It's often said that architecture involves a lot of multivariable calculus, and for my (high school) Multivariable calculus project, I wanted to do further research on that. However, so far I haven't been able to exactly determine what specific maths architects use and how they use it. For instance, I heard quite often that architects use integral calculus, but how exactly do they use it? Does anyone know a lot about these or can someone recommend me any books/articles that go pretty in-depth relating to this subject? Any help would really be appreciated!
2026-05-16 08:04:18.1778918658
multivariable calculus and architecture
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*I should clarify that I might be missing the point of the question entirely, and if so, please excuse me.
Source: I have worked professionally as an Architect for the past 5 years, and have completed my Master of Architecture degree.
Outside of the profession, the perceived level of mathematics is often overestimated. I never took calculus, and only went up to trigonometry. I do project design and management, and the only math that I use on a routine basis is basic geometry. The computer programs that we work with these days (sketchup, revit, autocad) do the heavy mathematic lifting, and we primarily focus on the 2D/3D representation and constructability concerns.
An example of a frequent calculation I do is determining the riser height of stairs between two floors of a building. 11'-6" between floors: 11 x 12" = 132". 132" + 6" = 138". The building code dictates a maximum riser height of 7" in commercial spaces, so 138" / 20 = 6.9" Very rudimentary stuff. Roof pitches are determined by well-established industry standards such as a 7:12 slope is about as steep as anyone can walk, and anything below 3:12 slope requires extra cost and waterproofing.
The myriad of concerns that Architects consider on a daily basis frequently revolve around numbers, but not in an intense number crunching way (we rely on engineers for that), and are more guidelines with which we work and not the primary focus.