Astronomy and Space + Pure Mathematics
Measure the Earth's circumference like Eratosthenes
Measure a stick's shadow at local noon in two cities and calculate the size of the Earth.
- DifficultyIntermediate
- Estimated time1 day
- Budget₹0
- ClassClass 9–12
- Team2–4 people
- You needHousehold materials
Prerequisites: Basic trigonometry (tangent), angles in a circle
Original · by TechnifyedExperimentInvestigationFree to doResearch orientedWell documentedTwo subjects
Overview
Around 240 BC Eratosthenes used the different shadow angles in two Egyptian cities to measure the Earth. With a partner school to the north or south, you can repeat it in a day.
Why build this?
You measure a planet with a stick and a ruler, and usually land within 10 percent.
What you will learn
- How shadow angle relates to latitude
- How to find local noon from the shortest shadow
- How to use proportion on a circle
- How ancient scientists reasoned
Skills you will use
Safety
- Never look at the Sun directly or through any lens or telescope. Use projection or certified solar filters only.
Materials and tools
- A straight 1 m stick
- Spirit level or plumb line
- Measuring tape
- A partner at least 500 km north or south
- Map to find the north-south distance
Tools and software
Step-by-step roadmap
Start
You will finish with: a value for the Earth's circumference with your error and a diagram of the geometry.
- 1
Prerequisites
Know this first: basic trigonometry (tangent), angles in a circle. Then collect the 5 items in the materials list.
- 2
Learn
- How shadow angle relates to latitude
- How to find local noon from the shortest shadow
- How to use proportion on a circle
- How ancient scientists reasoned
- 3
Plan
Write your question, your hypothesis and the one thing you will change. Draw the table you will fill in before you start.
- 4
Build
- Fix the stick exactly vertical on flat ground.
- Mark the tip of the shadow every five minutes round midday and find the shortest.
- Calculate the Sun's angle from the vertical: tan of the angle = shadow ÷ stick height.
- Get the same measurement from your partner on the same day.
- Find the north-south distance between the two places.
- Circumference = distance × 360 ÷ difference in angles.
- 5
Test
A good result lies between 36,000 and 44,000 km.
- 6
Document
Record every reading with its unit, photograph the setup and draw a graph of the result. Report structure
- 7
Present
Explain the question, the method and the graph in two minutes; keep the setup ready to demonstrate. Presentation structure · Viva questions
- 8
Publish
Share the report and photos with your class, a science fair or your school magazine.
Expected outcome
A value for the Earth's circumference with your error and a diagram of the geometry.
Other versions of this project
Beginner version
Use an online solar calculator for the second city's angle instead of a partner.
Advanced version
Repeat on three dates and average; estimate the uncertainty from your shadow measurements.
Research version
Organise five schools at different latitudes and fit a line to angle against distance.
Make this project better
- BasicUse an online solar calculator for the second city's angle instead of a partner.
- This projectMeasure the Earth's circumference like Eratosthenes
- AdvancedRepeat on three dates and average; estimate the uncertainty from your shadow measurements.
- ResearchOrganise five schools at different latitudes and fit a line to angle against distance.
Ways to do this project
Text marked "You write this" is a prompt for your own work; everything else is specific to this project.
- Problem
- You write thisWrite your question as: How does [what you change] affect [what you measure]?
- Hypothesis
- You write thisWrite it as: If [I change this], then [this will happen], because [reason].
- Variables
- You write thisName the one thing you change (independent), the thing you measure (dependent) and what you keep the same (controlled).
Materials and procedure are in Materials and the Roadmap.
Observation table
You write thisDraw a table with one column for what you change, one for each repeat reading and one for the average.
- Graph
- You write thisPlot what you changed along the bottom and what you measured up the side; use a bar chart for categories and a line graph for numbers.
- Results
- You write thisState what the graph shows in one or two sentences, with numbers.
- Conclusion
- You write thisSay whether the result supports your hypothesis and why you think so.
Display board
- Title and your name
- Question
- Hypothesis
- Materials
- Procedure (with photos)
- Data table and graph
- Conclusion
- What you would do next
Questions judges ask
- Why must the two places be north and south of each other?
- Why measure at local noon?
- What did Eratosthenes assume?
- What would you change if you did this again?
- What was your biggest source of error, and how did you reduce it?
- Where is this idea used in real life?
- Research question
- You write thisOne question you can answer with data, narrow enough to finish in the time you have.
- Hypothesis
- You write thisWhat you expect to find, and why.
- Variables
- You write thisWhat you change or compare, what you measure, and what you hold constant.
- Methodology
- Organise five schools at different latitudes and fit a line to angle against distance.
- Data collection
- You write thisSay what you will record, how many times, and how you will keep the records safe.
- Analysis
- You write thisChoose the table, chart or test that answers the question; report averages with their spread.
- Limitations
- You write thisList what could have affected the result: small sample, instrument limits, things you could not control.
Literature review
Find five to eight sources (your textbook, review articles, reports) and note what each says about your question. Group them by idea, not one after another, and end with what is still not known.
References
List every source you used in one style throughout (author, year, title, where it was published, link and the date you opened it).
Working as a team
2–4 people. Suggested roles:
Report and presentation
Report structure
- Title and question
- Background: the science behind it
- Hypothesis
- Materials
- Method (steps, with a diagram or photo)
- Observations (table)
- Results (graph and calculation)
- Sources of error
- Conclusion
- What you would do next
- References
Presentation structure
- The question
- Why it matters
- The idea behind it
- Setup (photo)
- Method in three steps
- Results (one clear graph)
- What the result means
- Errors and limits
- Conclusion and next step
Viva questions
Try answering before you open each one.
Why must the two places be north and south of each other?
So the angle difference comes only from latitude, not from time of day.
Why measure at local noon?
The Sun is then highest and the shadow points along the north-south line.
What did Eratosthenes assume?
That the Sun's rays are parallel and the Earth is a sphere.
What is the accepted value?
About 40,075 km at the equator.
Resources
Source and attribution
Original
Written by Technifyed. Free to use for your own school or college project; write the report in your own words. Added 1 Oct 2026.
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