Mental math tricks you can learn in five minutes

Each of these turns a slow calculation into one or two easy steps. Learn one, drill it until it's automatic, then move to the next.

Multiply a two-digit number by 11

Add the two digits and put the sum in the middle. If the sum is 10 or more, carry the 1 into the first digit.

Multiply by 9

Multiply by 10, then subtract the original number.

Multiply by 5

Five is half of ten. Halve the number, then multiply by 10.

Multiply by 25

Twenty-five is a quarter of a hundred. Divide by 4, then multiply by 100.

Square a number ending in 5

Take the tens digit, multiply it by the next number up, and write 25 after it.

Square any two-digit number

Round to the nearest ten, go the same distance the other way, multiply those two, and add the distance squared.

There's a full walkthrough in how to multiply two-digit numbers in your head.

Estimate a square root

Find the perfect squares either side, then refine: divide the number by your guess and average the result with your guess.

Why it works, and how close a single step gets, is in how to estimate square roots in your head.

Find the day of the week for any date

Give the year, the month and the day each a code, add them, and take the remainder after dividing by 7. It sounds heavy, but with the month codes memorised it takes seconds — it's the classic party trick of lightning calculators, and R3CK0N has a timed drill for it. The full method, with the codes, is in the day of the week trick.

Make the tricks stick

Tricks you've read about are slow; tricks you've drilled are instant. R3CK0N's Secret mode has a timed drill for each technique on this page — × 11, × 9, × 5 and × 25, squares, square roots and day-of-the-week — plus a Learn tab that walks through each chapter of Arthur Benjamin and Michael Shermer's Secrets of Mental Math, the book these methods come from.