Calculators are fast because most of the time they are not calculating! [

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They use hard wired tables of precalculated values for lots of things, and then do computation on the intervals between these values. (Remember log tables and times tables [

]) Also they are usually calculating to a much higher precision than your PC for mathematics, the digits you see on screen are usually not the complete accuracy that was used for calculating, hence most calculators have an "extended" mode that lets you see more digits or calculate with more.

Calculators get away with this kind of thing to be fast where desktop PCs can't. PCs are a general computer and have to deal with far far far more calculations happening of various kinds with multiple inputs and outputs. With a PC you can calculate the n'th root of tan(x) whilst browsing a Science Forum about why your PC is so much slower than a calculator!

Scientific and programmable calculators are faster than a PC mostly because they have extra hardware implementations for maths operations AND don't have anywhere near the software overheads of a PC, they usually have a single program operating system which straight away gives you massive performance.

If you wrote a calculator program for your PC that was the only thing running from boot (no Windows) it would be incredibly fast compared to your hand calculator.