Rule basis of the inheritance calculator

There are three verses in the Quran and four authentic hadiths which together form the rules of estate distribution in Islam.

The verses are 4:11-12 and 4:176. Following are the rules that can be deduced from them.

Verse 4:11

This verse sets the shares of sons, daughters, and parents. Further descendants and ascendants may be added by extrapolation.

• 1a. Sons share with daughters by a ratio of 2:1.
• 1a1. It follows that if there are no surviving children but grandchildren, grandsons share with granddaughters by a ratio of 2:1.
• 1b. If children are only female, two or more get two thirds and one gets a half.
• 1b1. It follows that if there are no surviving children but female grandchildren, two or more get two thirds and one gets a half.
• 1c. Parents get a sixth each if there are surviving children.
• 1c1. It follows that parents get a sixth each if there are surviving children or grandchildren.
• 1c2. It follows that if there are no surviving parents, grandparents get a sixth each if there are surviving children or grandchildren.
• 1d. If there are no surviving children nor siblings, the mother gets a third.
• 1d1. It follows that if there are no surviving children, grandchildren nor siblings, the mother gets a third.
• 1e. If there are no surviving children but there are surviving siblings, the mother gets a sixth.
• 1e1. It follows that if there are no surviving children nor grandchildren but there are surviving siblings, the mother gets a sixth.
• 1e2. The reduction of the mother's share when there are siblings implies that the deducted portion is given to the siblings.
• 1f. All of the above is paid after bequests and debts.
• 1g. The stated shares and the stated heirs are a mandate from God, for man may not realize who among his heirs will benefit his legacy more. It follows, therefore, that personal inclinations are not to be applied in the deduction of rules from the verses about inheritance.
• 1f1. A corollary of that is that, in cases where oversubscription or under-subscription occurs, redivision of the estate must be applied to all the heirs who receive a named share, without exception, and in proportion to their named shares relative to each other.

Verse 4:12

This verse sets the shares of spouses and siblings.

• 2a. The husband gets a half if decedent wife had no surviving children, a quarter otherwise.
• 2b. The wife gets a quarter if decedent husband had no surviving children, an eighth otherwise.
• 2c. If there are no surviving sons, grandsons or the father but only siblings and a spouse, one sibling gets a sixth, and two or more share a third equally.
• 2c1. It follows that siblings only become eligible for inheritance when sons and the father did not survive.
• 2c2. By the same token, it follows that siblings become eligible for inheritance only when, in addition, grandsons and grandfather did not survive.
• 2d. The above is paid after bequests and debts.
• 2d1. Together, rule 1f and rule 2d establish that bequests and debts are to be paid off before share distribution to heirs.

Verse 4:176

This verse sets the shares of siblings when there are no descendants, ascendants or spouses.

• 3a. If there are no surviving father nor children nor spouses but only sisters, they replace daughters. Thus, one sister gets a half and two or more share two thirds.
• 3a1. It follows that if there are also no surviving grandfather, grandchildren nor spouses but only sisters, they replace daughters. Thus, one sister gets a half and two or more share two thirds.
• 3b. If there are no surviving father nor children nor spouses but only brothers, they replace sons. Thus they share the remainder of the estate.
• 3b1. It follows that if there are also no surviving grandfather, grandchildren or spouses but only brothers, they replace sons. Thus, they share the remainder of the estate.
• 3c. If there are no surviving father, sons, grandsons or spouses but only siblings, they share the remainder of the estate by ratio of 2 for the brothers to 1 for the sisters.
• 3c1. It follows that if there are also no surviving grandfather, grandsons or spouses but only siblings, they share the remainder of the estate by ratio of 2 for the brothers to 1 for the sisters.

There are other verses that speak on inheritance matters or imply it, but they do not make specific share assignments, for instance 4:7, 4:33, 8:75, and 33:6.

The four hadiths address the order of distribution, the limit on bequests, what the scholars called "female agnation", and the rule that a surviving ascendant takes the place of his or her descendant who did not survive.

The first hadith

This hadith was rated authentic (Al-Bukhari 6732) and was narrated by Ibn Abbas (RA). It is decisive in determining the order of calculation of shares.

• 4. Heirs for whom a specific share is named in the Quran, e.g., daughters, mothers, and sisters, are to be given their shares first then the remainder is given to the nearest male relative.

The second hadith

This hadith was rated authentic (Al-Bukhari 2742) and was narrated by Ibn Abi-Waqqas (RA).

• 5. Bequests are limited to a third of the estate.

The third hadith

This hadith was rated authentic (Al-Bukhari 6736) and was narrated by Ibn Massoud (RA). It handles a special case on which the Prophet (PBUH) has ruled.

• 6. The special case of a daughter, a granddaughter and a sister was ruled on by the Prophet (PBUH). He ruled to give the daughter a half, the granddaughter a sixth and the sister a third. The observation that a half plus a sixth adds up to two thirds caused all scholars to conclude that daughters "agnate" with other female heirs in such a way that together they become as if they were two daughters.
• 6a. Since the share of the granddaughter was the reminder of two thirds and not an equal share of two thirds, it follows that degree of kinship counts in the share assignment.
• 6b. It may be concluded that in the case of one daughter and more than one granddaughter, the granddaughters share a sixth.
• 6c. Since two thirds is the most two daughters get, it can be concluded that in the case of two daughters and any number of granddaughters, the granddaughters get nothing.

The fourth hadith

This hadith was rated reasonably authentic (Al-Tirmithi 2099) and was narrated by Imran ibn Hucine (RA). It sets the shares of the paternal grandfather. Here are the rules that can be deduced from it.

• 7. The grandfather gets a sixth but may also get the remainder in addition if he is the nearest male relative (see Rule 4).
  The case was a grandfather and two daughters. The Prophet (PBUH) said to the grandfather that he gets a sixth, then called him back and said that he gets another sixth, which happens to be the remainder.
• 7a. It also establishes a rule that a grandfather takes the place of a father who did not survive.
• 7b. By replacing the father, it may be concluded that the grandfather becomes more eligible than brothers if the father did not survive.
• 7c. By a reverse token, it may be concluded that grandsons take the place of sons who did not survive.
• 7d. By replacing the son, it may be concluded that the grandson becomes more eligible than brothers if the son did not survive.
• 7e. By replacing the son, it may be concluded that grandsons share with daughters by a ratio of 2:1 if no sons have survived.

There is a fifth hadith, narrated by Burida (RA), rated less than authentic (Abu-Dawoud 2895), which sets the share of grandmothers.

• 8a. It follows that a grandmother does not inherit if the mother survived.
• 8b. By the same token, the grandfather does not inherit if the father survived.
• 8c. By the reverse token, the grandson does not inherit if the son survived.

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