Vedic Maths: Formulas, Tricks and Fast Calculation Methods

Vedic Maths is a collection of calculation methods based on place value, complements, algebraic identities and mental arithmetic. Common methods include multiplication by 11, squaring numbers ending in 5, multiplying numbers near a base such as 10 or 100, and the vertical-and-crosswise method. These techniques reduce written steps when applied with correct carrying and place-value grouping.

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What is Vedic Maths?

Vedic Maths refers to mental and written calculation techniques that simplify arithmetic using number patterns, algebraic identities, complements and place value.

The methods convert a calculation into smaller operations such as addition, subtraction, cross-multiplication or multiplication by a base. For example, 98 × 97 can be calculated using complements from 100: the deficits are 2 and 3, so the left part is 98 − 3 = 95 and the right part is 2 × 3 = 06. Therefore, 98 × 97 = 9506.

Vedic Maths Formula & Tricks

Important Formulas

Multiplication near a base
(B + a)(B + b) = B(B + a + b) + ab

B is a convenient base such as 10, 100 or 1000. The right-hand part must be written with as many digits as the base has zeros.

Difference of two squares
(a + b)(a − b) = a² − b²

Use this identity when two factors have the same central value and opposite deviations.

Squaring a number ending in 5
(10k + 5)² = 100k(k + 1) + 25

Multiply k by k + 1, append 25, and place the result in the correct hundreds position.

Two-digit multiplication
(10a + b)(10c + d) = 100ac + 10(ad + bc) + bd

The three components are the first-digit product, the two cross-products and the last-digit product. Carry values are then combined by place value.

Multiplication by 11
(10a + b) × 11 = 100a + 10(a + b) + b

For two digits without an overflow, place the sum of the digits between them. If the sum is 10 or more, carry to the left.

Quick Tricks

Multiply a two-digit number by 11

Write the first digit, add the two digits in the middle, and write the last digit. Apply carrying when the middle sum is 10 or more.

Example: 43 × 11 = 4(4 + 3)3 = 473. For 68 × 11, 6 + 8 = 14, so the result is 748 after carrying.
Square numbers ending in 5

Remove the final 5 to get k, multiply k by k + 1, and append 25.

Example: 85²: 8 × 9 = 72, so 85² = 7225.
Multiply numbers close to 100

Subtract each number's deficit from the other number for the left part. Multiply the deficits for the right part and use two digits.

Example: 97 × 94: deficits are 3 and 6. Left part = 97 − 6 = 91; right part = 3 × 6 = 18. Result = 9118.
Use difference of squares

Express the factors as numbers equally placed around a central value, then subtract the squares.

Example: 52 × 48 = (50 + 2)(50 − 2) = 50² − 2² = 2500 − 4 = 2496.

Vedic Maths Concepts

Base and complement method

The base method uses a nearby power of 10 and the complement or deviation of each number from that base.

For numbers below B, write each number as B − x. Then (B − x)(B − y) gives a left part of B − x − y and a right part of xy. The right part must contain the fixed number of digits determined by B. If it has fewer digits, add leading zeroes.

Example: 98 × 97 with B = 100: x = 2 and y = 3. Left part = 100 − 2 − 3 = 95; right part = 2 × 3 = 06. Hence, 98 × 97 = 9506.

Vertical-and-crosswise multiplication

For two two-digit numbers, multiply vertically at the units and tens places and crosswise for the middle place.

For (10a + b)(10c + d), calculate ac, then ad + bc, then bd. Arrange these as hundreds, tens and units, carrying whenever a component is 10 or more.

Example: 23 × 14: units 3 × 4 = 12; crosswise 2 × 4 + 3 × 1 = 11; tens product 2 × 1 = 2. Combining 2 | 11 | 12 with carrying gives 322.

Algebraic identities for fast multiplication

Algebraic identities replace a difficult product with simpler squares or products around a convenient central number.

The main identity is (a + b)(a − b) = a² − b². Another useful form is (a + x)(a + y) = a² + a(x + y) + xy. Choose a close round number for a to reduce the arithmetic.

Example: 103 × 97 = (100 + 3)(100 − 3) = 100² − 3² = 10,000 − 9 = 9,991.

