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Vedic Mathematics

Master the 16 Sutras of ancient Indian mathematics — calculate faster than a calculator, mentally. A complete 30-module course from foundations to calculus.

Start with Module 1 → Browse the curriculum
“The sutras apply to and cover each and every part of each and every chapter of each and every branch of mathematics.” — Swami Bharati Krishna Tirtha (1884–1960), founder of modern Vedic Mathematics
16Sutras
30Modules
3Levels
150+Hours
₹0Forever free

The 16 Sutras

Each Sutra is a short aphorism that encodes an entire mental-calculation technique — a master key that opens many doors at once.

Sutra 1
एकाधिकेन पूर्वेण
Ekadhikena Purvena
By one more than the previous one
Sutra 2
निखिलं नवतश्चरमं दशतः
Nikhilam Navatashcaramam Dashatah
All from 9 and the last from 10
Sutra 3
ऊर्ध्वतिर्यग्भ्याम्
Urdhva-Tiryagbhyam
Vertically and cross-wise
Sutra 4
परावर्त्य योजयेत्
Paravartya Yojayet
Transpose and apply
Sutra 5
शून्यं साम्यसमुच्चये
Shunyam Saamyasamuccaye
If the Samuccaya is the same, it is zero
Sutra 6
आनुरूप्ये शून्यमन्यत्
Anurupyena Shunyamanyat
If one is in ratio, the other is zero
Sutra 7
संकलनव्यवकलनाभ्याम्
Sankalana-vyavakalanabhyam
By addition and by subtraction
Sutra 8
पूरणापूरणाभ्याम्
Puranapuranabhyam
By the completion or non-completion
Sutra 9
चलनकलनाभ्याम्
Chalana-Kalanabhyam
Differences and similarities
Sutra 10
यावदूनम्
Yavadunam
Whatever the extent of its deficiency
Sutra 11
व्यष्टिसमष्टिः
Vyashti Samashti
Part and whole
Sutra 12
शेषाण्यङ्केन चरमेण
Shesanyankena Charamena
The remainders by the last digit
Sutra 13
सोपान्त्यद्वयमन्त्यम्
Sopaantyadvayamantyam
The ultimate and twice the penultimate
Sutra 14
एकन्यूनेन पूर्वेण
Ekanyunena Purvena
By one less than the previous one
Sutra 15
गुणितसमुच्चयः
Gunitasamuccayah
The product of the sum is the sum of the products
Sutra 16
गुणकसमुच्चयः
Gunakasamuccayah
The factors of the sum is the sum of the factors

Complete Curriculum

Thirty modules across three carefully sequenced levels. Modules marked “Available” are ready to study now; the rest are on the way.

🌱Level 1 — Foundation
Beginner · Ages 8–12 · 40–50 hours

Build rock-solid mental arithmetic — base systems, lightning multiplication, division, squares and verification.

Module 1 Available
Introduction to Vedic Mathematics
Conceptual Overview — all 16 Sutras
  • History & origin (Atharvaveda, Swami Bharati Krishna Tirtha)
  • Conventional vs Vedic methods
  • The 16 Sutras & 13 Sub-Sutras
  • The Base system (10, 100, 1000)
Module 2 Available
Vedic Addition & Subtraction
Sutra 7 — Sankalana-Vyavakalanabhyam
  • Left-to-right addition
  • The dot (Shudhha) method
  • Complement subtraction (Nikhilam)
  • Adding & subtracting near a base
Module 3 Available
Multiplication by Special Numbers
Sutra 1 & Sutra 14
  • Multiply by 11, 12–19
  • Multiply by 9, 99, 999
  • Multiply by 5, 25, 125
  • Multiply by 111, 1111
Module 4 Available
The Nikhilam Method — Multiplication Near Base
Sutra 2 — Nikhilam | Sub-Sutra 6
  • Base 10/100/1000 multiplication
  • Cross-subtraction & cross-addition
  • Mixed above/below base
  • Sub-base multiplication (50, 25)
Module 5 Available
Urdhva-Tiryak — General Multiplication
Sutra 3 — Urdhva-Tiryagbhyam
  • 2×2, 3×3, 4×4 multiplication
  • Vertical & cross-wise pattern
  • Managing carries
  • Application to algebra
Module 6 Available
Vedic Division — Part 1
Sutra 4 — Paravartya | Sutra 12
  • Division by 9, 8, 7
  • Paravartya (near-base divisors)
  • The flag (Dhvajanka) method intro
  • Remainder theorem & verification
Module 7 Available
Squares and Square Roots — Part 1
Sutra 10 — Yavadunam | Sub-Sutra 7
  • Squaring numbers ending in 5
  • Squaring near a base
  • 40–49 & 50–59 ranges
  • The Duplex (Dwandwa) method
Module 8 Available
Digital Roots & Casting Out Nines
Sutra 15 — Gunitasamuccayah
  • Digital root (Beejank)
  • Casting out nines
  • Verifying +, −, ×, ÷
  • Finding missing digits
Module 9 Available
Fractions & Decimals — Vedic Approach
Sutra 1 — Ekadhikena | Sutra 6
  • Recurring decimals (1/19, 1/29)
  • The 1/7 cyclic wheel (142857)
  • Two-flag method (1/13, 1/17)
  • Fraction arithmetic shortcuts
Module 10 Available
Foundation Assessment & Review
All 16 Sutras (review)
  • Module 1–9 review
  • Speed tests
  • Mental-math championship
  • Real-life applications
🚀Level 2 — Intermediate
Class 6–10 · Ages 12–16 · 50–60 hours

Scale the sutras to large numbers, algebra, geometry, trigonometry and number theory.

