The formula
For a molecule with C carbons, H hydrogens, N nitrogens, X halogens, and any number of oxygens or sulfurs: DoU = (2C + 2 + N − H − X) / 2. Oxygen and sulfur don't appear in the formula because they're divalent — they don't change the H count of a saturated structure.
Worked example: C₆H₆
Benzene. DoU = (2·6 + 2 − 6) / 2 = 8/2 = 4. That accounts for one ring + three double bonds = 4. Or one ring + a triple bond + a double bond. Or two rings + two double bonds. The formula tells you the total — figuring out the arrangement is the next step.
Worked example: C₅H₁₁N
DoU = (10 + 2 + 1 − 11) / 2 = 2/2 = 1. One ring OR one double bond. With an N in the structure, candidates include piperidine (a 6-membered saturated ring with N) or pent-2-enylamine (a chain with one double bond).
Why it's useful
When you have a molecular formula and need to guess at structures (from a mass spec problem, a synthesis exercise, or a natural product), DoU narrows the field hugely. A high DoU strongly suggests rings or aromatic systems; DoU = 0 means a fully saturated acyclic structure.
Draw this on the whiteboard
Open the OChem Board whiteboard — benzene rings, wedge/dash bonds, and a clickable periodic table built in. No account needed.