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Vedic Maths Tricks

18 simple shortcuts for faster multiplication, squares, roots, subtraction, division and answer-checking — with worked examples and practice questions.

What is Vedic Maths?

A set of mental-calculation shortcuts popularised by Jagadguru Swami Bharati Krishna Tirtha in his 1965 book Vedic Mathematics. Every trick below works because of ordinary place value and algebra, so you can trust it.

How to use this page: read the steps, follow the worked example, then solve the “Try it” question before opening the answer. Learn one trick a day and practise it for a few minutes.

Exam tip: in subjective board answers, show your normal step-wise working. Use these shortcuts for rough work, MCQs, quick checking and competitive exams.

Jump to a trick

Multiplication shortcuts

Seven tricks that remove most of the heavy multiplication.

1

Multiply by 11

Any 2-digit or 3-digit number
  1. Write the first and last digits apart.
  2. Put the sum of the two digits in the middle.
  3. If the sum is 10 or more, carry 1 to the left digit.
Example 123 × 11 → 2 | 2+3 | 3 → 253
Example 2 (with carry)57 × 11 → 5 | 5+7=12 | 7 → carry 1 → 6 | 2 | 7 → 627
3-digit numberAdd each pair of neighbouring digits: 214 × 11 → 2 | 2+1 | 1+4 | 4 → 2354
Try it: 45 × 114 | 4+5 | 5 = 495
2

Multiply by 5, 25 and 50

Halving and doubling
  • × 5 = × 10, then halve.
  • × 25 = × 100, then divide by 4.
  • × 50 = × 100, then halve.
  • ÷ 5 = × 2, then divide by 10.
Examples86 × 5 = 860 ÷ 2 = 430
48 × 25 = 4800 ÷ 4 = 1200
36 × 50 = 3600 ÷ 2 = 1800
135 ÷ 5 = 270 ÷ 10 = 27
Try it: 44 × 254400 ÷ 4 = 1100
3

Multiply by 9, 99 and 999

Round up, then subtract

Multiply by 10, 100 or 1000 and subtract the number once.

Examples67 × 9 = 670 − 67 = 603
46 × 99 = 4600 − 46 = 4554
123 × 999 = 123000 − 123 = 122877
Try it: 35 × 993500 − 35 = 3465
4

Multiply two numbers between 11 and 19

Add, shift, add
  1. Add the units digit of one number to the other number.
  2. Put a 0 at the end of that sum (multiply by 10).
  3. Add the product of the two units digits.
Example 114 × 17: 17 + 4 = 21 → 210; units product 4 × 7 = 28; 210 + 28 = 238
Example 216 × 18: 18 + 6 = 24 → 240; 6 × 8 = 48; 240 + 48 = 288
Try it: 13 × 1515 + 3 = 18 → 180; 3 × 5 = 15; 180 + 15 = 195
5

Multiply numbers close to 100

Sutra: Nikhilam Navatashcaramam Dashatah

Use base 100 when both numbers are near 100. (Base 10 or 1000 works the same way.)

  1. Find how far each number is from 100 (the deficit).
  2. Left part: subtract one number’s deficit from the other number (cross-subtract).
  3. Right part: multiply the two deficits and write it as 2 digits (for base 100).
Example 197 × 94: deficits 3 and 6. Left: 97 − 6 = 91. Right: 3 × 6 = 18. Answer 9118
Example 288 × 96: deficits 12 and 4. Left: 88 − 4 = 84. Right: 12 × 4 = 48. Answer 8448
Numbers above 100103 × 106: excesses 3 and 6. Left: 103 + 6 = 109. Right: 3 × 6 = 18. Answer 10918
Try it: 99 × 97Deficits 1 and 3. Left: 99 − 3 = 96. Right: 1 × 3 = 03. Answer 9603
6

Same first part, last digits add up to 10

Sutra: Antyayor Dashake’pi

Use this when the tens parts are equal and the units digits add up to 10 (like 47 × 43).

