Flat Vs Round Earth
Test three experiments to determine if the Earth is flat or round: sunset twice, disappearing objects, and stick shadows. Free online physics calculator with charts.
About This Calculator
The Flat Vs Round Earth Calculator lets you perform three classic physics experiments that demonstrate the Earth's curvature. Whether you are a student, educator, or science enthusiast, these experiments provide clear, repeatable evidence that the Earth is round. Each experiment tests a different prediction of the round Earth model against what a flat Earth would predict.
Experiment 1: Sunset Twice
This experiment proves the Earth is round by showing that you can see a sunset twice by moving upward quickly. When the sun sets, the Earth's horizon casts a shadow that rises upward at a predictable rate given by the formula t = 8 × √h, where t is the time in seconds for the shadow to rise by height h in meters. By moving from a low position (lying down) to a high position (standing up) faster than the shadow rises, you can see a portion of the sun again. Our calculator tells you exactly what percentage of a second sunset you should see based on your starting height, ending height, travel time, and location's sunset duration. Try the Lie Down Stand Up preset for a simple beach experiment, or the Skyscraper Lift preset to see how much more you can see from a fast elevator.
Experiment 2: Disappearing Objects
This experiment uses the Earth's curvature to hide part of a distant object. From a high viewpoint (such as standing up), you observe a distant object across a body of water. Then you lower your viewpoint (such as lying down or lowering a camera). The curvature of the Earth will hide part of the object from the lower viewpoint. The hidden height is calculated using the Earth's radius of 6,371 km and standard curvature formulas: first the distance to the horizon (a = √[(R + h)² - R²]), then the obscured height at distance d. On a flat Earth, lowering your viewpoint would reveal more of the object — never hide it. This experiment works best across a lake at least 2 km wide, using a camera with a zoom lens on a tripod for accurate measurements.
Experiment 3: Stick Shadows
This classic experiment, first performed by Eratosthenes in 240 BC, not only proves the Earth is round — it also measures its circumference. By planting a stick of known length in the ground at two different locations with a known north-south distance, and measuring the shadow length at local noon, you can calculate the Earth's circumference. The formula uses the difference in shadow angles (θ = arctan(shadow length / stick height)) to find the angular difference between the two locations, then scales up the north-south distance to the full circumference. Our calculator compares your result to the actual polar circumference of 40,008 km and shows your percentage accuracy.
Regional Notes
These experiments work anywhere in the world — the Earth's curvature affects all locations equally. The sunset duration varies by latitude (near the equator, sunsets are shorter at about 2 minutes; at higher latitudes like London, they can last over 3.5 minutes), which is why our calculator includes location presets. In the US and UK, you can use miles and feet instead of kilometers and meters by adjusting the conversion. The stick shadow experiment works best during the summer solstice (June 21) or winter solstice (December 21) when day length changes slowly, reducing measurement errors.
Frequently Asked Questions
How can the sunset twice experiment prove the Earth is round?
By moving upward quickly after the sun sets, you can get ahead of the Earth's shadow and see part of the sunset again. If the Earth were flat, no amount of upward movement would reveal the sun again after it set. Our calculator computes how much of a second sunset you should see based on your starting height, ending height, and travel time.
How does the disappearing objects experiment work?
The disappearing objects experiment uses the Earth's curvature to hide distant objects. By observing a distant object from a high viewpoint and then lowering to a low viewpoint, part of the object becomes hidden behind the curvature. On a flat Earth, lowering your viewpoint would not hide any part of a distant object. Our calculator determines how much height becomes hidden based on the distance to the object and the difference in viewpoint heights.
How can stick shadows measure the Earth's circumference?
The stick shadow experiment was first performed by Greek mathematician Eratosthenes around 240 BC. By measuring the shadow cast by a stick of known length at two different locations with a known north-south distance, you can calculate the angle difference and estimate the Earth's circumference. Our calculator compares your result to the actual polar circumference of 40,008 km.
What is the curvature of Earth per kilometer?
The Earth curves approximately 7.85 cm per kilometer (or about 8 inches per mile). This means that for every kilometer between you and an object, the curvature will obstruct nearly 8 cm of the object's bottom. This curvature is what causes ships to disappear hull-first over the horizon.
At what altitude can you see the curvature of Earth?
You need to be at an altitude of approximately 35,000 feet (10.5 km), which is about the cruising altitude of a passenger plane, to see the curvature of the Earth. However, it requires a completely clear horizon with no clouds and a field of view of at least 60 degrees, which is rarely possible from a plane window.
How far is the horizon at sea level?
At sea level with an eye height of 1.6 meters, the horizon is approximately 4.5 km (2.8 miles) away. The distance increases with height: from a height of 100 meters, the horizon extends to about 35.7 km, which is why you can see France from the Cliffs of Dover on a clear day.
What would happen if the Earth were flat?
If the Earth were flat, you would see the entire ship from afar even at great distances — it would start out very small and then get larger as it approached, with no part hidden by curvature. There would be no horizon in the way we experience it, no time zones (sunrise and sunset would occur at the same time everywhere), and the sun would not disappear below the horizon. None of these predictions match what we actually observe.
Can I prove the Earth is round at home?
Yes. The simplest proof is to watch a sunset while lying down on a beach. As soon as the sun disappears, stand up quickly — you will see a small portion of the sun again. This only works because the Earth's curved surface creates a shadow that rises as the sun sets. On a flat Earth, the sun would simply get smaller and disappear at the same time regardless of your height. Our calculator helps you predict exactly how much of the second sunset you should see.