Estimating the Earth's Circumference
A classic Fermi estimation using what we know about time zones and the United States.
What We Know
The Earth has 24 time zones (one for each hour). The continental US spans about 4 of these time zones (Eastern, Central, Mountain, Pacific). And we roughly know how wide the US is.
The Estimation
US Width
The continental US is roughly 2000-3000 miles wide:
us_width = 2000 to 3000 mile2400 [2000, 3000] mile {length}
Time Zone Width
The US spans about 4 time zones, so each time zone is:
us_timezones = 3 to 5
timezone_width = us_width / us_timezones630 [460, 870] mile {length}
Earth's Circumference
With 24 time zones around the Earth:
num_timezones = 24
earth_circumference = timezone_width * num_timezones15000 [11000, 21000] mile {length}
Convert to Kilometers
earth_circumference_km = earth_circumference as km24000 [18000, 34000] km {length}
Result
The Earth's circumference is approximately 15000 [11000, 21000] mile {length} or 24000 [18000, 34000] km {length}.
The actual value is about 24,901 miles (40,075 km) - let's see how close our estimate is!