Aṣl and taṣḥīḥ: the base of a case and its correction

Aṣl al-masʾala (the base)

Every case is worked on a single whole number, the aṣl, chosen so that each fixed share comes to a whole number of parts: the lowest common denominator of the fractions present. Since the Qurʾanic shares are halves, quarters, eighths, thirds and sixths, the classical bases are seven: 2, 3, 4, 6, 8, 12 and 24. Later scholars added two more, 18 and 36, for cases where the grandfather inherits with siblings and takes a third of what remains.

When only residuaries inherit, the base is simply their number of heads, with a male counted as two where brothers and sisters share. Three of the bases, 6, 12 and 24, can be raised by ʿawl when the shares exceed the estate.

Taṣḥīḥ (correcting the base)

Sometimes a group's parts cannot be split evenly among its members, for instance three brothers holding a number of parts that three does not divide. Taṣḥīḥ multiplies the base by the smallest number that gives every head a whole number of parts. The classical method compares each group's head count with its parts and keeps only the factor they do not share.

Nothing changes in what anyone receives. The same estate is simply cut into finer slices, so that it can be paid out in whole units.

In the calculator

The working panel shows the aṣl, any ʿawl or radd, and the taṣḥīḥ as separate steps, then each heir's portion per head. The shares are exact fractions of the estate, not rounded percentages.

Worked examples

Every share below is computed by the calculator's engine when this page loads. Open any example to change the family and see what moves.