Master All Topics of Vedic Mathematics

Discover ancient Indian techniques to solve complex problems with speed and accuracy. Click on any topic to explore detailed step-by-step explanations.

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Why Learn Vedic Mathematics?

Discover the powerful benefits of this ancient calculation system

10-15x Faster Calculations

Solve complex problems mentally with lightning speed using Vedic techniques.

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Creative Problem Solving

Develop innovative approaches to mathematical challenges.

Core Vedic Sutras

Learn the foundational principles of Vedic Mathematics

Ekadhikena Purvena

एकाधिकेन पूर्वेण

"By one more than the previous one"

This sutra is useful for squaring numbers ending with 5 and division.

Example: 25²

2 × (2+1) = 6, then 5² = 25 → 625

Nikhilam Navatashcaramam

निखिलं नवतश्चरमं दशतः

"All from 9 and the last from 10"

Used for subtraction and multiplication near base numbers.

Example: 1000 - 357

9-3=6, 9-5=4, 10-7=3 → 643

Urdhva-tiryagbhyam

ऊर्ध्वतिर्यग्भ्याम्

"Vertically and crosswise"

General multiplication formula for numbers of any size.

Example: 12 × 13

Vertically: 1×1=1, Cross: (1×3)+(2×1)=5, Vertically: 2×3=6 → 156

View All 16 Sutras & 13 Sub-Sutras

All 16 Vedic Sutras & 13 Sub-Sutras

Complete list of foundational principles with meanings and examples

16 Vedic Sutras

Ekadhikena Purvena

By one more than the previous one

एकाधिकेन पूर्वेण

Example: 35²

3 × 4 = 12, append 25 → 1225
Nikhilam Navatashcaramam

All from 9 and the last from 10

निखिलं नवतश्चरमं दशतः

Example: 1000 - 473

9-4=5, 9-7=2, 10-3=7 → 527
Urdhva-tiryagbhyam

Vertically and crosswise

ऊर्ध्वतिर्यग्भ्याम्

Example: 23 × 46

Right: 3×6=18 → write 8, carry 1
Cross: (2×6)+(3×4)=12+12=24 + carry 1=25 → write 5, carry 2
Left: 2×4=8 + carry 2=10 → 1058
Paravartya Yojayet

Transpose and apply

परावर्त्य योजयेत्

Example: 1/13

13 → 1 (bar 3), 1/13 = 0.076923 repeating
Sunyam Samyasamuccaye

When the sum is the same, that sum is zero

शून्यं साम्यसमुच्चये

Example: (x+3)/(x+5) = (x+2)/(x+6)

Sum of numerators: (x+3)+(x+2)=2x+5
Sum of denominators: (x+5)+(x+6)=2x+11
Equation: (2x+5)/(2x+11) = 1 → 2x+5=2x+11 → 0=6 (no solution)
Anurupyena

Proportionately

आनुरूप्येण

Example: 46 × 99

46 × 100 = 4600
4600 - 46 = 4554
Sankalana-vyavakalanabhyam

By addition and by subtraction

संकलनव्यवकलनाभ्याम्

Example: Solve 5x + 3y = 26, 3x + 5y = 30

Add: 8x + 8y = 56 → x+y=7
Subtract: 2x - 2y = -4 → x-y=-2
Solve: x=2.5, y=4.5
Puranapuranabhyam

By the completion or non-completion

पूरणापूरणाभ्याम्

Example: x² + 8x = 65

Complete square: x² + 8x + 16 = 65 + 16 = 81
(x+4)² = 81 → x+4=±9 → x=5 or x=-13
Chalana-Kalanabhyam

Sequential motion

चलनकलनाभ्याम्

Example: Derivative of x³

Using calculus concepts: d/dx(x³) = 3x²
Yavadunam

Whatever the extent of its deficiency

यावदूनम्

Example: 98²

100 - 98 = 2 (deficiency)
98 - 2 = 96
2² = 4 → 9604
Vyashtisamanstih

The whole as parts

व्यष्टिसमष्टिः

Example: (a+b)(c+d)

ac + ad + bc + bd
Shesanyankena Charamena

Remainder by last digit

शेषाण्यङ्केन चरमेण

Example: 1/19

Recurring decimal: 0.052631578947368421 repeating
Sopaantyadvayamantyam

Ultimate and twice penultimate

सोपान्त्यद्वयमन्त्यम्

Example: Solve cubic equations

For x³ - 6x² + 11x - 6 = 0
Possible roots: factors of 6 → 1,2,3
Ekanyunena Purvena

