Vedic Maths — Veda Topper

The 16 Vedic Maths Sutras (and 13 Sub-Sutras)

All of Vedic Mathematics is built on 16 short word-formulae called sutras and 13 supporting sub-sutras. Here is the complete list with plain-English meanings and what each one is used for — plus links to step-by-step tutorials.

Learn all of this live. Veda Topper runs online Vedic Maths classes for kids and adults, worldwide. Book a free demo class → · WhatsApp us →

The 16 Sutras

Sutra	Meaning	Mainly used for
1. Ekadhikena Purvena	By one more than the one before	Squaring numbers ending in 5; certain recurring decimals
2. Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10	Subtraction from a base; base multiplication
3. Urdhva-Tiryagbhyam	Vertically and crosswise	General multiplication of any two numbers
4. Paravartya Yojayet	Transpose and adjust	Division and solving equations
5. Shunyam Saamyasamuccaye	If the Samuccaya is the same, it is zero	Solving special equations
6. Anurupye Shunyamanyat	If one is in ratio, the other is zero	Simultaneous equations
7. Sankalana-Vyavakalanabhyam	By addition and by subtraction	Simultaneous equations
8. Puranapuranabhyam	By the completion or non-completion	Factorising and quadratics
9. Chalana-Kalanabhyam	Differences and similarities	Calculus and equations
10. Yavadunam	Whatever the extent of its deficiency	Squaring numbers near a base
11. Vyashtisamashtih	Part and whole	Averages and factorisation
12. Sheshanyankena Charamena	The remainders by the last digit	Recurring decimals
13. Sopantyadvayamantyam	The ultimate and twice the penultimate	Special divisions
14. Ekanyunena Purvena	By one less than the one before	Multiplying by a row of 9s
15. Gunitasamuchyah	The product of the sum	Checking factors of expressions
16. Gunakasamuchyah	All the multipliers	Factorisation checks

The 13 Sub-Sutras

Sub-Sutra	Meaning
1. Anurupyena	Proportionately
2. Shishyate Sheshasamjnah	The remainder remains constant
3. Adyamadyenantyamantyena	First by first and last by last
4. Kevalaih Saptakam Gunyat	For 7 the multiplier is 143
5. Vestanam	By osculation
6. Yavadunam Tavadunam	Lessen by the deficiency
7. Yavadunam Tavadunikritya Varganca Yojayet	Square the deficiency and add
8. Antyayordashake\u2019pi	When the last digits total 10
9. Antyayoreva	Only the last terms
10. Samuccayagunitah	The sum of the products
11. Lopanasthapanabhyam	By elimination and retention
12. Vilokanam	By observation
13. Gunitasamuccayah Samuccayagunitah	The product of the sum is the sum of the products

Learn them with worked examples

Reading the sutras is one thing; using them is another. Start with these hands-on tutorials, each with step-by-step examples and practice:

Multiply by 11 in one line
Square any number ending in 5 (Ekadhikena Purvena)
Base multiplication near 100 (Nikhilam)
Vertically and crosswise (Urdhva-Tiryagbhyam)
Square numbers near a base (Yavadunam)
Divide by 9 instantly
Subtract from 100/1000 (all from 9)

More Vedic Maths tricks

← Vedic Maths home Multiply by 11 in one line Square numbers ending in 5 Base multiplication (Nikhilam)Vertically & crosswise Squares near a base (Yavadunam)Instant division by 9 Subtraction: all from 9

Frequently asked questions

How many sutras are there in Vedic Maths?

There are 16 main sutras (word-formulae) and 13 sub-sutras that support them, covering multiplication, division, squares, roots, fractions, algebra and more.

Who compiled the 16 Vedic Maths sutras?

They were presented by Swami Bharati Krishna Tirtha in his book on Vedic Mathematics, and are now taught worldwide as fast mental-calculation methods.

Which sutra is the most useful for beginners?

Ekadhikena Purvena (squaring numbers ending in 5) and Nikhilam (subtraction and base multiplication) are the easiest wins for beginners.

Learn all of this live. Veda Topper runs online Vedic Maths classes for kids and adults, worldwide. Book a free demo class → · WhatsApp us →