The Doctrines of Aul and Radd — KSLU Family Law 2 Notes

The Doctrines of Aul and Radd

What if the fixed Quranic fractions do not add up to exactly one? Islamic law has two elegant mathematical safety-valves.

flowchart TD
    ROOT["Aul and Radd"]:::root
    ROOT --> AUL["Doctrine of AUL<br/>(Shares > Estate)"]:::aul
    ROOT --> RADD["Doctrine of RADD<br/>(Shares < Estate)"]:::radd
    AUL --> A1["Fixed shares sum to<br/>MORE than the whole estate"]:::prob
    A1 --> A2["Increase the denominator;<br/>each heir gets proportionally less"]:::sol
    RADD --> R1["Fixed shares sum to LESS<br/>than the estate + no residuaries"]:::prob
    R1 --> R2["Return the surplus to the<br/>Quranic heirs proportionally"]:::sol
    R2 --> R3["Husband & Wife<br/>EXCLUDED from Radd (Sunni)"]:::warn

    classDef root fill:#FFF8DC,stroke:#000,stroke-width:2px,color:#000;
    classDef aul fill:#F8D7DA,stroke:#721C24,color:#000;
    classDef radd fill:#D4EDDA,stroke:#155724,color:#000;
    classDef prob fill:#FFF3CD,stroke:#856404,color:#000;
    classDef sol fill:#E6F3FF,stroke:#1E3A8A,color:#000;
    classDef warn fill:#F8D7DA,stroke:#721C24,color:#000;
    linkStyle default stroke:#888,stroke-width:1px;

Aul (increase): when the fractions exceed 1, the common denominator is raised so they sum to one — every sharer is reduced proportionally. Example: husband 1/4 + two daughters 2/3 + full sister 1/6 → over a denominator of 12 that is 3 + 8 + 2 = 13/12; under Aul the denominator becomes 13, so the husband takes 3/13, daughters 8/13, sister 2/13 (Ghulam Waris v. Wazir Ali, 1928). Radd (return): when the fractions sum to less than 1 and there are no residuaries, the surplus is returned to the Quranic heirs in proportion — but under Sunni law the husband and wife are excluded from Radd (Bibi Sadiq v. Bibi Fatima, 1932). Under Shia law neither Aul applies in the same way, and the spouse can take by Radd.