[thirdhaf]

By 1870 pi was known to several hundred decimal digits, for something like this calculation where you have other large sources of error Archimedes approximation from 2 millennia earlier would probably be fine. (<1% error)

https://en.m.wikipedia.org/wiki/Chronology_of_computation_of...

[jjk166]

Note that pi to 40 digits is sufficient to calculate the circumference of the observable universe to subatomic precision.