  1. Left part: first digit × (first digit + 1).
  2. Right part: product of the two units digits, written as 2 digits.
Example 147 × 43: 4 × 5 = 20 | 7 × 3 = 21 → 2021
Example 262 × 68: 6 × 7 = 42 | 2 × 8 = 16 → 4216
Zero in the right part81 × 89: 8 × 9 = 72 | 1 × 9 = 09 → 7209
Try it: 34 × 363 × 4 = 12 | 4 × 6 = 24 → 1224
7

Vertically and crosswise (any 2-digit × 2-digit)

Sutra: Urdhva-Tiryagbhyam

For (ab) × (cd) find three numbers and then carry from right to left:

  1. Left: a × c (vertical)
  2. Middle: a × d + b × c (crosswise)
  3. Right: b × d (vertical)
Example 123 × 14: left 2 × 1 = 2; middle 2 × 4 + 3 × 1 = 11; right 3 × 4 = 12.
Write 2, carry 1 → 11 + 1 = 12, write 2, carry 1 → 2 + 1 = 3. Answer 322
Example 246 × 37: left 12; middle 4 × 7 + 6 × 3 = 46; right 42.
Write 2, carry 4 → 46 + 4 = 50, write 0, carry 5 → 12 + 5 = 17. Answer 1702
Try it: 32 × 21Left 6; middle 3 × 1 + 2 × 2 = 7; right 2 × 1 = 2. Answer 672

Squares and roots

Find squares in seconds and take square and cube roots of perfect numbers mentally.

8

Square of a number ending in 5

Sutra: Ekadhikena Purvena
  1. Multiply the digits before 5 by the next number.
  2. Write 25 after the result.
Examples35²: 3 × 4 = 12 → 1225
75²: 7 × 8 = 56 → 5625
115²: 11 × 12 = 132 → 13225

Why it works: (10a + 5)² = 100a(a + 1) + 25.

Try it: 95²9 × 10 = 90 → 9025
9

Square of a number near 50

Working base 50

Write the number as 50 ± d. Then:

  1. Left part: 25 ± d (add if above 50, subtract if below).
  2. Right part: d² written as 2 digits.
Examples52²: 25 + 2 = 27 | 2² = 04 → 2704
47²: 25 − 3 = 22 | 3² = 09 → 2209
58²: 25 + 8 = 33 | 8² = 64 → 3364
Try it: 54²25 + 4 = 29 | 4² = 16 → 2916
10

Square of a number near 100

Sutra: Yavadunam
  1. Find the difference d from 100.
  2. Left part: the number minus d (or plus d if above 100).
  3. Right part: d² as 2 digits. If it has 3 digits, carry the extra digit to the left.
Examples96²: d = 4. 96 − 4 = 92 | 16 → 9216
103²: d = 3. 103 + 3 = 106 | 09 → 10609
88²: d = 12. 88 − 12 = 76 | 144 → carry 1 → 77 | 44 → 7744
Try it: 99²d = 1. 99 − 1 = 98 | 01 → 9801
11

Square of any 2-digit number

Sutra: Dwandwa-yoga (duplex)

For (ab)² find a² | 2 × a × b | b² and carry from right to left.

Example 134²: 9 | 2 × 3 × 4 = 24 | 16. Write 6, carry 1 → 24 + 1 = 25, write 5, carry 2 → 9 + 2 = 11. Answer 1156
Example 267²: 36 | 84 | 49. Write 9, carry 4 → 88, write 8, carry 8 → 36 + 8 = 44. Answer 4489
Try it: 26²4 | 24 | 36. Write 6, carry 3 → 27, write 7, carry 2 → 4 + 2 = 6. Answer 676
12

Square root of a perfect square (up to 4 digits)

Works only for perfect squares

Step 1: the last digit. The last digit of the square tells the last digit of the root:

Square ends inRoot ends in
11 or 9
42 or 8
55
64 or 6
93 or 7
00

Step 2: the tens digit. Ignore the last two digits. The remaining number lies between two perfect squares — the smaller square’s root is the tens digit (n).

Step 3: choose between the two options. Compare the remaining number with n × (n + 1). If it is bigger, take the larger last digit; if smaller, take the smaller last digit.

