He was significantly more accurate than that. The degree of his error is slightly complicated by the stadia 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.

Here is a picture visually demonstrating how he performed his calculation.