Beginner's guide

So you're getting into mental math

Mental math is one of the few hobbies where you improve every day you practice. You can start with nothing at all and see real gains within two weeks. Here is what to buy once you decide to take it seriously.

By Colin B. · Published June 6, 2026 · Last reviewed June 6, 2026

a person is holding a piece of paper with numbers on it

Photo by Richard Bell on Unsplash

The 60-second version

If you only buy 3 things to start:

Secrets of Mental Math — Arthur Benjamin's bestselling intro: the tricks that stick, taught by a working mathemagician.
Tomoe Standard Soroban Abacus 13 Digits — A proper Japanese soroban for anyone who wants to train the visualization system used by champions.
Carson Dellosa Math Flash Cards 4-Pack — The cleanest all-operations flash card set for drilling arithmetic facts until they are automatic.

Budget total

$15

Typical total

$55

A training book is all you need to start. Add a soroban abacus and you are fully equipped for around $55. Mental math is one of the cheapest skills you can develop.

We earn commission on qualifying Amazon purchases — see our affiliate disclosure. Price tiers and budget totals shown above are editorial estimates; actual Amazon prices vary.

At a glance

Our top pick in each category

The fastest path through this guide — each best-starter pick by category. Scroll for the budget and upgrade alternatives.

Category	Top pick	Price	Where to buy
Training Books	Arthur T. BenjaminSecrets of Mental Math	$	See on Amazon →
Soroban Abacus	TomoeTomoe Standard Soroban Abacus 13 Digits	$$	See on Amazon →
Flash Cards	Carson DellosaCarson Dellosa Math Flash Cards 4-Pack	$	See on Amazon →
Math Games	St. Martins GriffinWill Shortz Presents KenKen Easy to Hard Vol. 3	$	See on Amazon →

Before you buy anything

A few things worth knowing first

Do not buy a book and skip the exercises. Every mental math book works, and none of them work without the drills. Budget fifteen minutes a day, not occasional reading sessions. Consistency beats intensity here.

Pick one method and stick with it for at least thirty days before second-guessing. Trick-based, soroban, Vedic: they all produce results, but switching early means you compound none of them.

A soroban is not required. Many serious practitioners never use one. If structured, physical training for mental calculation appeals to you, it is genuinely useful. Try a book first and buy the soroban only once you have committed to the practice.

The gear

What you actually need

Photo by Lewis Keegan on Unsplash

Training Books

Three philosophies dominate mental math teaching. The first is trick-based, where you learn specific shortcuts for each operation: how to multiply two-digit numbers, square numbers quickly, estimate on the fly. Arthur Benjamin and Bill Handley are the main authors here, and this is the fastest path to practical gains. The second is the soroban method, where a physical abacus transfers into mental visualization. World-record mental math champions mostly use this path. The third is Vedic Mathematics, an ancient Indian system with elegant rules for every arithmetic operation. Pick one philosophy and buy the matching book. Working through two books simultaneously is how people stall out.

Training Books — what's the difference?

A few common shapes, each making a different trade.

Trick-Based / Speed Math

Learn clever shortcuts for each operation. Fastest path to practical gains.

Best books: Benjamin, Handley
Time to results: 2 to 4 weeks
Ceiling: Two to three-digit operations

Best for Beginners who want practical daily gains from mental math

Tradeoff Each trick is operation-specific; unusual patterns need their own technique

↓ See our pick

Soroban Method

Visualize a mental abacus. Higher ceiling, longer ramp-up.

Key tool: Physical soroban + drill sheets
Time to results: 4 to 8 weeks
Ceiling: Competition-level calculation

Best for Anyone drawn to systematic, progressive skill-building

Tradeoff Requires weeks of physical bead drilling before speed appears

Vedic Mathematics

Apply ancient sutras to every arithmetic operation. Unified system.

Best books: Bathia, Tirthaji
Time to results: 4 to 6 weeks
Ceiling: Elegant but system-specific techniques

Best for People who want a unified framework rather than a collection of ad-hoc tricks

Tradeoff More complex to start; some sutras are harder to apply than direct shortcuts

↓ See our pick

Best starter

Arthur T. Benjamin

Secrets of Mental Math

Arthur Benjamin is a math professor who performs mental calculations live on stage. This book reads like he is teaching you directly: warm, specific, and full of actual techniques. You will finish the first chapter doing two-digit multiplication in your head. Work through it with paper and pencil; the exercises are the point.