√1369Ends in 9 → 3 or 7. Remaining 13 lies between 9 and 16, so n = 3. 3 × 4 = 12 and 13 > 12, so take the larger digit → 37
√7056Ends in 6 → 4 or 6. Remaining 70 lies between 64 and 81, so n = 8. 8 × 9 = 72 and 70 < 72, so take the smaller digit → 84
√3025Ends in 5 → last digit 5. Remaining 30 lies between 25 and 36, so n = 5 → 55
Try it: √5184Ends in 4 → 2 or 8. Remaining 51 lies between 49 and 64, so n = 7. 7 × 8 = 56 and 51 < 56, so smaller digit → 72
13

Cube root of a perfect cube (up to 6 digits)

Works only for perfect cubes

Learn the cubes of 1 to 9: 1, 8, 27, 64, 125, 216, 343, 512, 729. Each last digit of a cube points to exactly one last digit of the root:

Cube ends in1874563290
Root ends in1234567890
  1. The last digit of the cube gives the last digit of the root.
  2. Cross out the last three digits. The remaining number lies between two cubes — the smaller cube’s root is the tens digit.
³√4913Ends in 3 → 7. Remaining 4 lies between 1 and 8 → tens digit 1. Answer 17
³√175616Ends in 6 → 6. Remaining 175 lies between 125 and 216 → tens digit 5. Answer 56
Try it: ³√5832Ends in 2 → 8. Remaining 5 lies between 1 and 8 → tens digit 1. Answer 18

Add, subtract, divide and check

Mental methods for everyday calculations and quick error-checking.

14

Add and subtract by rounding

Round, calculate, adjust

Round one number to the nearest easy number, calculate, then correct the difference.

Examples698 + 457 = 700 + 457 − 2 = 1157 − 2 = 1155
845 − 298 = 845 − 300 + 2 = 545 + 2 = 547
1999 + 387 = 2000 + 387 − 1 = 2386
Try it: 599 + 246600 + 246 − 1 = 845
15

Subtract from 100, 1000, 10000

Sutra: All from 9 and the last from 10
  1. Subtract every digit from 9, except the last non-zero digit.
  2. Subtract that last non-zero digit from 10.
  3. Keep any trailing zeros as they are.
Examples1000 − 357: 9−3 = 6, 9−5 = 4, 10−7 = 3 → 643
10000 − 4286 → 5714
1000 − 370: 9−3 = 6, 10−7 = 3, keep 0 → 630
1000 − 48: treat as 048 → 952
Try it: 10000 − 67239−6 = 3, 9−7 = 2, 9−2 = 7, 10−3 = 7 → 3277
16

Divide by 9

No long division needed
  1. The first digit of the number is the first digit of the quotient.
  2. Each next quotient digit = the previous quotient digit + the next digit of the number.
  3. The last sum is the remainder. If it is 9 or more, add 1 to the quotient for each 9 and keep the leftover as the remainder.
Example 1134 ÷ 9: quotient digits 1, 1+3 = 4; remainder 4+4 = 8 → quotient 14, remainder 8
Example 2 (big remainder)2134 ÷ 9: quotient digits 2, 2+1 = 3, 3+3 = 6; remainder 6+4 = 10 → add 1 to quotient and remainder becomes 1 → quotient 237, remainder 1
Try it: 342 ÷ 9Quotient digits 3, 3+4 = 7; remainder 7+2 = 9 → quotient 38, remainder 0 → 38
17

Divisibility tests

Know the factors instantly
Divisible byTest
2Last digit is even
3Sum of digits is divisible by 3
4Last two digits are divisible by 4
5Last digit is 0 or 5
6Divisible by both 2 and 3
7Remove the last digit, double it and subtract from the rest. Repeat. If you reach 0 or a multiple of 7, it is divisible
8Last three digits are divisible by 8
9Sum of digits is divisible by 9
10Last digit is 0
11(Sum of digits at odd places) − (sum at even places) is 0 or a multiple of 11
Examples2728 by 11: (2+2) − (7+8) = −11 → divisible
5184 by 9: 5+1+8+4 = 18 → divisible
343 by 7: 34 − 2×3 = 28 → divisible
Try it: is 3465 divisible by 11?(3+6) − (4+5) = 0 → Yes (3465 = 11 × 315)
18

Check answers with the digit sum

Casting out nines
  1. Find the digit sum of each number, adding repeatedly until one digit is left (treat 9 as 0).
  2. Do the same operation (+, − or ×) on those digit sums and reduce again.
  3. The result must match the digit sum of your answer.
Correct answer237 × 46 = 10902. Digit sums: 237 → 12 → 3; 46 → 10 → 1. Product 3 × 1 = 3. Answer 10902 → 12 → 3. They match ✓
Wrong answer caught237 × 46 = 10912. Digit sum of 10912 → 13 → 4, but we expect 3. Mismatch — recheck!

Remember: a match does not guarantee the answer is right (for example, swapped digits give the same digit sum), but a mismatch always means there is a mistake.

Practice time

Solve these in your head or on paper, then tap “Answer” to check.

  1. 68 × 11
    Answer748
  2. 75²
    Answer5625
  3. 56 × 54
    Answer3024
  4. 98 × 96
    Answer9408
  5. 23 × 21
    Answer483
  6. 1000 − 648
    Answer352
  7. 64 × 25
    Answer1600
  8. 53²
    Answer2809
  9. √2209
    Answer47
  10. ³√12167
    Answer23
  11. Is 3465 divisible by 11?
    AnswerYes
  12. 97 × 93
    Answer9021

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More Vedic Maths Tricks: Level Up Your Mental Maths

Explore extra shortcuts for multiplication, division, percentages, fractions and number patterns. Each method includes a worked example and a question to practise.

These additional techniques build on the 18 tricks above. They use place value, algebra and number patterns to make calculations more efficient. The fastest method depends on the numbers, so always choose a strategy you understand and verify your answer.

More multiplication shortcuts

19. Multiply by 4 or 8

Double the number once for ×2, twice for ×4 and three times for ×8.

Example: 247 × 8
247 × 2 = 494
494 × 2 = 988
988 × 2 = 1976
Try it: 136 × 8
136 → 272 → 544 → 1088.

20. Multiply by 125

Since 125 × 8 = 1000, multiply by 1000 and divide by 8.

Example: 64 × 125 = 64 × 1000 ÷ 8 = 64000 ÷ 8 = 8000.
Try it: 32 × 125
32000 ÷ 8 = 4000.

21. Multiply by 101

Multiply by 100, then add the original number.

Example: 348 × 101 = 34800 + 348 = 35148.
Try it: 72 × 101
7200 + 72 = 7272.

22. Multiply by 12

Multiply by 10 and add twice the number: ×12 = ×10 + ×2.

Example: 46 × 12 = 460 + 92 = 552.
Try it: 125 × 12
1250 + 250 = 1500.

23. Multiply by 15

Multiply by 10 and add half of the result (equivalently, ×10 + ×5).

Example: 84 × 15 = 840 + 420 = 1260.
Try it: 62 × 15
620 + 310 = 930.

24. Multiply by 1250

Use 1250 = 10000 ÷ 8.

Example: 24 × 1250 = 240000 ÷ 8 = 30000.
Try it: 16 × 1250
160000 ÷ 8 = 20000.

Base methods: 1000 and nearby numbers

25. Multiply numbers close to 1000

Find each number’s signed difference from 1000. Cross-add or cross-subtract for the left part; multiply the differences for the right part. The right part must have exactly three digits, with carrying when needed.

Example: 997 × 994. Differences are −3 and −6. Left: 997 − 6 = 991. Right: 3 × 6 = 018. Answer: 991018.
Try it: 1002 × 1004
Left: 1002 + 4 = 1006. Right: 2 × 4 = 008. Answer: 1006008.

26. Square a number near 1000

For a number 1000 ± d, square it using (1000 ± d)² = 1000000 ± 2000d + d². For small d, this is often quick mentally.

Example: 1003² = 1000000 + 6000 + 9 = 1006009.
Try it: 998²
998² = (1000 − 2)² = 1000000 − 4000 + 4 = 996004.

27. Square using the difference of squares

Use a nearby round number: (a + b)(a − b) = a² − b². This is especially useful when a number is equally spaced from a convenient base.

Example: 48 × 52 = (50 − 2)(50 + 2) = 50² − 2² = 2500 − 4 = 2496.
Try it: 97 × 103
(100 − 3)(100 + 3) = 10000 − 9 = 9991.

Division, fractions and percentages

28. Divide by 5

Multiply by 2 and divide by 10. This is particularly convenient for whole numbers and decimals.

Example: 438 ÷ 5 = 876 ÷ 10 = 87.6.
Try it: 725 ÷ 5
1450 ÷ 10 = 145.

