Random sample of points to calculate K function on a large point set

For a point pattern analysis in R, I want to study a relatively large point dataset (about 1 million points) with a cross K function to compare different categories of points. Including a Montecarlo simulation for envelope, the calculation of K on this dataset is very intensive, and I would like to sample the data to be able to calculate it faster.

How can I estimate the error in the result of K if I take a random sample of points (e.g., 1% or 5% of the data)? Can it be derived mathematically or should I run a Montecarlo simulation to see how much the results differ?