Master List of Mental Calculation Techniques

I have always been interested in learning Mental Calculation, but I think many beginners would agree with me when I say that I am unsure of where to look to learn techniques. There are a lot of books discussing different techniques such as Arthur Benjamin’s, the Trachtenberg System, and using an abacus. To aid with this problem and thus help spread the popularity of mental calculation, I wanted to ask seasoned mental calculators on the forum: What are the techniques you keep readily at hand to answer a question?

With your answers, we could compile a master list which would look like this

Anchor Method
Trachtenberg System

Square Roots:
Duplex method

I think this would greatly help me and other beginners who would like to know what techniques are most helpful and what we should start learning if we’d like to excel at mental calculation.


Do you mean for competition or for general use?

Either would be fine, I wouldn’t expect much discrepancy (Is there a discrepancy?). I think general use may be better because those best for competition could be handpicked by the person reading the list.

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google “VEDIC MATHS”

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It can be useful.

In the book The new art of memory, founded upon the principles taught by M. Gregor von Feinaigle: and applied to chronology, history, geography, languages, systematic tables, poetry, prose, and arithmetic there is a method to sum and multiply with points. I wasn’t looking for that it that moment, so didn’t pay much attention.

Wonder if there are more.

I have a copy of the book Vedic Mathematics, but I’m sure there are other (newer) techniques mental calculators use.

Not sure what you mean… is there a link/example you could point me to?

The book is quite old, it’s in, just google it.

In other words “mental calculators” Wikipedia, same techniques, no need to download. There is World Cup for mental calculators are going on.