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Degree of Unsaturation Calculator
Find the degree of unsaturation, also called the index of hydrogen deficiency (IHD) or double bond equivalents, from a molecular formula. Nitrogen, oxygen, sulfur, halogens and ions are handled. Enter a SMILES string or compound name to see exactly how many rings and π bonds the molecule has.
Formulas may include N, O, S, P, B, Si, halogens and a charge (NH4+, C2H3O2-). A SMILES or name also gives the split into rings and π bonds. Drawing a structure? Use structure to SMILES first.
Degree of unsaturation formula
The degree of unsaturation (DoU), also called the index of hydrogen deficiency (IHD), double bond equivalents (DBE) or rings plus double bonds (RDB), counts how many pairs of hydrogen atoms a molecule is "missing" compared with a saturated, open-chain compound. Each ring and each π bond removes two hydrogens.
- C: carbon (and other tetravalent atoms such as Si).
- H and X: hydrogens and halogens (F, Cl, Br, I). A halogen takes one bond, just like H.
- N: nitrogen (and other trivalent atoms such as P and B). Each one adds a half.
- O and S are ignored: a divalent atom slots into a chain without changing the hydrogen count. CH₃CH₃ and CH₃OCH₃ both have DoU 0.
Equivalent form: DoU = (2C + 2 + N − H − X) / 2.
What each unit means
| Feature | Adds to DoU | Example |
|---|---|---|
| Ring | 1 | Cyclohexane C₆H₁₂ = 1 |
| C=C or C=O double bond | 1 | Ethene C₂H₄ = 1, acetone C₃H₆O = 1 |
| Triple bond (C≡C, C≡N) | 2 | Ethyne C₂H₂ = 2 |
| Benzene ring | 4 (1 ring + 3 π) | Benzene C₆H₆ = 4 |
| Naphthalene | 7 (2 rings + 5 π) | C₁₀H₈ = 7 |
Worked examples
- C₄H₉Br: 4 − (9 + 1)/2 + 0 + 1 = 0. Saturated, acyclic: a bromobutane.
- C₅H₅N (pyridine): 5 − 5/2 + 1/2 + 1 = 4. One ring plus three π bonds, aromatic like benzene.
- C₉H₈O₄ (aspirin): 9 − 8/2 + 1 = 6. Benzene ring (4) + two C=O (2). Oxygens are ignored.
- C₈H₈: DoU = 5. It could be styrene (benzene ring + one C=C) or cubane (5 rings). The DoU narrows the possibilities, and IR/NMR decide between them.
Ions and odd results
For an ion, add half the charge: DoU = C − (H + X)/2 + N/2 + 1 + q/2. This works for N-, O- and S-centred ions such as pyridinium C₅H₆N⁺ (4), ammonium NH₄⁺ (0) and acetate C₂H₃O₂⁻ (1). A carbocation, though, comes out one higher than its rings plus π bonds, because the empty p orbital counts as a unit. A half-integer answer for a neutral formula means a radical or a typo. A negative answer means no structure exists.
Using DoU in structure determination
Work out the DoU first, then use spectroscopy. A DoU of 4 or more usually signals an aromatic ring (check the IR for C=C stretches near 1600 and 1500 cm⁻¹ and the ¹H NMR for signals at 6.5–8 ppm). A DoU of 1 with a strong IR band near 1715 cm⁻¹ points to a C=O rather than a ring. Get the molecular formula from an empirical formula or exact mass calculation, then list real candidates with formula to structure.
Drawing structures for your notes? MolDraw is a free online chemical structure editor for molecules, reactions and lab diagrams.
Open MolDraw editorFrequently asked questions
How do you calculate degree of unsaturation?
Use DoU = C − (H + X)/2 + N/2 + 1, where X is the number of halogens. Oxygen and sulfur are ignored. For C₆H₆: 6 − 3 + 1 = 4.
What does a degree of unsaturation of 1 mean?
The molecule has either one ring or one double bond (C=C, C=O or C=N). Spectroscopy tells you which.
Why are halogens counted like hydrogen?
A halogen forms one bond, so in a formula it simply takes the place of a hydrogen atom.
Why is oxygen ignored in the DoU formula?
Oxygen forms two bonds, so inserting it into a chain (C–O–C or C–O–H) does not change the number of hydrogens needed.
Why does nitrogen add one half?
Nitrogen forms three bonds, so each N brings one extra hydrogen position compared with a divalent atom: +1 H, which is +½ in the DoU.
Is degree of unsaturation the same as IHD or DBE?
Yes. Index of hydrogen deficiency, double bond equivalents and rings-plus-double-bonds are all names for the same number.
How do I find the number of rings and π bonds separately?
The formula alone cannot separate them. Enter a SMILES or a compound name and the calculator counts rings (bonds − atoms + 1) and gives π bonds as DoU − rings.