Vedic Sutras: What are the 16 Sutras in Vedic Maths? Explained with Examples

Vedic Maths is an ancient Indian system of mathematics derived from the Vedas. The "father of Vedic math" is generally considered to be Jagadguru Shri Bharati Krishna Tirthaji Maharaja, also known as Shri Bharati Krishna Tirtha.

It includes mental techniques based on 16 powerful formulas, or "sutras," that simplify and speed up calculations. Knowing these sutras is helpful for students preparing for competitive exams. 

What is Vedic Maths? 

Vedic Maths is a system of calculation techniques based on ancient Indian scriptures. These sutras make arithmetic and algebraic operations much faster and easier. Unlike traditional methods, which rely on lengthy steps, Vedic methods help you arrive at answers mentally with minimal effort. 

Key Benefits:

• Fast mental calculations
• Builds confidence
• Improves focus and accuracy
• Useful in competitive exams

To know more about Vedic Maths, check out the bog given below,

How Many Sutras Are There in Vedic Maths?

There are 16 main Sutras (formulas) and 13 Sub-Sutras (sub-formulas) in Vedic Maths. These cover operations such as addition, subtraction, multiplication, division, squares, and square roots.

Overview of the 16 Vedic Maths Sutras

• Sankalana-Vyavakalanabhyam: Useful for solving equations through addition and subtraction.
• Puranapuranabhyam: Helps simplify addition or subtraction by completing numbers to the nearest base.

Example: 

86 + 14 → 86 is 4 less than 90, 

Add 4 to 14 and subtract it from 90,

90 + 10 = 100.

Vedic Maths Sutras for Multiplication

• Urdhva Tiryak Sutra: 

Multiply 23 × 12:

1. Multiply unit digits: 3 × 2 = 6
2. Cross-multiply and add: (2×2)+(1×3) = 7
3. Multiply tens: 2 × 1 = 2 → Final answer = 276

• Nikhilam Sutra: 

Multiply 97 × 96 (both near 100):

1. Base = 100; 100–97 = 3, 100–96 = 4
2. Subtract cross: 97–4 or 96–3 = 93
3. Multiply the deficits: 3 × 4 = 12 → Answer = 9312

Vedic Maths Sutras for Division

• Paravartya Yojayet: Used for dividing numbers without the long division method.

Example: Dividing 145 by 9 using recurring decimals.

1. Ekadhikena Purvena

Meaning: “By one more than the previous one”
Use: Squaring numbers ending in 5
Example:
→ 25² = (2 × 3) | 25 = 625
(2 is before 5, 2 × (2+1) = 6, write 25 → 625)

2. Nikhilam Navatashcaramam Dashatah

Meaning: “All from 9 and the last from 10”
Use: Multiply numbers close to base 10, 100, etc.
Example:
→ 96 × 97 = ?
Base = 100; 100–96 = 4, 100–97 = 3
Cross-subtract: 96–3 = 93
Multiply deficits: 4 × 3 = 12 → 9312

3. Urdhva Tiryagbhyam

Meaning: “Vertically and crosswise”
Use: General multiplication
Example:
→ 23 × 12
Step-by-step: (2×1), (2×2)+(3×1), (3×2) → 276

4. Paravartya Yojayet

Meaning: “Transpose and adjust”
Use: Solving equations and simple division
Example:
Solve: 1 / (1 + x) using adjustment
(Used in algebraic simplifications)

5. Shunyam Saamyasamuccaye

Meaning: “If the sum is the same, the total is zero”
Use: Solve algebraic equations with equal sums
Example:
(x + 2)(x + 3) – (x + 2)(x + 3) = 0

6. Anurupyena Shunyamanyat

Meaning: “If one is zero, the other is equal”
Use: Proportions and equations
Example:
If a × b = 0, and b ≠ 0, then a = 0

7. Sankalana-Vyavakalanabhyam

Meaning: “By addition and subtraction”
Use: Solving simple equations
Example:
x + y = 10 and x – y = 4
Add and subtract to find x and y

8. Puranapuranabhyam

Meaning: “By the completion or non-completion”
Use: Addition or subtraction using nearest base
Example:
97 + 6 = ? → 97 is near 100; 100 + 3 = 103

9. Chalana-Kalanabhyam

Meaning: “Calculations using motion”
Use: Algebra and calculus
Example:
(Used for factorisation and simplifying variable expressions)

10. Yavadunam

Meaning: “Whatever the extent of its deficiency”
Use: Squaring numbers below base
Example:
→ 96² = ?
Base = 100; 100–96 = 4
96 – 4 = 92; 4² = 16 → 9216

11. Vyashtisamanstih

Meaning: “Part and whole are equal”
Use: For breaking and combining terms
Example:
(2 + 3)² = 4 + 6 + 9 = 25 (Expand and simplify)

12. Shesanyankena Charamena

Meaning: “Remainder by the last digit”
Use: Checking divisibility and remainders
Example:
To find remainder of a number divided by 9

13. Sopaantyadvayamantyam

Meaning: “The ultimate and twice the penultimate”
Use: Factorising algebraic expressions
Example:
Used in polynomial simplification techniques

14. Ekanyunena Purvena

Meaning: “One less than the previous”
Use: Multiplying numbers just below base
Example:
→ 99 × 98 = ?
Base = 100; 100–99 = 1, 100–98 = 2
99–2 = 97; 1 × 2 = 02 → 9702

15. Gunitasamuccayah

Meaning: “The product of the sum is the same”
Use: Factorising expressions
Example:
(a + b)(a – b) = a² – b²

16. Gunakasamuccayah

Meaning: “The factors of the sum are equal”
Use: Simplifying algebraic expressions
Example:
Common factorisation of quadratic equations

• Enable faster problem solving
• Encourage mental math and avoid over-reliance on calculators
• Great for competitive exams like Olympiads, NTSE, and entrance tests

Can Kids Learn Vedic Maths Sutras?

Yes! Kids as young as 8 years old can start learning basic Vedic Maths techniques. Start with:

• Ekadhikena Purvena for squaring numbers ending in 5
• Urdhva Tiryak for simple multiplication
• Make it fun using games, flashcards, or apps

To know how Vedic Maths can improve children's mathematical ability check out the blog given below, 

Common Misunderstandings about Vedic Sutras

How to Practice Vedic Sutras at Home

• Start with one sutra per week
• Use apps like Maths Tricks, Vedic Maths India, or Fun with Numbers
• Make flashcards for daily revision

Traditional vs Vedic Maths Comparison Table

Learning Vedic Sutras Made Easy with Interval

Vedic Maths is a smart, effective way to improve calculation speed and develop a love for numbers. Start with basic sutras and practice regularly. Combine with traditional math for the best of both worlds.

At Interval Learning, we offer personalized Vedic Maths coaching for students of all ages.

Learn the 16 sutras step-by-step
Interactive 1-on-1 sessions
Fun, engaging techniques with real-life examples

Start your Vedic Maths journey today with expert support from Interval Learning!