Module 11 Available
Advanced Multiplication — Urdhva Extended
Sutra 3 | Sutra 11 — Vyashti Samashti
  • 4×4 & 5×5 multiplication
  • Polynomial multiplication
  • Different digit counts
  • Vinculum & mixed-base
Module 12 Available
Advanced Division — Paravartya & Straight Division
Sutra 4 | Sutra 12
  • Paravartya for divisors above base
  • Dhvajanka (flag) division
  • 3-digit divisors
  • Osculation divisibility tests
Module 13 Available
Cubes and Cube Roots
Sutra 10 — Yavadunam | Anurupyena
  • Cubing 2-digit numbers (ratio method)
  • Mental cube roots
  • Cubes near a base
  • Pattern recognition
Module 14 Available
Advanced Squares & Square Roots
Sutra 3 (Duplex) | Sutra 10
  • Multi-digit Duplex
  • 3 & 4-digit squaring
  • Algebraic squaring
  • Single-line square roots
Module 15 Available
Algebra — Vedic Approach to Equations
Sutra 5 | Sutra 6 | Sutra 7
  • Linear equations via Shunyam Samya
  • Special equation types
  • Simultaneous equations
  • Vedic 2×2 systems
Module 16 Available
Factorization & Algebraic Products
Sutra 3 | Sutra 4 | Sutra 15 & 16
  • Factoring quadratics
  • Adyamadyena method
  • Products of binomials/trinomials
  • HCF of polynomials
Module 17 Available
Coordinate Geometry — Vedic Shortcuts
Sutra 3 | Sub-Sutra 12 — Vilokanam
  • Distance, midpoint, section
  • Equation of a line
  • Area of a triangle
  • Collinearity by observation
Module 18 Available
Trigonometry — Vedic Insights
Sutra 9 | Sutra 11
  • Standard-angle patterns
  • Identity verification
  • Compound angles via Urdhva
  • Product-to-sum formulas
Module 19 Available
Number Theory — Vedic Perspective
Sutra 12 | Sub-Sutra 5 — Veshtanam
  • Osculation divisibility
  • Modular arithmetic
  • Last digits of large powers
  • Cyclic numbers (142857)
Module 20 Available
Intermediate Assessment
All Sutras (review)
  • Timed multiplication championship
  • Algebraic competition problems
  • JEE-style applications
  • Capstone project
🏆Level 3 — Advanced
Competitive · Age 16+ · 60–70 hours

Apply Vedic methods to higher algebra, calculus, matrices, statistics and exam strategy.

Module 21 Available
Higher Algebra — Cubic & Quartic Equations
Sutra 5 | Sutra 4 | Sutra 9
  • Cubics by inspection
  • Sum & product of roots
  • Quartics (Vyashti-Samashti)
  • Partial fractions
Module 22 Available
Matrices & Determinants — Vedic Methods
Sutra 3 | Sutra 7
  • 2×2 & 3×3 determinants
  • Matrix multiplication via Urdhva
  • Inverse of a 2×2
  • Cramer's rule
Module 23 Available
Calculus — Vedic Differential Calculus
Sutra 9 — Chalana-Kalanabhyam
  • Derivatives of polynomials
  • Product & quotient rules
  • Higher-order derivatives
  • Maxima & minima
Module 24 Available
Calculus — Vedic Integral Calculus
Sutra 8 — Puranapuranabhyam
  • Integration by completing the square
  • Integration by parts
  • Partial fractions integrals
  • Area under curves
Module 25 Available
Statistics & Probability — Vedic Computation
Sutra 11 | Sub-Sutra 1 — Anurupyena
  • Mean, median, mode shortcuts
  • Variance via working mean
  • Permutations & combinations
  • Bayes' theorem
Module 26 Available
Complex Numbers — Vedic Approach
Sutra 3 | Sutra 10
  • Multiplication & division
  • Modulus & argument
  • De Moivre's theorem
  • nth roots of unity
Module 27 Available
Series & Sequences — Vedic Patterns
Sutra 1 | Sutra 14 | Sutra 15
  • AP & GP sums
  • Sum of squares & cubes
  • Binomial theorem
  • Telescoping series
Module 28 Available
Geometry — Vedic Constructions & Proofs
Sub-Sutra 12 | Sutra 11
  • Pythagorean triples
  • Heronian triangles
  • Circle theorems by observation
  • Conic sections
Module 29 Available
Applied Vedic Math — Competitive Exam Focus
All 16 Sutras integrated
  • JEE Main & Advanced
  • CAT / GMAT reasoning
  • Time-speed-distance
  • When to use Vedic vs conventional
Module 30 Available
Research Topics & Original Extensions
Research & synthesis
  • Algebraic justifications
  • Vedic math in VLSI & cryptography
  • Ancient Indian mathematics
  • New mnemonics & extensions

Calculate at the speed of thought

Every module includes clear theory, worked examples graded simple to hard, practice drills with answer keys, and an online test bank — all free, forever.

Begin the journey →