Degree of Unsaturation Calculator
Four is the signature of a benzene ring — three double bonds plus the ring itself.
The formula
DoU = (2C + 2 + N - H - X) / 2
Rings and double bonds are the same to this count
Every ring and every pi bond removes two hydrogens from what the carbon skeleton could otherwise hold. The formula counts those missing pairs, so cyclohexane and hex-1-ene both come out at one and nothing in the number distinguishes them. A triple bond counts twice; a benzene ring counts four.
Oxygen drops out completely
Oxygen and sulfur are divalent, so inserting one into a chain does not change the hydrogen count at all — and so it does not appear in the formula. Ethanol and dimethyl ether are both C₂H₆O with zero degrees of unsaturation. Nitrogen, being trivalent, adds one hydrogen and therefore enters with a plus sign; halogens replace a hydrogen and enter with a minus.
What it is actually for
Given a molecular formula from mass spectrometry, this is the first thing to compute. A result of four immediately suggests an aromatic ring, which narrows the field enormously before a single spectrum has been interpreted. A negative result means the formula is wrong.
Empirical is not molecular
Every method on these pages returns a ratio, because that is all a composition can determine. Glucose, formaldehyde and acetic acid all reduce to CH₂O, and no amount of elemental analysis will separate them. A molar mass from mass spectrometry or a freezing-point depression is what turns the ratio into a formula, and it has to come from a second, independent measurement.