Horizon Distance Calculator
Calculate the distance to the visible horizon based on your height above sea level. Includes radar horizon, radio horizon, and line-of-sight calculations with atmospheric refraction. Perfect for navigation, aviation, and radio communications.
What Is the Horizon?
The horizon is the apparent line that separates the Earth from the sky. Due to the curvature of the Earth, the visible horizon is a circle around the observer where the line of sight is tangent to the Earth's surface. The distance to the horizon depends on the observer's height above sea level and atmospheric conditions.
This calculator computes three types of horizon distances:
- Visual Horizon: The distance to the visible horizon, accounting for atmospheric refraction (standard factor k = 1.143).
- Radar Horizon: The horizon for radar signals, which can bend more due to atmospheric conditions (typically k ≈ 1.333).
- Radio Horizon: The horizon for radio communications, which can be extended by atmospheric ducting (typically k ≈ 1.33-1.5).
How Does the Horizon Distance Calculator Work?
The calculator uses the standard horizon distance formula:
d = √(2 · R · h) · k
Where:
d = Horizon distance (km)
R = Effective Earth radius (km)
h = Observer height (km)
k = Refraction factor (dimensionless)
For line of sight to a target at height ht:
dtotal = √(2·R·h) · k + √(2·R·ht) · k
The radar horizon uses a factor of k ≈ 1.333 (4/3 Earth radius), while the radio horizon can range from k ≈ 1.33 to 1.5 depending on atmospheric conditions. The dip angle is the angular depression of the horizon below the horizontal plane.
Why Use This Horizon Distance Calculator?
- Three Horizon Types: Visual, radar, and radio horizon calculations.
- Target Visibility: Calculate the line-of-sight distance to a target object.
- Refraction: Adjustable refraction factor for different atmospheric conditions.
- Visual Representation: Animated diagram shows the geometry of the horizon.
- Free & Private: No registration, no data storage.
❓ Horizon Distance Calculator FAQ
What is the distance to the horizon?
The distance to the horizon is the maximum distance at which the Earth's surface is visible from a given height above sea level. It depends on the observer's height and atmospheric refraction.
What is the formula for horizon distance?
The standard formula is d = √(2·R·h), where R is the Earth's radius (6371 km) and h is the observer's height above sea level. With refraction, d = √(2·R·h)·k, where k ≈ 1.143.
What is the effective Earth radius?
The effective Earth radius is the radius of a hypothetical Earth that would produce the same horizon distance as the actual Earth with atmospheric refraction. For standard refraction, R_eff = R × k ≈ 7284 km.
What is the refraction factor (k)?
The refraction factor accounts for the bending of light (or radio waves) by the atmosphere. For visual horizon, k ≈ 1.143. For radar, k ≈ 1.333. Higher k values mean the horizon is farther away.
How does height affect the horizon distance?
The horizon distance is proportional to the square root of the height. Doubling the height increases the horizon distance by about 41% (√2 ≈ 1.414).
How does atmospheric refraction affect the horizon?
Atmospheric refraction bends light (or radio waves) downward, allowing the horizon to appear farther away. The standard refraction factor for visual light is k ≈ 1.143, which increases the horizon distance by about 14%.
What is the dip angle?
The dip angle is the angular depression of the horizon below the horizontal plane. For an observer at height h, the dip angle is approximately dip = arccos(R/(R+h)). It is typically measured in arcminutes or degrees.
How far can I see from a cruise ship?
From a cruise ship deck about 10 meters above sea level, the visual horizon is about 11.3 km (7 miles). From the bridge at 20 meters, it's about 16 km (10 miles).
How far can I see from an airplane?
At cruising altitude (10,000 m / 33,000 ft), the visual horizon is about 357 km (222 miles). From 35,000 ft, it's about 370 km (230 miles).
How far can a radar see?
The radar horizon is about 15-20% farther than the visual horizon due to atmospheric ducting and refraction. For a radar at 10 m height, the radar horizon is about 13-14 km.
What is the line of sight between two objects?
The line of sight distance between two objects is the sum of their individual horizon distances: d_total = d(h1) + d(h2). This calculator includes a target height option to compute this.
What is the maximum distance to the horizon on Earth?
The theoretical maximum distance to the horizon on Earth is from the highest point (Mt. Everest, 8,848 m), which gives a horizon distance of about 336 km (209 miles). From an airplane at 10,000 m, it's about 357 km.