Distance to Horizon Calculator

About the Distance to Horizon Calculator

Calculates the distance to the visible horizon from your eye height above sea level, accounting for the Earth's curvature.

How to use

Enter your eye height above the surface in metres, then click Calculate.

Worked example

From 1.7 m (standing) → about 4.7 km; from a 100 m cliff → about 35.7 km.

How to use this calculator

1. Enter your height above ground or sea level.
2. Choose the unit for your height if the tool asks for it.
3. Read the horizon distance shown by the calculator.
4. Use the example or formula if you want to check the result by hand.

The formula explained

• \(d\) = distance to the horizon
• \(h\) = height above the Earth's surface in the same distance unit system used by the calculator, usually meters
• \(3.57\) = a constant for the Earth's curvature when using kilometers for distance and meters for height

Step by step method

1. Take the height above the Earth's surface and make sure it is in the unit the calculator expects.
2. Square root the height value.
3. Multiply that square root by 3.57 to get the approximate distance to the horizon in kilometers.
4. If needed, convert the answer into your preferred distance unit.

Worked example

Suppose you are standing on a 25 meter high cliff and want to know how far away the horizon is.

1. Use the formula \(d \approx 3.57\sqrt{h}\).
2. Substitute \(h = 25\): \(\sqrt{25} = 5\).
3. Multiply: \(3.57 \times 5 = 17.85\).

Tips and common mistakes

• This calculator gives an approximate line of sight distance to the geometric horizon, not the distance to visible objects.
• Make sure height is measured from the Earth's surface, not just from the floor of a room.
• Higher viewpoints increase horizon distance quickly, but the relationship is with the square root of height, not a straight line.
• Atmospheric refraction can make the real visible horizon a little farther than the basic formula suggests.

Frequently asked questions