The accuracy he achieved and in that time period with the information available to him is frankly staggering. The degree of his error is slightly complicated by the stadion not being a historically exact figure, but his calculation showed the Earth to be 252,000 stadia in circumference. Accounting for the variability in the exact length of the stadia dependent on what definition was used in the calculation, that gives us in kilometers 39,060km on the lower end and 40,320km on the upper. The actual circumference of the Earth is 40,075km. This gives him an error range of between -2.4% and +0.8%.
He also didn't just use a stick but used extensive geographic charts to calculate the distance between the 2 cities where he measured the shadow. It was a monumental achievement and is shockingly accurate. I also believe this knowledge was lost to time and for quite a long time after we did not have any measurements even close to this accuracy.
Here is a picture visually demonstrating how he performed his calculation.