By one less than previous

एकन्यूनेन पूर्वेण

Example: 12 × 99

12 × 100 = 1200
1200 - 12 = 1188
Gunitasamuchyah

Product sum

गुणितसमुच्चयः

Example: (x+2)(x+3)=x²+5x+6

Product of constants: 2×3=6
Gunakasamuchyah

Sum of products

गुणकसमुच्चयः

Example: Quadratic roots

For ax²+bx+c=0, α+β=-b/a, αβ=c/a

13 Sub-Sutras

Anurupyena

Proportionately

Example: 63 × 99

63 × 100 = 6300
6300 - 63 = 6237
Sisyate Shesasamjnah

The remainder remains constant

Example: 29 ÷ 8

Quotient 3, remainder 5
Adyamadyenantyamantyena

The first by the first and the last by the last

Example: (2x+3)(3x+4)

First: 2x×3x=6x²
Outer: 2x×4=8x
Inner: 3×3x=9x
Last: 3×4=12
Combine: 6x² + 17x + 12
Kevalaih Saptakam Gunyat

For 7 the multiplicand is 143

Example: 7 × 142857

7 × 142857 = 999999
Vestanam

By osculation

Example: Check divisibility by 19

For 57: 5 + 7×2 = 5+14=19 (divisible)
Yavadunam Tavadunam

Whatever the deficiency, lessen it further

Example: 93²

100 - 93 = 7
93 - 7 = 86
7² = 49 → 8649
Yavadunam Tavadunikrtya Varganca Yojayet

Whatever the deficiency, lessen it further and set up the square

Example: 88²

100 - 88 = 12
88 - 12 = 76
12² = 144 → 7600 + 144 = 7744
Antyayordasake'pi

When final digits add up to 10

Example: 34 × 36

First part: 3×(3+1)=12
Last part: 4×6=24 → 1224
Antyayoreva

Only the last terms

Example: (x+5)(x+6)

x² + (5+6)x + 5×6 = x²+11x+30
Samuccayagunitah

The sum of the products

Example: (a+b)²

a² + 2ab + b²
Lopanasthapanabhyam

By elimination and retention

Example: Factorize x² + 5x + 6

(x+2)(x+3)
Vilokanam

By mere observation

Example: 5 + x = 10

x = 5
Gunita Samuchchayah Samuchchaya Gunita

Product sum equivalence

Example: Verify (a+b)(c+d)

ac + ad + bc + bd

Back to Main Sutras

Comprehensive Topics Coverage

Click on any topic to view detailed step-by-step explanations

Arithmetic Operations

Addition & Subtraction

Completing the whole
Addition from left to right
Addition of list of numbers
Base method subtraction
Completing the whole subtraction

Multiplication

Base method
Sub-base method
Complimentary numbers
Multiplication by numbers with all 9s
Multiplication by 11
Vertically and crosswise

Division

Nikhilam method
Paravartya method
Argumental division
Straight division

Squaring & Cubing

Squaring

Numbers ending in 5
Decimals and fractions
Numbers near 50
Near base and sub-base
General method from left to right
Algebraic squaring

Cubing

Cube roots of exact cubes
General cube roots

Square Roots

Vargamula method
Reverse squaring
Perfect squares
General method

Advanced Topics

Algebra

Factorization of quadratics
Solving linear equations
Polynomial multiplication
Simultaneous equations
Quadratic equations
Cubic equations

Calculus

Differentiation of power form
Chain rule
Product of functions
Integration by partial fractions
Integration by parts

Geometry & Trigonometry

Pythagoras' theorem
Coordinate geometry
Trigonometric ratios
Analytical conics

Addition: Completing the Whole

Learn the Vedic method for adding numbers by completing to the nearest whole

1 Understanding the Concept

The 'completing the whole' method involves breaking numbers into parts that complete to a round number (like 10, 100, etc.) for easier addition.

Example:

To add 47 + 68: 47 = 50 - 3, 68 = 70 - 2. Add 50 + 70 = 120, then subtract the deficiencies: -3 -2 = -5. Final result: 120 - 5 = 115

2 Identify the Base

Choose a convenient base number (like 10, 100, 1000) that is close to the numbers you're adding.

