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My initial thoughts were how does a spreadsheet do it? but it's a different kind of beast.
In search of a parser toolkit I had come across this https://github.com/handsontable/hyperformula which uses chevrotain to parse spreadsheet formulas and decided to use chevrotain for the parsing.
I made a list of calculators like this which were shared here on HN over time https://gist.github.com/SMUsamaShah/6546011091d53380354484a3...
From these https://bbodi.github.io/notecalc3/ and https://notepadcalculator.com/ are the most programmer friendly (supporting <<, ^, binary, hex etc)
Emacs has literate-calc-mode which I use with org-mode: https://github.com/sulami/literate-calc-mode.el