A free mental math trainer. Pick an operation and a size, then answer as fast as you can. A right answer moves you on at once, and a 60-second sprint makes a quick mental math test.
No best yet for these settings
First problem
11 + 54 = ?
Two two-digit numbers. As many as you can in 60 seconds.
Mental math, also called mental arithmetic or mental calculation, means working sums out in your head, without paper, a calculator or a phone. It starts with adding, subtracting, multiplying and dividing, and goes on to squares, roots, logarithms and the day of the week for any date. It gets faster with short, regular practice and a few good methods. The sections below say what to drill first, which tricks to learn, how often to practice and where to go next.
Build from the small facts that every bigger sum leans on. Stay on a step until a sprint feels easy, then move up.
Pairs that make 10 and 100, like 7 + 3 and 64 + 36. Quick adding starts here, and Sum Stack drills the pairs to 10 as a game.
Every multiplication and division trick rests on them. If a few facts always slow you down, see How to Memorize Multiplication Tables.
Work from the left, tens first, with the first trick below. 47 + 38 becomes 47 + 30 = 77, then 77 + 8 = 85.
Break the bigger number apart: 47 × 6 is 240 + 42 = 282. Division runs the same steps backwards.
Once two digits feel easy, step up a size, or mix all four operations so you have to switch on the fly.
These three cover most of what the trainer asks. After a sprint, the result screen names the one that fits each of your slowest problems.
Add the biggest part first, the way you read. You hold one running total instead of a row of carried digits.
Taking away works the same way. 92 − 47 is 92 − 40 = 52, then 52 − 7 = 45. Arthur Benjamin's Secrets of Mental Math, written with Michael Shermer, works from the left too.
The forum's Master List of Mental Calculation Techniques has more methods like this.
When a number sits just below a round one, use the round number, then fix the difference.
For taking away, 83 − 29 is 83 − 30 = 53, then add back 1 to make 54. It is the quickest fix for numbers that end in 7, 8 or 9.
The forum's Master List of Mental Calculation Techniques has more methods like this.
Split the bigger number into tens and ones, multiply each part, then add the results.
Division splits the same way. 312 ÷ 6 is 300 ÷ 6 = 50 and 12 ÷ 6 = 2, so 52. The Trachtenberg System has its own rule for each multiplier from 3 to 9, 11 and 12.
The forum's Master List of Mental Calculation Techniques has more methods like this.
Short sessions on most days usually beat one long session a week, and they are easier to keep up. Here is a ten-minute session.
Move up a size when a sprint feels easy and you rarely need a second try. When you start holding several numbers in your head at once, memory techniques help. The guide to memorizing numbers with a memory palace covers holding long numbers in mind while you calculate, and the Major System turns digits into words you can picture.
When drills get dull, these games train the same skills. They are free and play in the browser, with nothing to download.
Make the target number from a handful of tiles with + − × ÷, while every result you make turns face down.
Estimate square and cube roots to one decimal before the timer runs out.
Divide a floor into rectangular rooms. Every clue is a small sum, and its answer is the room's size.
Shoot down falling rocks by loading the prime factors of their numbers.
Work out each customer's change and build it from coins and notes before the queue loses patience.
Meteors carry dates. Work out the day of the week and fire the rocket from that day's chamber.
Build prime towers beside a winding road. Each hit divides an enemy's number, and it pops at 1.
Steer falling digit blocks into a well so touching blocks add to 10, and set up chains as the blocks above fall in.
Steer a probe down to the Moon and land it where a fraction, a root or a percentage sits on the number line.
Read each invader's binary number, from 3 to 8 bits, and type it in decimal to shoot it down.
Keep the Hi-Lo running count in your head as cards slide out of a six-deck shoe.
Memorize a launch code, then fire the answers to the saucers that ask about its digits.
More games, for memory as well as math, are on the games page.
Mental math is doing arithmetic in your head, without paper, a calculator or a phone. It starts with adding, subtracting, multiplying and dividing, and can go on to squares, roots, logarithms and calendar dates.
Nearly. Mental math is the everyday and school name, and mental arithmetic means the same. Mental calculation is the name the forum and the competitions use, and it often means harder work, such as multiplying long numbers, finding square roots and naming the day of the week for any date.
Practice for a few minutes most days at a level that is hard but not hopeless, learn the three tricks above, and look at your slowest problems after each sprint. Most of the speed comes from knowing number bonds and times tables without stopping to think.
It counts correct answers per minute. In a 60-second sprint that is how many you got right. In 20 problems it is your right answers divided by your time in minutes. A wrong try costs no points, but the clock keeps running while you fix it.
In this browser, one best for each mix of operation, size and mode. Clearing your browser's data for the site removes them.
Flash anzan is mental abacus addition: numbers appear one after another and you add them on an imagined soroban, the Japanese abacus. Each soroban rod has one bead above the bar worth 5 and four below worth 1 each. The Flashing Random Number Generator lets you try it.
Yes. The Mental Calculation World Cup began in 2004. Its classic events include adding ten ten-digit numbers, multiplying two eight-digit numbers, finding square roots of six-digit numbers to eight significant digits, and naming the day of the week for dates between 1600 and 2100.
Mental math is the process of doing mathematical calculations in your head without using paper, calculators, computers, or other devices. It includes addition, subtraction, division, multiplication, and much more.
Mental math is a fun skill that can be useful in school studies and life.
You can also learn more about mental math tricks and strategies by joining our free mental calculation forum.
Join the Mental Calculation Forum
Here are some articles and discussions about mental math techniques:
