as the distance to horizon formula.
d = 3.57 * √h
Where:
- d is the distance in kilometers
- h is the height of the observer in meters
How do you calculate distance to the horizon?
Determine the observer’s height above the Earth’s surface.
Choose the appropriate formula based on your needs (with or without atmospheric refraction).
Plug in the values to the chosen formula.
Perform the calculation to get the result.
Suppose you’re on the observation deck of the Empire State Building, which is approximately 381 meters (1,250 feet) above street level.
d = 3.57 √381
d ≈ *69.7 km
This means that on a clear day, you could theoretically see about 69.7 kilometers (43.3 miles) to the horizon in any direction from the Empire State Building’s observation deck.
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