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)

= 263710.1

≈ 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:

dis the distance to the horizonRis the radius of the Earth (approximately6,371 kmor3,959 miles)his 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

6,371,000100) ≈ 35,676 meters or about35.7 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:

dis the distance in kilometershis the height of the observer in meters

## How do you calculate distance to the horizon?

Determine the observer’s heightabove the Earth’s surface.

Choose the appropriate formulabased on your needs (with or without atmospheric refraction).

Plug in the valuesto the chosen formula.

Perform the calculationto 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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