Ginti Vedic

Vedic Square Calculator

Type a number and watch the Vedic sutra square it, step by step, next to the school method.

Number to square

Try a classic example

97²

9,409

Solved with Yavadunam

Sutra used

Yavadunam

यावदूनं तावदूनीकृत्य वर्गं च योजयेत्

“Whatever the deficiency, lessen by that much and set up its square”

97 is only 3 below 100, so the square comes from that small difference.

Watch it worked out: Yavadunam

Step 5 of 5

Join the two parts: 94 | 09, so 97² = 9,409.

What you entered

Number: 97

1
Pick the base: the power of 10 nearest the number
97 is near 100= base 100 (2 zeros)
2
How far below the base is it? That is the deficiency
97 − 100= (−3)
3
Left part: lessen the number by the deficiency
97 − 3= 94
4
Right part: square the difference
(−3)²= 9
5
Join the parts, writing the right part with 2 digits
94 | 09= 9,409

Result

Square: 9,409

97 is only 3 below 100, so the square comes from that small difference.

What you entered

Number: 97

1
Digit sum of 97
9 + 7 = 16 → 1 + 6 = 7= 7
2
Digit sum of 97
9 + 7 = 16 → 1 + 6 = 7= 7
3
Multiply the two digit sums and reduce
7 × 7 = 4 + 9 = 13 → 1 + 3 = 4= 4
4
Digit sum of the answer 9,409
9 + 4 + 0 + 9 = 22 → 2 + 2 = 4= 4
5
Compare the two
4 and 4= 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

Number: 97

1
97 × the units digit of 97
97 × 7= 679
2
97 × the tens digit of 97
97 × 9 × 10= 8,730
3
Add the partial products
679 + 8,730= 9,409

Result

Square: 9,409

Both give 9,409. Long multiplication writes out 2 partial products; the Vedic method builds the square directly.

Vedic working for the squares people practise most

Each row is the last line of the Vedic working this calculator shows, with the sutra it picks. In Yavadunam and Ekadhikena the bar separates the left part from the right part; in the duplex each part between bars is one column of the answer before carries.

Square	Sutra	Working	Answer
97^2	Yavadunam (3 below 100)	94 \| 09	9,409
96^2	Yavadunam (4 below 100)	92 \| 16	9,216
104^2	Yavadunam (4 above 100)	108 \| 16	10,816
112^2	Yavadunam, with a carry	124 + 1 \| 44 = 125 \| 44	12,544
988^2	Yavadunam (12 below 1000)	976 \| 144	976,144
1003^2	Yavadunam (3 above 1000)	1,006 \| 009	1,006,009
35^2	Ekadhikena Purvena	3 x 4 = 12 \| 25	1,225
65^2	Ekadhikena Purvena	6 x 7 = 42 \| 25	4,225
115^2	Ekadhikena Purvena	11 x 12 = 132 \| 25	13,225
43^2	Duplex	16 \| 24 \| 9	1,849
78^2	Duplex	49 \| 112 \| 64	6,084
321^2	Duplex	9 \| 12 \| 10 \| 4 \| 1	103,041

Yavadunam writes the right part with as many digits as the base has zeros, which is why 1003^2 ends in 009. A right part that is too long carries into the left part, as in 112^2. The duplex parts are added from the right with carries: for 78^2, 64 gives 4 carry 6, 112 + 6 = 118 gives 8 carry 11, and 49 + 11 = 60, so 6,084.

Yavadunam: square 97 from its distance to 100

Yavadunam ("whatever the deficiency") squares a number close to a power of 10. 97 is 3 below 100, so lessen it by 3 to get 94 for the left part, and square the 3 for the right part, written with two digits as 09: 97² = 9409. Above the base the difference is added instead: 104 is 4 over, so 108 | 16 = 10816. When the squared difference has too many digits, carry the extra into the left part: 112² = 124 | 144 = 125 | 44 = 12544.

The duplex: square any number column by column

Dwandwa-yoga builds a square one column at a time from duplexes. A digit on its own gives its square, a pair of digits gives twice their product, and three digits give twice the outer pair plus the square of the middle one. For 43²: the units column is 3² = 9, the tens column is 2 × 4 × 3 = 24 (write 4, carry 2), and the hundreds column is 4² + 2 = 18, so 43² = 1849. Each pair is counted once and doubled, so it needs fewer products than multiplying 43 by 43.

Frequently asked questions

Which Vedic method should I use to square a number?

If the number ends in 5, use Ekadhikena Purvena: multiply the part before the 5 by one more than itself and append 25 (65² → 6 × 7 = 42, so 4225). If it is close to 10, 100 or 1000, use Yavadunam with the distance from that base (97² → 94 | 09 = 9409). For anything else the duplex works with any number of digits. The calculator picks the quickest and lets you switch.

What is a duplex in Vedic maths?

The duplex of one digit is its square; of two digits, twice their product; of three, twice the product of the outer pair plus the square of the middle; of four, twice the outer pair plus twice the inner pair. Each column of a square is the duplex of the digits that meet in that column, plus any carry from the column to its right.

Do the sutras really come from the Vedas?

Jagadguru Swami Bharati Krishna Tirthaji attributed them to an appendix of the Atharvaveda in his 1965 book Vedic Mathematics, but they have not been found in any known Vedic text, and historians of mathematics regard them as his own modern formulations. The methods are correct arithmetic either way, and every answer here is checked against ordinary multiplication.

How do I check a square with the digit-sum (Beejank) test?

Reduce the number to one digit by adding its digits repeatedly, square that digit and reduce again. It must equal the reduced digit sum of the answer. For 97: 9 + 7 = 16 → 7, and 7 × 7 = 49 → 13 → 4; the answer 9409 gives 9 + 4 + 0 + 9 = 22 → 4. A match doesn't prove the answer, but a mismatch always means a slip.