Mīrāth is the Islamic law of inheritance: the rules by which a person's wealth passes to their relatives after death. It is also called ʿilm al-farāʾiḍ — the science of the fixed shares — because its heart is a set of precise fractions that the Qurʾan assigns to named relatives. The Prophet ﷺ called it half of all knowledge, and the early community treated a mistake in it as a serious matter, since an error quietly takes from one heir what belongs to another.
What happens before the heirs inherit
An estate is not divided immediately. Four claims are settled first, in order: the cost of a dignified burial; then all debts, whether owed to people or to God; then any bequest (waṣiyya) the deceased made to someone who is not already an heir, capped at one third of what remains. Only what is left after these is the estate that the fixed shares divide.
This is why the calculator lets you enter debts, funeral costs and a bequest: it nets the estate down to the amount that is actually shared, and it will not let a bequest exceed its one-third limit.
Two kinds of heir
Heirs fall into two groups. The fixed-share heirs (aṣḥāb al-furūḍ) — such as the spouse, the parents and the daughters — take a named fraction: a half, a quarter, an eighth, two thirds, a third or a sixth. The residuary heirs (al-ʿaṣaba) — chiefly the sons and the male agnatic line — take whatever remains after the fixed shares are paid. Some relatives, like a daughter beside her brother, move between the two roles depending on who else survives.
On top of this sits a system of blocking (ḥajb), where a nearer relative can reduce or exclude a more distant one, and two balancing mechanisms — ʿawl and radd — for when the shares do not fit the estate exactly.