How matching by name works
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The traditional method reads a janma nakshatra from the first syllable of a name - the naam akshar. Each of the 27 nakshatras owns four syllables, so a name beginning with "Chu", "Che", "Cho" or "La" points at Ashwini, and so on through the list. From that nakshatra the Moon sign follows, and from both the eight kootas of the Ashtakoota system can be scored exactly as they would be from a birth chart.
What the method cannot do is know which nakshatra somebody was actually born under. A name is given days after a birth and is often chosen for the sound rather than the star, so the syllable and the birth can disagree. Where they disagree, every number below changes.
When to use birth details instead
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If you have the date, time and place of birth for both people, use those. The free matching tool scores the same eight kootas from the real Moon positions, adds the mangal dosha comparison, and is the version worth acting on. The name method is for the conversation before anybody has asked for a birth certificate.
What the eight kootas measure
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The Ashtakoota system scores eight factors and adds them to 36. Varna looks at the ego balance, Vashya at who naturally gives way, Tara at the birth stars, Yoni at physical compatibility, Graha Maitri at the friendship between the two Moon lords, Gana at temperament, Bhakoot at the distance between the Moon signs, and Nadi at constitution and progeny.
Nadi carries eight points and Bhakoot seven, which is why those two doshas are the ones people hear about: they are where the largest number of gunas can be lost at once. The table on this page lists all eight with their points.
What the score does not tell you
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A number out of 36 is a starting point for a conversation, not a verdict on two people. The tradition itself treats a low score as a reason to look at the charts more closely - at cancellations, at the strength of the seventh house, at the Moon - rather than as an answer. Nothing on this site will tell you to call off a marriage, and anything that does should be read with that in mind.