The Calculation of Inheritance Shares

The actual calculation of inheritance shares is one of the most technically demanding aspects of Islamic jurisprudence, requiring facility with fractions, knowledge of the rules governing different heir combinations, and familiarity with the special mechanisms — 'awl (proportional increase) and radd (return) — used to address cases where the designated shares do not sum to the total estate. Siddiqi's treatment of these calculation methods is systematic and accessible, providing the reader with the mathematical tools needed to apply Islamic inheritance law in practice.

The basic approach to calculating Islamic inheritance shares begins with identifying all the surviving heirs and determining which category each falls into. Next, the estate must be valued and certain prior claims addressed: funeral expenses must be paid first, then outstanding debts of the deceased, then the provisions of any valid Islamic will (limited to one-third of the estate). Only after these prior claims have been satisfied does the remaining estate become available for distribution among the heirs.

To calculate the shares, scholars begin by identifying a common base number (asl al-masa'la) from which each heir's share can be expressed as a whole number rather than a fraction. This is found by taking the least common multiple (LCM) of the denominators of all the fractional shares in the particular case. For example, if the heirs are a wife (one-eighth), a son, and a daughter, the LCM of 8 (the wife's denominator) gives a base of 8: the wife receives 1 share, and the remaining 7 shares are divided between the son and daughter in a two-to-one ratio — the son receives 4.67 and the daughter 2.33 shares, which requires adjustment to whole numbers.

The mechanism of 'awl addresses the situation where the total of the designated fractional shares exceeds one — that is, where the Quranic heir shares collectively claim more than the total estate. This arises in specific combinations of heirs. The solution established by the Companions — and universally accepted by Sunni scholars — is to increase the base number proportionally so that each heir receives a proportionally reduced share. For example, if the shares total to seven-sixths of the estate (i.e., the denominators sum to 7 while the base is 6), the base is increased to 7 and each heir receives their originally designated number of shares out of 7 rather than 6, resulting in a proportional reduction of each heir's share.

The mechanism of radd (return) addresses the opposite situation: where the Quranic heirs' designated shares sum to less than the total estate and there is no residuary heir to receive the remainder. In this case, the scholars of the majority view hold that the remainder should be returned to the Quranic heirs in proportion to their shares, so that the entire estate is distributed rather than going to the state. The Hanafi school excludes the spouse from the radd, while the Maliki and some Hanbali scholars permit the state (bayt al-mal) to receive the unallocated portion.

The inheritance of a hermaphrodite (khuntha mushkil) — a person whose biological sex cannot be definitively determined — is addressed in classical Islamic jurisprudence with the precautionary principle: such a person receives the lesser of what they would receive as male and as female, until their sex can be determined. Contemporary medical knowledge regarding intersex conditions has been addressed by contemporary fiqh councils, who have generally maintained the precautionary approach while acknowledging the relevance of current medical determinations.

Siddiqi provides numerous worked examples throughout this chapter to make the calculation methods concrete and manageable, noting that while the mathematics can become complex in cases involving many heirs, the basic principles are accessible to any educated Muslim who applies them systematically.