What we like

Written by a working mathemagician who performs live; not purely theoretical
Each chapter covers one skill, easy to practice in short daily sessions
Covers multiplication, squares, estimation, and memory tricks in one volume

What to know

Trick-based approach means unusual number patterns require separate techniques
Exercises require paper; not a pure read-and-absorb experience

See on Amazon →

Specialty pick

Dhaval Bathia

Vedic Mathematics Made Easy

If you prefer a single unified system over a collection of tricks, Vedic mathematics is the most systematic alternative. Bathia's intro is far more accessible than Tirthaji's original text and covers the core sutras clearly. Not a first book for most people, but the right book for anyone who tried trick-based and wanted the underlying structure.

What we like

Systematic framework covers all operations from a unified set of rules
Accessible rewrite of the dense original Tirthaji text

What to know

Harder starting curve than trick-based books; needs arithmetic fluency first
Some sutras are more complex to apply than a direct shortcut

See on Amazon →

Upgrade pick

Bill Handley

Speed Mathematics: Secret Skills for Quick Calculation

Handley goes deeper than one-liners and teaches the reasoning behind each technique, which means the methods transfer to new problems you have not seen before. Best read after you have practiced for a month or two with a simpler intro. It fills in the mathematical why behind shortcuts you have already half-learned.

What we like

Explains the reasoning behind techniques, not just the steps to follow
Covers practical applications: checking answers, estimation, exam strategy

What to know

Assumes basic mental math familiarity; not ideal as a first book
Dense in the middle chapters; takes patience to work through

See on Amazon →

Soroban Abacus

The soroban is a Japanese abacus and the physical training tool behind most mental math world records. The method: you learn to place and remove beads for arithmetic operations, drill until your hands do it without thought, then transfer the tactile movements to pure mental visualization. A standard 13-column soroban handles any number you will calculate at beginner or intermediate level. Build quality matters because the tactile feedback of well-made beads is what makes high-volume drilling feel clean and precise. A cheap plastic abacus teaches the movements but makes the process more frustrating than it needs to be.

Best starter

Tomoe

Tomoe Standard Soroban Abacus 13 Digits

Tomoe is the standard for serious soroban study in Japan. The beads click precisely, the frame stays straight, and the tactile feedback is markedly better than a budget version. The 13-column board handles any calculation you will encounter at beginner through intermediate levels. This is a lifetime tool if you commit to the method.

What we like

Japanese-made with precise bead action; tactile feedback improves drilling speed
13 columns handle any calculation at beginner through intermediate levels
Frame stays true over years of use; a genuine lifetime tool

What to know

Steep learning curve; expect two weeks before bead movements feel natural
Shipping from Japan can add lead time; order at least a week ahead

See on Amazon →

Budget pick

Yellow Mountain Imports

Yellow Mountain Imports 13-Column Soroban Abacus

A solid mid-range soroban at a fair price for exploring whether the method resonates before committing to a Tomoe. Yellow Mountain Imports builds a clean 13-column board that teaches the movements correctly. Upgrade to Tomoe once you know the practice will stick.

What we like

Under $15 and adequate for learning the basic bead movements
Lightweight and replaceable if soroban practice turns out not to suit you

What to know

Looser beads with softer click feedback slow the early drilling phase
Frame can warp under heavy daily use; not a long-term tool

See on Amazon →

Specialty pick

FPOUT

Portable Mini Japanese 13-Digit Soroban

A compact soroban fits in a coat pocket, letting you drill during commutes or short breaks. Not ideal as your only soroban since the small beads are harder to manipulate, but a good complement to a full-size board once you are past the beginner stage and looking to accumulate more daily practice volume.

