Degree of unsaturation calculator explained
The degree of unsaturation (also called index of hydrogen deficiency) tells you how many rings and multiple bonds a molecular formula can contain. This calculator takes atom counts for {carbon}, {hydrogen}, {nitrogen}, and halogens {halogens_atoms} and applies the relationship to display the total unsaturation {dou}.
Use it to vet proposed structures, interpret high-resolution mass spectra, or teach how heteroatoms shift hydrogen counts.
How the conversion works
Each ring or pi bond removes two hydrogens from the fully saturated formula . Incorporating heteroatoms leads to:
where , , , and are the counts of carbon, hydrogen, nitrogen, and halogen atoms. Oxygen and sulfur do not appear because they do not change the hydrogen requirement for saturation.
Units and conversions
| Parameter | Meaning | Notes |
|---|---|---|
| Carbon atoms | Sum across the entire formula. | |
| Hydrogen atoms | Include exchangeable hydrogens (e.g., OH). | |
| Nitrogen atoms | Each adds one hydrogen to the numerator. | |
| Halogen atoms | Cl, Br, I, or F count the same. | |
| Degree of unsaturation | Integer or half-integer value. |
Half-integer results typically indicate radicals or protonated ions; neutral molecules yield whole numbers.
Worked examples
- Benzene
Formula CH.
The four units correspond to three double bonds plus one ring.
- Caffeine
Formula CHNO.
That matches the known structure with four double bonds and two rings.
Tips and pitfalls
- Treat halogens as hydrogens because each replaces one hydrogen in a saturated chain.
- Oxygen and sulfur do not affect , but watch for peroxide or sulfoxide structures that add hidden rings.
- Use to prioritize NMR experiments: a large value signals aromatic or highly unsaturated systems.
- Negative or non-integer answers usually mean the formula input is incorrect or represents an ion; verify the atom counts before relying on the result.