29. Divide by 25

Since 100 ÷ 25 = 4, multiply the dividend by 4 and divide by 100.

Example: 675 ÷ 25 = 2700 ÷ 100 = 27.
Try it: 1450 ÷ 25
5800 ÷ 100 = 58.

30. Find 5%, 10% and 15%

10% means divide by 10; 5% is half of 10%; 15% is 10% + 5%.

Example: 15% of 360 = 36 + 18 = 54.
Try it: 15% of 240
10% = 24 and 5% = 12. Total = 36.

31. Find 25%, 50% and 75%

25% is one quarter, 50% is one half, and 75% is three quarters.

Example: 75% of 280 = ¾ × 280 = 3 × 70 = 210.
Try it: 25% of 760
760 ÷ 4 = 190.

32. Convert common fractions to percentages

Memorise a few useful equivalents to speed up mental calculations.

FractionPercentage
1/250%
1/333⅓%
1/425%
1/520%
1/812.5%
3/475%
1/1010%
Try it: Convert 3/5 to a percentage
3 × 20% = 60%.

33. Multiply by 12.5

Because 12.5 = 100 ÷ 8, multiply by 100 and divide by 8.

Example: 72 × 12.5 = 7200 ÷ 8 = 900.
Try it: 48 × 12.5
4800 ÷ 8 = 600.

Choose the right trick for your class

Classes VI–VIIIPractise ×11, ×5, ×25, ×9, rounding, divisibility rules, fraction equivalents and percentages.
Classes IX–XPractise near-base multiplication, squares, roots of perfect numbers, algebraic identities and estimation to check answers.
Classes XI–XIIUse mental arithmetic to improve numerical fluency, estimation, simplification and checking calculations. Show complete mathematical working wherever an examination requires it.
Important learning tip: A shortcut is useful only when its conditions are satisfied. For example, the “same first part, last digits add to 10” multiplication trick applies to numbers such as 43 × 47, not to every pair of two-digit numbers. Always check place values, carries and the final result.

Vedic Maths practice quiz

Try each question before opening the answer. Work without a calculator first, then verify using a conventional method.

  1. 86 × 125 = ?
    Show answer and method
    86 × 1000 ÷ 8 = 86000 ÷ 8 = 10750.
  2. 1002 × 1005 = ?
    Show answer and method
    Differences +2 and +5. Left part 1007; right part 010. Answer 1007010.
  3. 15% of 480 = ?
    Show answer and method
    10% = 48 and 5% = 24. Total = 72.
  4. 875 ÷ 25 = ?
    Show answer and method
    875 × 4 ÷ 100 = 3500 ÷ 100 = 35.
  5. 104 × 96 = ?
    Show answer and method
    (100 + 4)(100 − 4) = 10000 − 16 = 9984.
  6. 25% of 1240 = ?
    Show answer and method
    1240 ÷ 4 = 310.
  7. 998² = ?
    Show answer and method
    (1000 − 2)² = 1000000 − 4000 + 4 = 996004.
  8. 348 × 101 = ?
    Show answer and method
    34800 + 348 = 35148.

Frequently asked questions

What is Vedic Mathematics?

Vedic Mathematics is a system of calculation techniques popularised by Bharati Krishna Tirtha’s book Vedic Mathematics, published in 1965. Many commonly taught tricks can be explained through standard arithmetic, algebra and place value.

Do these tricks replace standard methods?

No. They complement standard methods. Students should understand the underlying mathematics and use the approach that is most reliable for a given problem.

Can school students use these methods in exams?

They can be useful for mental calculations and checking work. Students should follow the examination’s instructions and show required steps in written-answer questions.

How should beginners practise?

Choose one technique, study two worked examples, solve five to ten questions, and check answers using a standard method. Move to the next technique only after the first feels reliable.

Are all these methods part of the original ancient Vedas?

Historical claims about the origin of specific techniques are debated. It is safest to describe these as techniques taught in the modern Vedic Mathematics system rather than claim every shortcut is directly documented in ancient Vedic texts.

For teachers and parents: Use these examples as supplementary practice alongside the prescribed textbook and classroom instruction. Encourage students to explain why a shortcut works, not merely memorise its steps.
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