Dasha balance at birth
The dasha balance at birth is the part of the first dasha still to run after birth. It depends on how far the Moon has travelled through its nakshatra at the birth moment.
What it is
If the Moon is a quarter of the way through its nakshatra, three quarters of that nakshatra's lord's years remain. A Moon near the end of its nakshatra leaves little balance, and one near the start leaves nearly the full period.
How it is worked out or read
Balance equals the lord's years times (1 minus the fraction of the nakshatra crossed). The fraction is the Moon's position within the nakshatra, from 0 to 1. A year is taken as 365.25 days in the tool.
Where it appears on this site
The balance appears in the dasha tool as the first period. The nakshatra boundary method explains the Moon's exact position.
Why the first period is only partly run
A person's first dasha is not the full period of the lord of the birth nakshatra. The Moon has already moved part of the way through that nakshatra when the child is born, so part of the period has already passed in the sense of the timeline. The balance is the portion that still lies ahead. This is one of the most important details of the Vimshottari system, because it means that two people with the same nakshatra but different positions within it will have different starting points for their timelines.
The balance is the lord's full years multiplied by the fraction of the nakshatra still to be crossed. A Moon at the very start of its nakshatra leaves almost the full period, and a Moon near the end leaves very little. The reader should check the Moon's exact degree within the nakshatra before trusting the balance, since a few minutes' error in the birth time can change the balance noticeably when the Moon is near a boundary.
A worked example in detail
Take a Moon at 6 degrees 40 minutes into a nakshatra that spans 13 degrees 20 minutes. Exactly half of the nakshatra has been crossed, so half the lord's years remain. For Venus, with twenty years, the balance is ten years. The first dasha therefore runs from the birth date for ten years, and then the Sun's six years follow, then the Moon's ten, and so on through the Vimshottari order. The tool performs the same arithmetic and shows the dates.
If the same Moon were three-quarters through its nakshatra, a quarter of the lord's years would remain. For Venus that is five years. The two births would share the same nakshatra and the same lord, but their first periods would differ by five years. This is why the exact Moon degree matters for the dasha reading, and why a careful reader notes it.
Checking the balance by hand
To check a balance by hand, find the Moon's sidereal longitude at birth, subtract the start of its nakshatra, and divide by 13 degrees 20 minutes to get the fraction crossed. Subtract that fraction from one, multiply by the lord's years, and you have the balance in years. Multiply by 365.25 to get days. The result should match the tool's first period to within a day, after allowing for rounding in the Moon's position.
A reader who wants a second check can compare the Moon's nakshatra and its end time in the panchang for the birth date. If the birth time falls near the end of a nakshatra, the reader should check which nakshatra the Moon occupied at the exact moment, because the lord changes at the boundary and the whole timeline changes with it.