The 16 Sutras of Vedic Maths
Ancient Indian wisdom for lightning-fast mental calculation. Master all 16 sutras (formulae) discovered by Swami Bharati Krishna Tirthaji from the Atharva Veda — and solve complex problems in seconds without a calculator.
📖 What is Vedic Maths?
Vedic Mathematics is an ancient system of mathematics rediscovered between 1911 and 1918 by Swami Bharati Krishna Tirthaji from the Atharva Veda. The entire system rests on just 16 sutras (aphorisms or formulae) and 13 sub-sutras that together can solve problems across arithmetic, algebra, geometry, trigonometry, calculus, and even conics — often in a single line.
Unlike conventional methods that require pages of working, Vedic sutras let you compute mentally in seconds. Students who learn these techniques regularly report 10x to 15x faster calculation speeds, fewer errors, and a huge boost in confidence — especially for CBSE Class 6–10 board exams and competitive exams like JEE, NEET, SSC, Bank, and Olympiads.
🕉️ All 16 Sutras Click any sutra to learn the trick · examples · practice questions
Square any number ending in 5 instantly, and convert recurring decimals like 1/19, 1/29 into their full decimal form effortlessly.
SUTRA 02Lightning-fast subtraction and multiplication of numbers close to bases like 10, 100, 1000 — perfect for huge numbers like 98 × 97.
SUTRA 03The universal multiplication formula — multiply any two numbers of any length in just one line. The most powerful sutra in Vedic Maths.
SUTRA 04Solve linear algebraic equations and perform division by numbers above the base in seconds — without long division stress.
SUTRA 05Spot the hidden zero in complex equations and solve special algebraic problems where standard methods would take ages.
SUTRA 06Used for proportional reasoning, simplifying ratios, and solving simultaneous equations where one variable becomes zero by symmetry.
SUTRA 07Solve simultaneous linear equations quickly using direct addition and subtraction of equations — without lengthy substitution methods.
SUTRA 08Factorize quadratic equations and solve them faster by completing the square mentally — a game changer for Class 10 algebra.
SUTRA 09A powerful sutra used in calculus for differentiation, approximation, and identifying patterns in sequences and series.
SUTRA 10Square and cube numbers near a base (like 96², 104³) in one step using the deficiency or surplus from the base.
SUTRA 11Used in advanced factorization where you split an expression into smaller parts and re-combine for an elegant solution.
SUTRA 12Convert any vulgar fraction into its full decimal form by tracking remainders and the last digit — magical for fractions like 1/7, 1/13.
SUTRA 13A specialised sutra for solving certain algebraic equations involving the last and second-last terms — extremely useful in proofs.
SUTRA 14Multiply any number by a series of 9s (like 99, 999, 9999) in a single step — a beautiful and instant pattern-based trick.
SUTRA 15A quick verification rule — use it to check if your factorization of any polynomial is correct without re-multiplying everything.
SUTRA 16Used in higher algebra to verify and construct polynomial factorizations — a perfect cross-check for complex Class 10 problems.
🚀 Why Should You Learn Vedic Maths?
If you are a student preparing for CBSE board exams or competitive exams, Vedic Maths is one of the most valuable skills you can pick up. Here is why thousands of Indian students are switching to this ancient system every year.
📜 The History & Origin of Vedic Maths
The system of Vedic Mathematics that we know today was reconstructed by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja (1884–1960), the Shankaracharya of Govardhana Matha in Puri, between 1911 and 1918. Following years of intense study of the Atharva Veda — particularly its Sthapatya Upaveda — he claimed to have rediscovered the foundational principles of an entire mathematical system encoded within just 16 short Sanskrit aphorisms.
These 16 sutras were originally compiled into a 16-volume work, but tragically the manuscripts were lost. From memory, in his final years, Tirthaji produced a single introductory volume titled "Vedic Mathematics", published posthumously in 1965 by Motilal Banarsidass. This single book ignited a global revival of interest in ancient Indian mathematics, and today Vedic Maths is taught in schools across India, the United Kingdom, the United States, and many other countries.
What makes the sutras so special?
Each sutra is a compressed mental algorithm. They are not just shortcut tricks — they are general principles, applicable across multiple branches. For example, Urdhva-Tiryagbhyam is used in arithmetic for multiplication, in algebra for multiplying polynomials, and in matrix mathematics for determinants. One sutra, three branches — that is the elegance of the Vedic system.
🎓 How to Start Learning Vedic Maths
Many students get overwhelmed because they try to memorize all 16 sutras at once. That is the wrong approach. Vedic Maths is a practice-based skill, not a memorization exercise. Here is a tested learning path that has worked for thousands of CBSE Class 6 to 10 students:
- Start with Sutra 3 — Urdhva-Tiryagbhyam. This is the most powerful sutra and the foundation of fast multiplication.
- Move to Nikhilam (Sutra 2). Learn to use base numbers (10, 100, 1000) for instant multiplication.
- Practice Ekadhikena Purvena (Sutra 1). The squaring-of-5 trick is the most rewarding for beginners — it builds confidence.
- Use Yavadunam (Sutra 10) for cubes and squares. Once Nikhilam is solid, this sutra extends naturally to higher powers.
- Move into algebraic sutras gradually. Paravartya Yojayet, Sopaantyadvayamantyam, and Gunitasamuccayah work best alongside your school algebra chapters.
- Daily 15-minute practice. Consistency beats intensity. Solve 10 problems per day using Vedic methods and within 60 days you will outperform calculators on most problems under 5 digits.
📘 Vedic Maths for CBSE Class 6 to 10 Students
If you are a CBSE student between Class 6 and Class 10, Vedic Maths directly helps you with several NCERT chapters. Here are the key intersections:
- Class 6 & 7 — Number Play, Integers, Fractions: Sutras 1, 2, and 14 give elegant tricks for large numbers and multiples of 9, while Shesanyankena Charamena converts fractions to decimals quickly.
- Class 8 — Squares, Cubes, Algebra Play: Yavadunam is custom-built for squaring and cubing, and Urdhva-Tiryagbhyam handles polynomial multiplication.
- Class 9 & 10 — Polynomials, Quadratic Equations: Puranapuranabhyam handles quadratic factorization elegantly, while Paravartya Yojayet simplifies division and identities.
Pair these Vedic tricks with the free NCERT MCQ practice on BachelorPulse — it is a serious unfair advantage. Try our chapter-wise quizzes from the home page.