About the Degree of Unsaturation Calculator
This degree of unsaturation calculator finds the double bond equivalents (DBE), also called the index of hydrogen deficiency (IHD) or rings plus double bonds, from a molecular formula. Type a formula such as C6H6 or C8H10N4O2 and it reports how many rings and π bonds the structure must contain, along with the atom counts it used.
It is a standard first step in organic structure determination: once mass spectrometry or elemental analysis gives a molecular formula, the degree of unsaturation narrows down which structures are possible before you interpret IR and NMR spectra. A value of 4 or more often signals an aromatic ring; 0 means a fully saturated, acyclic compound.
The general formula 1 + Σnᵢ(vᵢ − 2)/2 is used, so halogens count like hydrogen, nitrogen and phosphorus add half a unit each, and divalent oxygen and sulfur have no effect. Sulfur and phosphorus are assumed to be in their usual low valences (2 and 3). A fractional result usually means the formula is a radical or an ion, or contains a typo.
With the default inputs, the degree of unsaturation (rings + π bonds) is 6. Change any value above to recalculate instantly.
How to use the degree of unsaturation calculator
- 1Type the molecular formula, for example C7H6O2.
- 2Check that the formula was read correctly in the “Formula read as” line.
- 3Read the degree of unsaturation: each unit is one ring or one π bond.
- 4Use the result to shortlist structures before interpreting IR and NMR data.
Formula and method
A saturated, acyclic compound with C carbons and N nitrogens holds 2C + 2 + N monovalent atoms (hydrogens or halogens). Each ring or π bond removes two of them, so the degree of unsaturation is the hydrogen shortfall divided by two. Halogens replace hydrogen one-for-one, so they are counted with H; oxygen and sulfur insert into chains without changing the hydrogen count, so they are ignored.
The general form sums over every atom with valence vᵢ: monovalent atoms contribute −½, divalent atoms 0, trivalent atoms +½ and tetravalent atoms +1, plus one. A triple bond counts as two degrees of unsaturation, and a benzene ring as four (one ring plus three C=C).
- C
- Number of carbon (and other tetravalent) atoms
- H
- Number of hydrogen atoms
- X
- Number of halogen atoms (F, Cl, Br, I)
- N
- Number of nitrogen (and other trivalent) atoms
- vᵢ, nᵢ
- Valence and count of element i
Worked examples
Caffeine, C₈H₁₀N₄O₂
DBE = 8 − 10/2 + 4/2 + 1 = 6. Caffeine has two fused rings and four double bonds (two C=O, one C=C and one C=N), which adds up to six.
Benzene, C₆H₆
A saturated six-carbon chain would have 14 hydrogens; benzene has 6, a shortfall of 8, so DBE = 8 ÷ 2 = 4 — one ring plus three C=C double bonds.
Vinyl chloride, C₂H₃Cl
Chlorine counts like hydrogen, giving 4 monovalent atoms. DBE = 2 − 4/2 + 1 = 1, matching the single C=C bond in CH₂=CHCl.
tert-Butanol written with parentheses, (CH₃)₃COH
The formula expands to C₄H₁₀O. A saturated four-carbon compound has 2×4 + 2 = 10 hydrogens, exactly what is present, so there are no rings or double bonds; the oxygen has no effect.
Frequently asked questions
How do you calculate the degree of unsaturation?+
Use DBE = C − (H + X)/2 + N/2 + 1, where C, H, X and N are the numbers of carbons, hydrogens, halogens and nitrogens. Ignore oxygen and sulfur. For C₆H₁₂O this gives 6 − 6 + 1 = 1 ring or double bond.
Is degree of unsaturation the same as index of hydrogen deficiency?+
Yes. Degree of unsaturation, index of hydrogen deficiency (IHD), double bond equivalents (DBE) and rings plus double bonds (RDB) are different names for the same number: how many pairs of hydrogens are missing compared with a saturated acyclic compound.
Why is oxygen ignored in the formula?+
Oxygen forms two bonds, so inserting it into a chain (C–O–C) or as an OH group does not change how many hydrogens the skeleton can carry. Only atoms with valence other than 2 change the saturated hydrogen count.
What does a degree of unsaturation of 4 mean?+
Four rings and/or π bonds in total. Because a benzene ring alone accounts for exactly four, a DBE of 4 or more in a compound with at least six carbons often suggests an aromatic ring, which you can confirm with ¹H NMR signals near 7 ppm.
Why did I get a half-integer?+
A neutral, closed-shell molecule always has a whole-number DBE. A value like 2.5 means the formula has an odd number of monovalent plus trivalent atoms — it is a radical or an ion, or a hydrogen count is wrong.