Earth Curvature Calculator

The calculator includes 3 different formulas for curvature and 3 for line of sight.
You can download the calculator by clicking the link here: Download

How To Use The Calculator

Only enter numbers in the yellow boxes

The first step is to input Earth's circumference (in miles). The entire calculator refers to these numbers. So if you input earth's circumference to be 50,000 miles then the curvature and line of sight equations will change according to that.

I also included a conversion calculator. Use the yellow boxes to input miles, feet, inches, or kilometers.

The next step is to input the distance for curvature. So if you input 1 mile it will change the rest of the equations to 1 mile. In the example you can see that the curvature is 8 inches for 1 mile using the Zetetic equation and 7.99 inches using the Pythagorean Theorem and Trigonometry Formula. All equations (besides Zetetic) are affected by the dimensions of the earth above.

The last part of the calculator is line of sight. Input an eye level and height of an object (in feet) and it will calculate the distance to the horizon for each height. (input height above sea level to be exact)

This will calculate the maximum distance you can be from the object before it disappears under the horizon. If you know the distance to the object it will calculate how much of the object is visible above the horizon and how much is hidden below it. So in the example, if your eye level is at 6 feet above sea level and you are 6 miles away from a 10 foot object above sea level then 4 Feet of the object is visible while 6 feet is hidden below the horizon.

It is important to include sea level in your calculation. If you are viewing a 80 foot building and it begins at 20 feet above sea level than use a height of 100 feet. Also be aware the amount that is calculated for visible and hidden considers the whole height as one object. (Example: If the amount visible for the total 100 foot height is 40 feet then you should only be seeing half of the 80 foot building).

I also included an approximate refraction formula if anyone needs it. I got the formula from this Wikipedia article.

If you would like to know more about the equations I use I explain it in my post here

Well that's it! Please feel free to point out and correct any mistakes I have made. That is how we all learn and I want this to be as useful as possible. Don't hesitate to let me know if you have any criticisms, questions, and/or suggestions. I hope this helps as you research, hypothesize, theorize, test and analyze! Thanks for reading!