This directory contains many mental calculation articles, tools and resources to explore. There’s something here for everyone—from beginners to experts!
Good training tools are essential when training mental calculation—in fact, an important part of my role as a coach is to recommend the best training drills for my students.
For any queries, send me (Daniel Timms) a message.
📐 Advanced Methods
- Human Calendar Method — learn the algorithm used by experts
- Cross-Multiplication — multiply huge numbers at exceptional speed
- Cross-Division — divide by long numbers such as 4.52188
- Fraction Addition and Subtraction — with advice on when and how simplify answers
- Fraction Multiplication and Division — including conversion between mixed and improper form
- Square Roots:
- Fast Method to Estimate Square Roots — to 3–5 decimal places
- Method for Exact Square Roots — where you know the answer will be an integer
- Accurate Method for Square Roots — to unlimited decimal places (2-digit division method)
- Deep Roots:
- Fast Method to Estimate Deep Roots — to 2–3 decimal places
- Method for Exact Cube Roots — where you know the answer will be an integer
- Accurate Method for Cube Roots — to unlimited decimal places
- Difficult Roots and Difficult Powers — logarithm method
- Logarithms and Antilogarithms — product-building method
- Hectoc strategies
🧙 Psychology of Training
- What is Mental Math?
- Verbal Mental Calculation
- Top 10 Tips when Competing in Mental Calculation
- Optimizing Working Memory for Mental Calculation
- Spaced Repetition for Memorizing Data
- Tracking Mental Calculation Training Performance
- Maximum Possible Processing Speed of the Human Brain
- Calculating the Size of the Working Memory of the Human Brain
🏃♀️ Competition Preparation Resources
- Official Memoriad Software: the main program “Memoriad Simulator” is the one used in the Memoriad competitions. Download this first, then optionally any of the other plugins listed on the same page for more training options. The main software trains all Mental Math and Memory events featured in past Memoriad events – although the flash anzan online training is a separate program.
- Pegasus: Excel-based tool for generating practice questions for many calculation categories, and used in the Mind Sports Olympiad. Maintained by George Lane.
- Mind Sports Olympiad (online): halfway down this page you’ll find a video simulator of the 2021 semi-final so you can try the questions and see what score you would have achieved!
- Mind Sports Olympiad (traditional): the 2018 written paper with answers is available in PDF format.
- Junior Mental Calculation World Championship: main JMCWC resources page to prepare for this competition.
- GMCA Simulators: a new online league is using these mental calculation simulators, which anyone can use to practise.
📆 Human Calendar Training
- K-Train: very old HTML page for training calendar dates. Works only in Internet Explorer. Used by some of the most successful mental calendar calculators.
- Calendar Trainer: browser-based trainer developed by memory champion Katie Kermode.
- MentalCal: iPhone app that trains you to calculate calendar dates, and provides global leaderboards. Download from iTunes here.
- Day of Week Genius: Android and iOS app with training to perform calendar calculations.
⭐ Resources to Improve Mental Maths
- Training Tools: currently only available for my students (mostly adults). Please contact me if you’re intersted in my coaching or in using these tools when they are available.
- Video course: Practical Mental Mathematics by me (Daniel Timms) aimed at beginners and intermediates.
- CMItalia Arithmetic: simulators for +–×÷ provided by a group of Italian mental calculators (in Italian language).
⚽ Other Mental Calculation Games
- Hectoc: a new calculation game (and training app) invented by Yusnier Viera.
- Abaku: a new game for teaching arithmetic used in many schools in Czechia.
- MathDash: online multiplayer arena to compete with other mathematicians at mental math and Mathematics.
🧠 Other Mind Sports
- Practical Mental Math: tool to generate rules for converting between currencies without a calculator.
- Speed Reading: new course showing the latest science-based techniques for speed reading (Seberson Method).
- Art of Memory: various tools to help with memory sports training.
📰 Discussion Groups
- Art of Memory forum has a section dedicated to mental calculation.
- Message board about Mental Calculation on Groups.io
- World Mental Calculation Facebook Page with updates from this site.
🏆 Records and Results
- Ralf Laue maintains a list of top calculation scores for several categories at recordholders.org
- Memoriad maintains a list of everyone’s top score for each Memoriad category.
- International Memoriad competition results are here for 2008, 2012 and 2016.
- Mental Calculation World Cup results are here for all past competitions.
📚 Books
- Dead Reckoning: Ronald Doerfler’s book describes some intermediate and advanced calculation algorithms and short-cuts for multiplication, division, factorization, roots and logarithms.
- Practical Mental Arithmetic: published in 2024, Scott Horne’s book offers a complete overview of mental arithmetic including advanced topics such as trigonometric calculations and calendar dates.
- The Mental Calculator’s Handbook: written by accomplished mental calculation competitors Robert Fountain and Jan van Koningsveld, this book explains many techniques—simple and advanced—in a clear and logical way.
- The Secrets of Mental Math: one of the most respected books about learning Mental Math is written by Arthur Benjamin.
- Mental Calculation, an Art, Apart: Willem Bouman’s book carries a wealth of knowledge and easy-to-follow detailed techniques -from one of the world’s leading mental calculators.
- Mit Kleinen Tricks Groß Beeindrucken: Dinah Spring’s new book (in German) shares dozens of mental math tricks for arithmetic, calendar dates, and more. Dinah organizes Hectoc and regional mental math competitions in Germany.