Core rules
Radd (الرد)
When the fixed shares add up to less than the estate and there's no residuary heir, Radd gives the surplus back to the heirs other than the spouse.
Radd (literally "return") is the inverse of Awl. When prescribed fixed shares add up to less than the estate and there's no residuary heir to take the remainder, Radd returns the surplus to the eligible fixed-share heirs in proportion to their original shares.
A simple example
A man dies leaving only one daughter. The Quran prescribes her 1/2. There's no son, father, or brother, so nobody is there to take the residue.
Without Radd, the surplus 1/2 would go to a distant relative or the public treasury. With Radd, the daughter inherits the whole estate.
Two conditions
Radd triggers only when both hold:
- Total fixed shares are less than the whole estate.
- No residuary heir is present (no son, grandson, full brother, paternal uncle, etc.).
The spouse exception
In the majority opinion, spouses do not take part in Radd. The reasoning is that spouses are connected to the deceased only by marriage, not by blood. A husband or wife takes their fixed share but is excluded from the surplus redistribution. The rest of the surplus is split among the blood-related fixed-share heirs.
A shortcut
You don't have to compute the redistribution step by step. Replace the original denominator with the sum of numerators, keeping numerators the same.
Example: mother (1/6) + daughter (1/2) = mother (1/6) + daughter (3/6). Numerators sum to 4. New denominator: 4. So mother gets 1/4 and daughter gets 3/4. The ratio between them is preserved.
Where the schools differ
The Hanafi and Hanbali schools apply Radd as the default. Maliki was historically reluctant and preferred that the surplus go to the public treasury (Bayt al-Mal). Today Maliki scholars generally apply Radd when the treasury isn't organised to receive it. Shafi'i historically sat between the two, and applies it routinely today.