About the Egyptian Earth Circumference Method
The old Egyptian method is linked with Eratosthenes. He used sunlight, distance, and geometry. At Syene, the noon sun was almost overhead. At Alexandria, a vertical stick made a shadow. The shadow angle was about 7.2 degrees. That angle is one fiftieth of a circle. Multiplying the ground distance by fifty gave an estimate for Earth’s circumference.
How the Calculator Recreates the Idea
This calculator follows that same idea. It turns a measured arc distance and a central angle into a full circle. You may enter the angle directly. You may also enter stick heights and shadow lengths. The tool then finds each solar zenith angle with arctangent. The difference between those angles becomes the central angle.
Why Unit Choice Matters
A stadia conversion is included because ancient distance units vary. Some studies use about 157.5 meters per stadium. Others use about 185 meters. The custom box lets you test both assumptions. This is useful because the final circumference changes directly with distance.
Accuracy and Uncertainty
The calculator also supports uncertainty. Distance errors and angle errors are combined as relative error. Small angle mistakes can create large changes. That is why careful noon timing matters. The two sites should lie close to the same meridian. Otherwise, longitude separation can distort the result.
You can compare your result with a reference circumference. The default reference is close to the mean modern Earth value. You can enter another value for classroom exercises. The percent error shows how far the estimate is from that reference.
Learning Value
The method is simple, but it is powerful. It shows how shadows can measure a planet. It also connects surveying with trigonometry. A short baseline, a clear shadow, and a known angle can reveal a huge scale.
Use the example table to test typical cases. Then adjust distance, angle, and stadium length. Download the result when you need a record. The CSV file is useful for spreadsheets. The PDF file is useful for reports and assignments.
For best learning value, keep notes beside each trial. Record the city pair, date, noon method, and distance source. Repeat the calculation with another stadium length. The comparison shows which assumption drives the answer. It also helps students see why ancient measurements could be impressive, even when inputs were uncertain or incomplete records.