Worked examples
Test cases
Every case below is computed live by the same engine that powers the calculator — proof, not a static chart. Each shows the surviving heirs and their exact shares.
Fixed shares
الفُروضThe six Qurʾanic fractions (½, ¼, ⅛, ⅔, ⅓, ⅙) assigned to the named heirs.
Wife & a son
- Wife 1/8
- Son 7/8
Wife ⅛ with a child; the son takes the rest.
Husband & a full sister
- Husband 1/2
- Full sister 1/2
Each takes ½.
Wife, a son & a daughter
- Wife 1/8
- Son 7/12
- Daughter 7/24
Wife ⅛; son and daughter split the residue 2:1.
Both parents & a son
- Mother 1/6
- Father 1/6
- Son 2/3
Each parent ⅙; the son takes the residue.
Residuary heirs
العَصَبةAfter the fixed shares, the nearest male agnate (or a sister made residuary) takes the remainder.
Mother & father
- Mother 1/3
- Father 2/3
Mother ⅓, father takes the residue ⅔.
A daughter & a full brother
- Daughter 1/2
- Full brother 1/2
Daughter ½; the brother takes the residue.
Husband, a daughter & a full brother
- Husband 1/4
- Daughter 1/2
- Full brother 1/4
Husband ¼, daughter ½, brother the residue ¼.
Blocking
الحَجبA nearer heir excludes a more distant one — fully, or by reducing their share.
Wife, a son & a grandson
- Wife 1/8
- Son 7/8
- Son's son excluded
The son blocks the son's son entirely.
Mother, father & a full brother
- Mother 1/3
- Father 2/3
- Full brother excluded
The father excludes the brother; mother ⅓, father ⅔.
A son & two full brothers
- Son 1
- Full brother×2 excluded
A son excludes all the siblings.
Over-subscription (ʿawl)
العَولWhen the fixed shares add up to more than the whole, the base is raised and every share scaled down.
Husband & two full sisters
- Husband 3/7
- Full sister×2 4/7
Base 6 → 7. Husband 3⁄7, sisters 4⁄7.
Husband, two daughters & father
- Husband 3/13
- Daughter×2 8/13
- Father 2/13
Base 12 → 13.
Husband, mother & two full sisters
- Husband 3/8
- Mother 1/8
- Full sister×2 1/2
Base 6 → 8.
Return of surplus (radd)
الرَّدّWhen shares fall short and there is no residuary heir, the surplus returns to the fixed-share heirs — the spouse excluded.
Mother & a daughter
- Mother 1/4
- Daughter 3/4
Surplus returns to both: mother ¼, daughter ¾.
A sole daughter
- Daughter 1
She takes the entire estate by radd.
Wife & a daughter
- Wife 1/8
- Daughter 7/8
Wife keeps ⅛; the rest returns to the daughter (spouse excluded from radd).
Named special cases
المسائل المُلقَّبةThe famous, awkward compositions that every faraid student learns by name.
Umariyyatān — husband, father & mother
- Husband 1/2
- Mother 1/6
- Father 1/3
Mother takes ⅓ of the remainder after the husband, not ⅓ of the whole.
Umariyyatān — wife, father & mother
- Wife 1/4
- Mother 1/4
- Father 1/2
Mother takes ⅓ of the remainder after the wife.
al-Mushtaraka — husband, mother, 2 maternal & a full brother
- Husband 1/2
- Mother 1/6
- Maternal brother×2 2/9
- Full brother 1/9
Shāfiʿī/Mālikī: the full brother shares the maternal siblings' ⅓. Ḥanafī/Ḥanbalī: he takes nothing.
al-Akdariyya — husband, mother, grandfather & a full sister
- Husband 1/3
- Mother 2/9
- Father's father 8/27
- Full sister 4/27
The most famous case of all — base 27 after ʿawl and a 2:1 re-split between grandfather and sister.
Where the schools differ
الجَدّ والإخوةThe grandfather competing with the siblings — Ḥanafī blocks them; Mālikī, Shāfiʿī and Ḥanbalī share with them (muqāsama). Switch schools on the calculator to compare.
Grandfather & two full brothers (Mālikī)
- Father's father 1/3
- Full brother×2 2/3
Muqāsama: each of the three takes ⅓. Under Ḥanafī the grandfather would take everything.
Grandfather & a full sister (Shāfiʿī)
- Father's father 2/3
- Full sister 1/3
Muqāsama 2:1 — grandfather ⅔, sister ⅓. Under Ḥanafī the grandfather would take everything.
Mother, grandfather & two full brothers (Shāfiʿī)
- Mother 1/6
- Father's father 5/18
- Full brother×2 5/9
Grandfather takes the better of ⅙-of-estate, ⅓-of-remainder, or muqāsama.
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