What is the formula to determine the needed reserves for a condo association given the size and age of the condo properties?

The basic way is to identify the components, establish the useful life of each, estimate the replacement cost, then deposit the mathematical amount necessary each period to fund the replacement: there really is NO specific formula.

Set a standard for replacement:
Say any item that would cost $10000 to replace

Now you take the useful life span of the item if new say 20 years and estimate the useful life remaining say ten years

That equates to 5000 dollars for 10 more years of useful life or 500 per year to be put in the reserves provided you all ready have 5000 in the reserves, or 1000 a year if you do not.

NOTE: You must have experience in the evaluation of the components of a property age, environment, general condition, , the roofing, landscape, mechanical systems, and more.

Another answer:
A formal reserve study produced by a licensed reserve study specialist can give you the remaining useful life of each of the components that the association's members own in common, and approximate a replacement, refurbishment or major repair cost at the end of each useful life.

In Washington State, the state law requires that an association budget for a reserve study each year, wherein every three years, a formal study be done and during the in-between years, the study be updated.

It's up to the board to decide how fully to fund reserves that are set aside each month in order to pay for major replacements identified in the reserve study.

This decision is generally made on the basis of the membership's ability to successfully pay a special assessment that may be required during the year that the replacement occurs. The special assessment can be in the amount of a substantial portion, a small portion, any or all of the replacement cost.