Vedic Mathematics is an ancient system of mathematics that originated in India. It’s based on a collection of mental calculation techniques and shortcuts derived from ancient Sanskrit texts called the Vedas, specifically the Atharva Veda.
Vedic Math was rediscovered and systematized in the early 20th century by Swami Bharati Krishna Tirthaji Maharaj, who compiled it into 16 main sutras (formulas) and 13 sub-sutras (corollaries). These sutras provide quick methods to solve complex arithmetic, algebraic, and geometric problems.
The 16 Vedic Sutras (Main Formulas)
Here are a few key ones with meanings:
| Sutra | Meaning (Simplified) | Use |
|---|---|---|
| 1. Ekadhikena Purvena | “By one more than the previous one” | Useful in squaring numbers ending in 5 (e.g., 35²) |
| 2. Nikhilam Navatashcaramam Dashatah | “All from 9 and the last from 10” | Used for quick multiplication near powers of 10 |
| 3. Urdhva–Tiryagbhyam | “Vertically and crosswise” | General multiplication formula |
| 4. Paravartya Yojayet | “Transpose and adjust” | Useful in division and algebraic operations |
| 5. Sunyam Samyasamuccaye | “When the sum is the same, that sum is zero” | Solving algebraic equations |
| 6. Anurupye Shunyamanyat | “If one is in ratio, the other is zero” | Solving equations proportionally |
(There are 10 more sutras and 13 sub-sutras for specialized problems.)
Examples
Example 1: Squaring numbers ending in 5
Let’s use Ekadhikena Purvena (By one more than the previous one)
Example: 35²
👉 Take the first digit (3)
👉 Multiply by one more than itself: 3 × 4 = 12
👉 Append 25 to the result → 1225
Answer: 35² = 1225 ✅
Example 2: Multiplying numbers near 100
Using Nikhilam Sutra
Example: 97 × 96
👉 Base = 100
👉 Deficiencies: 97 is -3, 96 is -4
👉 Cross subtract: 97 – 4 = 93
👉 Multiply deficiencies: (-3)×(-4)=12
👉 Combine → 9312
Answer: 97 × 96 = 9312 ✅
Benefits of Vedic Math
- Speed: Greatly reduces calculation time.
- Simplicity: Uses patterns and logic rather than rote formulas.
- Mental agility: Strengthens concentration and number sense.
- Applicability: Works for arithmetic, algebra, geometry, calculus, etc.
Modern Relevance
Vedic Math is taught in many schools and coaching centers today because it:
- Helps students perform faster in competitive exams.
- Builds confidence in math through intuitive methods.
- Encourages creative problem-solving rather than memorization.