Vedic Math Formulas

The Sixteen Sutras of Vedic Math

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Vedic Math essentially rests on the 16 Sutras or mathematical formulas as referred to in the Vedas. Sri Sathya Sai Veda Pratishtan has compiled these 16 Sutras and 13 sub-Sutras:

  1. Ekadhikina Purvena
    (Corollary: Anurupyena)
    Meaning: By one more than the previous one
  2. Nikhilam Navatashcaramam Dashatah
    (Corollary: Sisyate Sesasamjnah)
    Meaning: All from 9 and the last from 10
  3. Urdhva-Tiryagbyham
    (Corollary: Adyamadyenantyamantyena)
    Meaning: Vertically and crosswise
  4. Paraavartya Yojayet
    (Corollary: Kevalaih Saptakam Gunyat)
    Meaning: Transpose and adjust
  5. Shunyam Saamyasamuccaye
    (Corollary: Vestanam)
    Meaning: When the sum is the same that sum is zero
  6. (Anurupye) Shunyamanyat
    (Corollary: Yavadunam Tavadunam)
    Meaning: If one is in ratio, the other is zero
  7. Sankalana-vyavakalanabhyam
    (Corollary: Yavadunam Tavadunikritya Varga Yojayet)
    Meaning: By addition and by subtraction
  8. Puranapuranabyham
    (Corollary: Antyayordashake'pi)
    Meaning: By the completion or non-completion
  9. Chalana-Kalanabyham
    (Corollary: Antyayoreva)
    Meaning: Differences and Similarities
  10. Yaavadunam
    (Corollary: Samuccayagunitah)
    Meaning: Whatever the extent of its deficiency
  11. Vyashtisamanstih
    (Corollary: Lopanasthapanabhyam)
    Meaning: Part and Whole
  1. Shesanyankena Charamena
    (Corollary: Vilokanam)
    Meaning: The remainders by the last digit
  2. Sopaantyadvayamantyam
    (Corollary: Gunitasamuccayah Samuccayagunitah)
    Meaning: The ultimate and twice the penultimate
  3. Ekanyunena Purvena
    (Corollary: Dhvajanka)
    Meaning: By one less than the previous one
  4. Gunitasamuchyah
    (Corollary: Dwandwa Yoga)
    Meaning: The product of the sum is equal to the sum of the product
  5. Gunakasamuchyah
    (Corollary: Adyam Antyam Madhyam)
    Meaning: The factors of the sum is equal to the sum of the factors