<aside> 🚧 This page is a heavy work in progress.
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Desmos is the most useful website you can have to do any math with. You can easily copy paste all any math snippets from the documentation into it and it works instantly. All graphs from the osu!at wiki use it in documentation as well.
The curves are literally the building blocks of every skill’s calculators. Take Slider Aim’s acc factor, for example:
It all starts out with combo scaling.
$$ f_{curve}\left(x\right)=\frac{1}{\left(x\cdot6\right)+1} $$
$x$ = number of 50s in the map
$$ h_{curve}\left(x\right)=\frac{1}{x+1} $$
$x$ = number of 100s in the map
$$ A_{ccFactor}=\left(\frac{c}{n}\cdot h_{curve}\left(h\right)\cdot f_{curve}\left(f\right)\right) $$