Last updated: 2026-06-16

The degree of unsaturation, also called the index of hydrogen deficiency, counts how many rings and multiple bonds a molecule contains. Each ring and each pi bond removes two hydrogen atoms relative to the fully saturated formula, so a single number summarizes how far a molecule departs from being saturated. This calculator computes it from the atom counts in a molecular formula — the usual first step when deducing a structure from a formula in organic chemistry.

The formula

For a compound containing carbon, hydrogen, trivalent atoms such as nitrogen, and monovalent halogens:

$\text{DoU} = \frac{2C + 2 + N - H - X}{2}$

A saturated, open-chain hydrocarbon $C_nH_{2n+2}$ returns zero. Each ring or double bond adds one to the count; a triple bond adds two because it contains two pi bonds.

Worked example

Benzene, $C_6H_6$:

The four degrees fit benzene exactly: one for the ring and three for its alternating double bonds. Reaching a value of four is a common cue to suspect an aromatic ring.

Why oxygen drops out

Oxygen is divalent, so inserting it into a chain — as in an alcohol or an ether — does not change how many hydrogens the carbon skeleton can hold. The same is true of sulfur. Because these atoms leave the hydrogen capacity untouched, they never appear in the formula. Nitrogen, being trivalent, raises the hydrogen capacity by one and so contributes a $+N$ term, while monovalent halogens behave just like hydrogens and are subtracted.

A negative result signals an impossible formula, usually too many hydrogens or halogens, and is worth rechecking. Once you know how many rings and pi bonds are present, tools such as the Formal Charge Calculator help assign the bonding in a candidate Lewis structure, and the Percent Composition Calculator confirms the formula against elemental analysis data.