Example:

For 88 + 97, base is 100. Deficiencies: 100-88=12, 100-97=3

3 Cross-Subtract

Subtract the deficiencies from the opposite number to get the main part of the result.

Example:

88 - 3 = 85 or 97 - 12 = 85

Practice Questions

Q1. Add 56 + 79 using completing the whole method

56 needs 4 to reach 60, 79 needs 1 to reach 80

60 + 80 = 140

140 - (4 + 1) = 135

Q2. Add 94 + 87 using completing the whole

94 needs 6 to reach 100, 87 needs 13 to reach 100

100 + 100 = 200

200 - (6 + 13) = 181

Interactive Vedic Calculator

Experience Vedic Mathematics techniques with step-by-step explanations

Vedic Math Calculator

Ancient techniques for modern calculations

Multiplication

Division

Squaring

Percentage

Multiplication using Urdhva-tiryagbhyam (Vertically & Crosswise)

Step-by-Step Solution

Enter two numbers and click multiply to see the Vedic method

Division using Nikhilam Method (All from 9, last from 10)

Step-by-Step Solution

Enter dividend and divisor to see the Vedic method

Squaring using Ekadhikena Purvena (By one more than the previous)

Step-by-Step Solution

Enter a number to see the Vedic squaring method

Percentage Calculation

Step-by-Step Solution

Enter values and select calculation type

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About Vedic Mathematics Mastery

Vedic Mathematics Mastery is dedicated to preserving and teaching the ancient Indian system of mathematics that offers simplified techniques for complex calculations.

Our Mission

Our mission is to make Vedic Mathematics accessible to everyone, helping students, teachers, and enthusiasts worldwide to improve their calculation speed, mental agility, and overall mathematical understanding.

What is Vedic Mathematics?

Vedic Mathematics is a collection of techniques derived from ancient Indian scriptures called the Vedas. The system is based on 16 sutras (formulae) and 13 sub-sutras that cover all branches of mathematics, from basic arithmetic to advanced calculus.

Our Team

Our team consists of mathematicians, educators, and technology experts passionate about making mathematics enjoyable and accessible. We combine traditional teaching methods with modern technology to create an engaging learning experience.

Why Choose Us?

Comprehensive Content: Covering all 16 sutras and 13 sub-sutras
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Master All Topics of Vedic Mathematics

Why Learn Vedic Mathematics?

10-15x Faster Calculations

Improve Mental Agility

Creative Problem Solving

Core Vedic Sutras

Ekadhikena Purvena

Example: 25²

Nikhilam Navatashcaramam

Example: 1000 - 357

Urdhva-tiryagbhyam

Example: 12 × 13

All 16 Vedic Sutras & 13 Sub-Sutras

16 Vedic Sutras

Example: 35²

Example: 1000 - 473

Example: 23 × 46

Example: 1/13

Example: (x+3)/(x+5) = (x+2)/(x+6)

Example: 46 × 99

Example: Solve 5x + 3y = 26, 3x + 5y = 30

Example: x² + 8x = 65

Example: Derivative of x³

Example: 98²

Example: (a+b)(c+d)

Example: 1/19

Example: Solve cubic equations

Example: 12 × 99

Example: (x+2)(x+3)=x²+5x+6

Example: Quadratic roots

13 Sub-Sutras

Example: 63 × 99

Example: 29 ÷ 8

Example: (2x+3)(3x+4)

Example: 7 × 142857

Example: Check divisibility by 19

Example: 93²

Example: 88²

Example: 34 × 36

Example: (x+5)(x+6)

Example: (a+b)²

Example: Factorize x² + 5x + 6

Example: 5 + x = 10

Example: Verify (a+b)(c+d)

Comprehensive Topics Coverage

Arithmetic Operations

Addition & Subtraction

Multiplication

Division

Squaring & Cubing

Squaring

Cubing

Square Roots

Advanced Topics

Algebra

Calculus

Geometry & Trigonometry

Addition: Completing the Whole

Example:

Example:

Example:

Practice Questions

Interactive Vedic Calculator

Vedic Math Calculator

Addition: Completing the Whole

Other Ways to Reach Us

Information We Collect

How We Use Your Information

Cookies and Tracking Technologies

Third-Party Services

Data Security

Changes to This Policy

Intellectual Property Rights

User Conduct

Disclaimer of Warranties

Limitation of Liability

Advertisements

Changes to Terms

Our Mission

What is Vedic Mathematics?