Ginti Vedic

Vedic Multiplication Calculator

Type two numbers and see the Vedic sutra that solves them fastest, worked step by step next to the school method.

First number

Second number

Try a classic example

97 × 96

9,312

Solved with Nikhilam Navatashcaramam Dashatah

Sutra used

Nikhilam Navatashcaramam Dashatah

निखिलं नवतश्चरमं दशतः

“All from 9 and the last from 10”

Both numbers are within 4 of 100, so the working uses small differences instead of the numbers.

What you entered

First number: 97Second number: 96

1
Pick the base: the power of 10 nearest both numbers
97 and 96 are both near 100= base 100 (2 zeros)
2
Find each number's difference from the base (for a number below it: all from 9, the last from 10)
97 − 100 = (−3), 96 − 100 = (−4)= (−3) and (−4)
3
Left part: cross-add one number and the other's difference
97 − 4 (or 96 − 3)= 93
4
Right part: multiply the two differences
(−3) × (−4)= 12
5
Join the parts, writing the right part with 2 digits
93 | 12= 9,312

Result

Product: 9,312

Both numbers are within 4 of 100, so the working uses small differences instead of the numbers.

What you entered

First number: 97Second number: 96

1
Digit sum of 97
9 + 7 = 16 → 1 + 6 = 7= 7
2
Digit sum of 96
9 + 6 = 15 → 1 + 5 = 6= 6
3
Multiply the two digit sums and reduce
7 × 6 = 4 + 2 = 6= 6
4
Digit sum of the answer 9,312
9 + 3 + 1 + 2 = 15 → 1 + 5 = 6= 6
5
Compare the two
6 and 6= match: the answer checks out

Result

Check: Passes

Casting out nines catches most slips in a written answer, but not all of them: swapping two digits of the answer leaves its digit sum unchanged.

What you entered

First number: 97Second number: 96

1
97 × the units digit of 96
97 × 6= 582
2
97 × the tens digit of 96
97 × 9 × 10= 8,730
3
Add the partial products
582 + 8,730= 9,312

Result

Product: 9,312

Both methods give 9,312. Long multiplication writes out 2 partial products and adds them up; the Vedic method builds the answer directly, which is why it suits mental maths.

Vedic working for the multiplications people practise most

Each row is the last line of the Vedic working this calculator shows, with the sutra it picks. In Nikhilam and Ekadhikena the bar separates the left part from the right part; in Urdhva-Tiryagbhyam each digit comes from one vertical-and-crosswise column.

Problem	Sutra	Working	Answer
8 x 7	Nikhilam (base 10)	5 \| 6	56
97 x 96	Nikhilam (base 100)	93 \| 12	9,312
88 x 93	Nikhilam (base 100)	81 \| 84	8,184
104 x 108	Nikhilam (base 100)	112 \| 32	11,232
112 x 115	Nikhilam, with a carry	127 + 1 \| 80 = 128 \| 80	12,880
104 x 96	Nikhilam, with a borrow	100 - 1 \| 100 - 16 = 99 \| 84	9,984
998 x 997	Nikhilam (base 1000)	995 \| 006	995,006
1004 x 1012	Nikhilam (base 1000)	1,016 \| 048	1,016,048
65 x 65	Ekadhikena Purvena	6 x 7 = 42 \| 25	4,225
105 x 105	Ekadhikena Purvena	10 x 11 = 110 \| 25	11,025
43 x 12	Urdhva-Tiryagbhyam	5 \| 1 \| 6	516
123 x 456	Urdhva-Tiryagbhyam	5 \| 6 \| 0 \| 8 \| 8	56,088

With base 100 the right part is always written with two digits and with base 1000 with three, which is why 998 x 997 ends in 006. A right part that is too long carries into the left part; a negative one borrows from it. Every answer is also confirmed by long multiplication and the digit-sum (Beejank) check.

How Nikhilam turns 97 × 96 into two tiny sums

Nikhilam Navatashcaramam Dashatah ("all from 9 and the last from 10") works with each number's distance from a nearby power of 10. 97 and 96 are 3 and 4 below 100. Cross-subtract to get the left part: 97 − 4 = 93. Multiply the distances for the right part: 3 × 4 = 12. Join them: 9312. Above the base the distances are positive (104 × 108 → 112 | 32 = 11,232), and when the right part runs past the base's number of zeros you carry into the left part.

Urdhva-Tiryagbhyam: one line, any numbers

"Vertically and crosswise" builds the answer one column at a time. For 43 × 12: the units column is 3 × 2 = 6; the tens column is the crosswise pair 4 × 2 + 3 × 1 = 11, so write 1 and carry 1; the hundreds column is 4 × 1 plus the carry = 5. Reading the written digits gives 516. It is ordinary place-value arithmetic arranged so the whole answer comes out in one line, which is why it is popular for mental maths.

Squaring numbers that end in 5

Ekadhikena Purvena ("by one more than the previous one") squares any number ending in 5 in two moves. Take the part before the 5 and multiply it by one more than itself, then append 25. For 65²: 6 × 7 = 42, so the answer is 4225. For 105²: 10 × 11 = 110, giving 11,025.

Frequently asked questions

What is Vedic maths?

A collection of 16 short rules (sutras) and 13 sub-rules for fast mental calculation, set out by Jagadguru Swami Bharati Krishna Tirthaji in the book Vedic Mathematics, published in 1965. The best-known sutras cover multiplication, squaring and division; this calculator implements the three used most for multiplication.

Do the sutras really come from the Vedas?

Tirthaji attributed them to an appendix of the Atharvaveda, but they have not been found in any known Vedic text, and historians of mathematics such as S. G. Dani regard them as his own modern formulation. The arithmetic is valid either way: every answer on this page is also checked with ordinary long multiplication.

When should I use Nikhilam instead of Urdhva-Tiryagbhyam?

Use Nikhilam when both numbers are close to the same power of 10, such as 98 × 97 or 1004 × 1012: the working uses the small differences instead of the numbers. Urdhva-Tiryagbhyam works for any pair, so it is the general method. The calculator picks the quicker one automatically, and you can switch to see the other.

How does the digit-sum (Beejank) check work?

Reduce each number to a single digit by adding its digits repeatedly (97 → 16 → 7). Multiply those two digits and reduce again. The result must equal the reduced digit sum of the answer. It catches most slips in a written answer, but not all: swapping two digits of the answer leaves its digit sum unchanged.

Is Vedic multiplication faster than normal multiplication?

For suitable numbers, clearly: squares ending in 5 and numbers near 10, 100 or 1000 need one or two small multiplications instead of several partial products. For arbitrary numbers Urdhva-Tiryagbhyam does about the same amount of arithmetic as long multiplication, but it produces the answer in a single line, which is what makes it practical to do in your head.