Squaring numbers near a base

A number near a base can be squared by using its deviation from that base.

If n = B + d, then n² = B² + 2Bd + d². For a number below the base, d is negative, so the middle term is subtracted. This method works with bases such as 10, 100 and 1000.

Example: 98² = (100 − 2)² = 10,000 − 400 + 4 = 9,604.

Place-value carrying and padding

Vedic Maths methods still require standard carrying, borrowing and fixed place-value grouping.

When the base is 100, the right section represents two digits; when the base is 1000, it represents three digits. A product such as 6 must therefore be written as 06 for base 100. Any excess above the allowed width is carried to the left section.

Example: 96 × 98 with base 100: left part = 96 − 2 = 94 and right part = 4 × 2 = 08, giving 9408.

Vedic Maths Video Lessons

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Vedic Maths Multiplication Tricks

Learn practical Vedic Maths techniques for simplifying multiplication calculations. This lesson explains efficient methods to multiply numbers more quickly and accurately in quantitative aptitude problems.

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Practice Vedic Maths Questions

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1The Highest Common Factor of two numbers is 15 and their Least Common Multiple is 360. What is the product of the two numbers?→ 2A person sells an article at the profit of 30 percent. Cost price and selling price both are increased by 40 percent. What will be the new profit percentage?→ 3A trader buys 20 kg of rice for ₹1,000. He sells the rice at the rate of ₹60 per kg. What is the percentage profit made by the trader?→ 4How many numbers among 9003, 6012, 3330, 1001 are divisible by 3?→ 54 bells ring together at a certain time. After this, they rang at intervals of 6, 8, 10 and 15 seconds respectively. After how many minutes will they be ringed together for the first time?→ 6Simplify: (2√3)/√12→ 7How many numbers among 1210, 1331, 1442, 1553 are divisible by 11?→ 8Amit purchases an old scooter for ₹5,600. He spends ₹1,400 on its repairs and sells it to Sumit for ₹7,700. Find the profit percentage of Amit.→ 9A three-digit number is such that the sum of the number and its square root is 132 . Find the number.→ 10Successive discounts of 20% and 29% are equivalent to a single discount of:→

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Quick Revision Notes

Vedic Maths Revision Points

Recall these formulas, methods and place-value rules for quick calculations.

  • For numbers near B, use (B + a)(B + b) = B(B + a + b) + ab.
  • In base-100 calculations, always write the right section using two digits.
  • Use (a + b)(a − b) = a² − b² for factors equally spaced around a central number.
  • For a number ending in 5, (10k + 5)² = 100k(k + 1) + 25.
  • For two-digit multiplication, calculate first-digit, crosswise and last-digit products, then carry from right to left.
  • For multiplication by 11, place the digit sum between the original digits and handle any carry.
  • A negative deviation must retain its negative sign in base and algebraic calculations.
  • Leading zeroes in a right-hand base section are necessary for correct place value.

Vedic Maths FAQs

How do you calculate 98 × 97 using Vedic Maths?

Using base 100, the deficits are 2 and 3. The left part is 98 − 3 = 95 and the right part is 2 × 3 = 06, so 98 × 97 = 9506.

What is the formula for squaring a number ending in 5?

For n = 10k + 5, n² = 100k(k + 1) + 25. For example, 75² = 100 × 7 × 8 + 25 = 5625.

How does the multiplication-by-11 shortcut work for 57 × 11?

Add the digits and place the sum between them: 5(5 + 7)7. Since the sum is 12, carry 1 to 5, giving 627.

What is the vertical-and-crosswise result of 24 × 13?

The components are 2 × 1 = 2, 2 × 3 + 4 × 1 = 10, and 4 × 3 = 12. Combining and carrying gives 312.

Why is 98 × 97 written as 95 | 06 rather than 95 | 6?

The base is 100, so the right section must contain two digits. Therefore, 2 × 3 = 06, and the complete result is 9506.

How can 103 × 97 be calculated using an identity?

Write the factors as (100 + 3)(100 − 3). Using a² − b², the result is 100² − 3² = 10,000 − 9 = 9,991.

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