There is an assumption that architects need to know a lot of math. My experience is that some calculator work is about the extent of what you need to know. However, there are times when a spreadsheet can make life easier. The document below came from a client’s request to know how large of a building could be built on his site. After several schemes to try to maximize the site, which took hours each, the light dawned. There is a way to determine the answer mathematically!
Zoning puts several limits on projects - setbacks, height limitation, parking requirement. This problem requires sophisticated math to solve, but fairly unsophisticated math to get an approximation. Into the spread sheet you put various guesses. The answer you get tells you what your next guesses should be. After a little trial and error you have better information than a half dozen schemes.
The second part of the spreadsheet below reverses the problem. How big of a site do we need for a building of 'X' SF?
In both cases some knowledge of site topography and building characteristics are critical. For instance, a site with too steep of a slope could be difficult to maximize. Or a three-story building with only 5,500 SF per floor might have less useable SF than a one or two-story solution because of the space tied up in steps, elevator, toilet rooms and even exterior wall thickness (multi-storied buildings have a higher ratio of exterior wall to floor area). Math doesn't tell you this, experience and common sense tell you this.
Math and especially spreadsheets can be timesavers, but a calculator has all the math you need to know.
The document is downloadable as a PDF.