Arudha = projection of reality. If the 7th house (marriage) is in Taurus and its lord (Venus) is in Libra, the Arudha of the 7th (Dara Pada) is calculated by the distance 7th → Venus (6 houses), projected forward from Venus (6 houses forward from Libra = Taurus). Dara Pada = Taurus.
General formula: Measure house cusp → lord's house (distance D). Count D forward from lord's house to find the arudha sign.
Exceptions (Swasthe Arudha, "exception arudhas"):
Lord in 1st from house: Arudha = 10th from house.
Lord in 7th from house: Arudha = 4th from house.
Example: 7th lord in the 1st house (7th itself, if lord is in the 7th) → Arudha = 10th from 7th = 4th house. This is why powerful upapadas often fall in the 4th; it indicates spouse or partnership gains grounded in property and family.
Arudhas are computed for all 12 houses (plus Upapada Lagna from the 12th). Arudha Lagna (AL, from the 1st) = perceived public image. Upapada Lagna (UL, from the 12th) = spouse's family and marriage circumstances.
The calculator computes all 12 arudhas. You will interpret AL placement, UL placement, and the status of karaka planets relative to them.
The calculation. Count from the house to its lord. Then count the same distance again, starting from the lord. The sign you land on is the arudha of that house. If the 1st lord sits in the 5th, count four signs from the lord to reach the 9th, which becomes the Arudha Lagna.
The two exceptions. An arudha may not rest in the house itself, nor in the 7th from it. Either result is displaced by ten signs. The first case arises when a lord occupies its own house; the second when the lord sits in the 7th from its own house. Forgetting these exceptions is the most common computational error in Jaimini.
What an arudha means. The arudha is the image of a house: how its matters appear to others, as distinct from what they are. The distinction between reality and perception is the core idea, and it is why Arudha Lagna can be strong while the lagna itself is weak, or the reverse.
Checking your work. Compute the arudha for all twelve houses in a familiar chart and look at the distribution. If several arudhas pile into one sign, that concentration is itself meaningful. If you find an arudha sitting in its own house, you have missed an exception and should recompute.