The Vedic Mathematics Sutras

This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in some cases a translation of the Sanskrit is not given in the text and comes from elsewhere.

This formula 'On the Flag' is not in the list given in Vedic Mathematics, but is referred to in the text.

The Sixteen Sutras

         Sutra     Translation

By one more than the one before
 2    All from 9 and the last from 10

Vertically and Crosswise

Transpose and Apply

If the Samuccaya is the Same it is Zero

If One is in Ratio the Other is Zero


By Addition and by Subtraction


By the Completion or Non-Completion

Differential Calculus

By the Deficiency

Specific and General

The Remainders by the Last Digit

The Ultimate and Twice the Penultimate

By One Less than the One Before
15 The Product of the Sum

All the Multipliers


Note: The current Shankaracharya of Puri, Jagadguru Swami Nishchalananda Saraswati, has said (in 2008) he will be able to locate all the above sutras in the Vedic texts, but has so far only found one.

See also the article "The Sutras of Vedic Mathematics", by Kenneth Williams, published in the Journal of the Oriental Institute.

The Sub Sutras

           Sub Sutra      Translation
 1   Proportionately

 The Remainder Remains Constant

 The First by the First and the Last by the Last
 4   For 7 the Multiplicand is 143

 By Osculation

 Lessen by the Deficiency

 Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency

 Last Totalling 10

 Only the Last Terms

 The Sum of the Products

 By Alternate Elimination and Retention

 By Mere Observation
13    The Product of the Sum is the Sum of the Products

 On the Flag



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