What we like

Pocket-sized for drilling during commutes and waiting-room breaks
Good supplement once bead movements are solid on a full-size board

What to know

Small beads are harder to manipulate precisely; not recommended as a first abacus
Column count varies by version; confirm 13 columns before buying

See on Amazon →

Flash Cards

Before mental math tricks can work at speed, arithmetic facts need to be automatic. Someone still thinking through 7 times 8 cannot perform two-digit multiplication techniques, because working memory is spent on the basic fact rather than the trick. Flash cards are the fastest tool for burning arithmetic facts into long-term memory. Work through addition, subtraction, and multiplication through 12 until every fact comes up in under two seconds. That sounds tedious. It is, briefly. The payoff is that every technique you learn afterward suddenly works at speed, because the foundation no longer slows you down.

Best starter

Carson Dellosa

Carson Dellosa Math Flash Cards 4-Pack

A single box covering addition, subtraction, multiplication, and division through 12 is the most efficient drill set available. The goal is to hit every basic fact in under two seconds without hesitation. These cards cover the full range and hold up to daily handling. Run through the whole box daily until you are automatic on every card.

What we like

All four operations in one box; no need to buy separate sets
Randomizable format mimics real unpredictability better than worksheets
Laminated cards hold up to months of daily handling

What to know

Solo drilling gets monotonous; combine with a timer or a partner for best results
No progress tracking built in; keep a simple tally yourself

See on Amazon →

Specialty pick

School Zone

School Zone Math War Multiplication Game Cards

Math War turns arithmetic drilling into a competitive game: flip two cards, first to call out the product wins both. The competitive pressure triggers faster recall than solo practice. Works with any two players and is genuinely useful for anyone who finds solo drilling too tedious to sustain.

What we like

Game format makes drilling genuinely engaging; competitive pressure speeds recall
Works with two or more players, so practice can double as family time

What to know

Primarily covers multiplication facts; add separate cards for other operations
Requires a partner; solo drilling still needs regular flash cards

See on Amazon →

Math Games

Once the basic facts are automatic, you need volume of practice on actual problems in varied contexts. Puzzle books and math games give you structured problem sets that force mental arithmetic rather than rote fact recall. KenKen puzzles are particularly useful because they require arithmetic reasoning in grids that take five to fifteen minutes each. ThinkFun's Math Dice adds a competitive element with a fast dice-rolling format. These are not drills; they are environments where mental math has a purpose, which is what sustains a practice beyond the first month.

Best starter

St. Martins Griffin

Will Shortz Presents KenKen Easy to Hard Vol. 3

KenKen is a grid puzzle that requires arithmetic reasoning, not just rote recall. Figure out which combination of numbers fits both the cage constraint and the Latin-square rule. A 3x3 puzzle takes about three minutes; a 6x6 can run fifteen. The difficulty scales with your speed, and the puzzle format keeps practice from feeling like work.

What we like

Requires arithmetic reasoning, not just fact recall; genuinely builds skill
Three difficulty levels in one book; scales as your speed improves
Short puzzles fit easily into a daily fifteen-minute practice habit

What to know

Early puzzles still require pencil; not pure mental math until 4x4 and up
Puzzle books are consumable; budget for new ones every few months

See on Amazon →

Specialty pick

ThinkFun

ThinkFun Math Dice

Roll the two target dice, then combine the five source dice using any arithmetic to hit the target number. Fast, tactile, works solo or with competitors. The constraint-based format forces mental arithmetic in combinations no flash card pack can replicate. Sessions take under ten minutes and the randomness keeps every round fresh.

What we like

Tactile, fast, works solo or with competitors in under ten minutes
Constraint format forces arithmetic in varied combinations flash cards cannot replicate

What to know

Scoring system is cryptic at first; budget five minutes to read the rules
Focuses on basic arithmetic; does not directly train multi-digit techniques

See on Amazon →

Going deeper

Your first 30 days of mental math

The first technique takes under two hours to learn. The first month is about making it automatic. Here is what actually happens, and how to avoid the mistakes that stall most beginners.

Read the guide →

Save your money

What you don't need yet

Beginners get pressured to buy a lot of stuff that doesn't help them play better. Here's what we'd skip on day one.

