How to Calculate the Distance to the Horizon
Measure your "height of eye.", Add your "local elevation" if you're standing on a raised surface, such as a hill, building or boat., Multiply by 13m if you took the measurement in meters, or multiply by 1.5ft if you took the measurement in feet...
Step-by-Step Guide
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Step 1: Measure your "height of eye."
Measure the length between the ground and your eyes in meters or feet.
One way to calculate this is to measure the distance between your eyes and the top of your head.
Subtract this value from your total height and what will be left is the distance between your eyes and the surface you're standing on.
If you are standing exactly at sea level, with the bottom of your feet level with the water, this is the only measurement you'll need. -
Step 2: Add your "local elevation" if you're standing on a raised surface
How many meters or feet above the true horizon are you standing? 1 meter? 4,000 feet? Add that number to your height of eye (in the same units, of course). ,, If you used meters, your answer will be in kilometers, and if feet, the answer will be in miles.
The distance calculated is a straight line from your eyes to the horizon.
The actual distance you'll travel to get to the horizon will be longer because of surface curvature and (on land) irregularities.
Proceed to the next method below for a more accurate (but complicated) formula. , It's based on a triangle formed by your observation point (your eyes), the true horizon point (what you're looking at) and the center of the Earth.
By knowing the radius of the Earth and measuring your height of eye and local elevation, that leaves only the distance between your eyes and the horizon as unknown.
Since the sides of the triangle that meet at the horizon actually form a right angle, we can use the Pythagorean theorem (good old a2 + b2 = c2) as the basis for this calculation, where:
• a = R (the radius of the Earth)
• b = the distance to the horizon, unknown
• c = h (your height of eye) + R -
Step 3: such as a hill
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Step 4: building or boat.
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Step 5: Multiply by 13m if you took the measurement in meters
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Step 6: or multiply by 1.5ft if you took the measurement in feet.
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Step 7: Take the square root to find the answer.
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Step 8: Understand how this calculation works.
Detailed Guide
Measure the length between the ground and your eyes in meters or feet.
One way to calculate this is to measure the distance between your eyes and the top of your head.
Subtract this value from your total height and what will be left is the distance between your eyes and the surface you're standing on.
If you are standing exactly at sea level, with the bottom of your feet level with the water, this is the only measurement you'll need.
How many meters or feet above the true horizon are you standing? 1 meter? 4,000 feet? Add that number to your height of eye (in the same units, of course). ,, If you used meters, your answer will be in kilometers, and if feet, the answer will be in miles.
The distance calculated is a straight line from your eyes to the horizon.
The actual distance you'll travel to get to the horizon will be longer because of surface curvature and (on land) irregularities.
Proceed to the next method below for a more accurate (but complicated) formula. , It's based on a triangle formed by your observation point (your eyes), the true horizon point (what you're looking at) and the center of the Earth.
By knowing the radius of the Earth and measuring your height of eye and local elevation, that leaves only the distance between your eyes and the horizon as unknown.
Since the sides of the triangle that meet at the horizon actually form a right angle, we can use the Pythagorean theorem (good old a2 + b2 = c2) as the basis for this calculation, where:
• a = R (the radius of the Earth)
• b = the distance to the horizon, unknown
• c = h (your height of eye) + R
About the Author
John Hernandez
Brings years of experience writing about DIY projects and related subjects.
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