Enter the distance, drop, observer height, or horizon distance into the calculator to determine Earth’s curve measurements.
Related Calculators
- Horizon Distance Calculator
- Line of Sight Calculator
- Height Distance Calculator
- Angle of Elevation Calculator
- Viewing Angle Calculator
- All Construction Calculators
Earth Curve Formula
The following equations are used to calculate the drop due to curvature and the horizon distance based on the observer's height.
Drop = d^2 / (2R) Horizon = \sqrt(2R * h)
- Where Drop is the vertical drop in meters
- d is the distance in meters
- R is Earth's radius (approximately 6,371,000 m)
- Horizon is the distance to the horizon in meters
- h is the observer's height in meters
To calculate the drop, square the distance and divide by twice Earth's radius; to calculate the horizon, multiply the observer's height by 2R and take the square root.
What is an Earth Curve Calculator?
Definition:
An Earth Curve Calculator estimates the curvature of the Earth by determining the vertical drop over a given distance or by calculating the distance to the horizon from an observer’s height.
How to Calculate Earth Curve Measurements?
Example Problem:
The following example outlines the steps and information needed to calculate Earth's curve measurements.
First, consider a distance of 1000 m.
Next, calculate the drop using the formula above:
Drop = d^2 / (2R)
Drop = 1000^2 / (2 * 6371000)
Drop ≈ 0.0785 m
Then, consider an observer height of 2 m.
Now, calculate the horizon distance using the corresponding formula:
Horizon = sqrt(2R * h)
Horizon = sqrt(2 * 6371000 * 2)
Horizon ≈ 5048.3 m
FAQ
What does the Earth Curve Calculator compute?
It calculates the vertical drop due to Earth’s curvature based on distance and determines the horizon distance based on an observer’s height.
What assumptions are made in these calculations?
The calculator assumes a spherical Earth with a constant radius of approximately 6,371,000 m and does not factor in atmospheric refraction or terrain variations.
How should I use the calculator?
For each calculation pair (Distance/Drop and Observer Height/Horizon), provide one value and leave the other blank so the calculator can compute the missing measurement.