Competition registration — Before you compete you need months of consistent daily practice. Sign up only once your calculation speed genuinely surprises people around you.
A full Vedic Mathematics curriculum — The complete Vedic system has 16 sutras and takes years to master. Start with a single accessible intro; the advanced sutras do not make sense until arithmetic fluency is already solid.
Abacus school enrollment (UCMAS, Abacus Master) — Structured programs are legitimately effective but priced for children in weekly classes. Self-directed study from a book and a soroban reaches the same place for a fraction of the cost.
Premium mental math apps — Free tools like Anki handle fact drilling without a subscription. Paid apps add gamification, not better results. Spend the money on a real book instead.
Multiple calculation books — Buy one book. Read it. Practice until the techniques are automatic. Then decide if you want a different approach. Collecting books without finishing them is not learning.

First week

Your first seven days

A short, real plan to get from gear-on-doorstep to actually playing.

Time yourself on ten random two-digit multiplication problems to establish your starting baseline. · Action
Buy a training book. Secrets of Mental Math is the default pick for most beginners. · Buy
- Jump to our pick: Secrets of Mental Math
Read the first two chapters and work through every exercise before moving on. Passive reading changes nothing. · Learn
- Art of Memory Forum · The most active community for mental calculation; good for technique questions and motivation
Drill your multiplication tables through 12 until every fact comes up in under two seconds. · Action
Commit to fifteen minutes of daily practice. Shorter than a podcast episode, and the gains compound faster than you expect. · Action
At the end of day seven, time yourself on the same ten multiplication problems. Write down the improvement. · Action

FAQ

Common questions

Do I need a soroban to learn mental math?

No. The soroban is one training method among several, and many accomplished practitioners never use one. Start with a book. Buy a soroban only if the structured, bead-based training approach sounds appealing after a few weeks of practice.

How long until I can do two-digit multiplication in my head?

Most people learn the technique in one to two hours of study. Doing it reliably under pressure without hesitation takes two to four weeks of daily fifteen-minute practice. The technique is fast to learn; automating it takes consistent repetition.

What is the difference between mental math and being good at math?

Mental math is arithmetic speed: multiplication, estimation, and large-number manipulation done without paper. Being good at math is about reasoning through abstract problems. They overlap but are distinct skills. You can be strong at mental math and weak at algebra, and vice versa.

Is mental math worth learning if I have a smartphone?

Yes, for a few reasons. Mental estimation catches input errors before they matter. Arithmetic fluency speeds up any task involving numbers. Being able to multiply quickly in conversation is a practical skill that surprises people and builds genuine confidence with numbers.

What is Vedic Mathematics?

A system of mental calculation techniques attributed to ancient Indian texts, reconstructed and published by Bharati Krishna Tirthaji in 1965. The 16 core sutras cover everything from multiplication to square roots. It has a devoted following but is more complex to start than the trick-based Western approach. Try a simpler intro book first.

Can adults learn mental math, or is it mostly for children?

Adults learn mental math well, often faster than children because they have more context for why the techniques work. Children in soroban programs benefit from structured physical training and neuroplasticity, but self-directed adult learners consistently reach high skill levels with consistent daily practice.

What competitions exist for mental math?

The Mental Calculation World Cup in Germany, the World Abacus and Mental Math Championship, and various national competitions. In the US, Math Olympiad and MATHCOUNTS are adjacent but require formal mathematics beyond arithmetic. Start local: many abacus schools run informal competitions for newer practitioners.

Going further

Where to next

Related hobbies

Browse by category

Authoritative sources

Art of Memory Forum — The most active online community for mental calculation, memory sports, and speed math. The mental math subforum has technique breakdowns, training logs, and progress threads. Start here to find a community and ask questions.
Mental Calculation World Cup — The top international competition for mental calculation. The website has category definitions, current records, and videos of competitors at work. Useful for understanding what the upper end of the skill looks like.
Arthur Benjamin: Mathemagics TED Talk (YouTube) — Benjamin's TED talk is the best single introduction to what mental math looks and feels like in practice. Watch it before you buy anything to confirm the hobby is for you.
Anki (Free Flashcard Software) — Free, cross-platform spaced-repetition software. Download a pre-made mental math deck or build your own multiplication table deck for daily drilling. More effective than paper cards once you are past the early stages.
UCMAS — One of the largest abacus and mental math training organizations worldwide. Primarily serves children through structured programs, but useful as a reference for understanding the soroban curriculum even if you study independently.

Excited man in glasses celebrating in front of blackboard.

Photo by Vitaly Gariev on Unsplash