What is the formula for degree of unsaturation?

Degree of unsaturation equals C minus (H plus X) divided by 2, plus N divided by 2, plus 1, where C is the number of carbon atoms, H is the number of hydrogen atoms, X is the number of halogen atoms (F, Cl, Br, I), and N is the number of nitrogen atoms. Oxygen and sulfur do not appear in the formula because they are divalent and do not change the hydrogen count needed for a saturated structure.

How do you use degree of unsaturation to find a structure?

Once you have the degree of unsaturation, you know how many rings and pi bonds the structure must contain in total. A value of 0 means a fully saturated acyclic molecule (an alkane or similar), 1 means one ring or one double bond, 2 could mean two double bonds, one ring plus one double bond, or two rings, and 4 is the typical value for a benzene ring (one ring plus three double bonds, though it is often treated as a single aromatic unit). You then use other evidence, such as IR or NMR spectra, to decide which arrangement is correct.

Degree of Unsaturation Calculator

Work out the degree of unsaturation (also called the index of hydrogen deficiency) for any organic molecule. Enter the number of carbon, hydrogen, nitrogen, oxygen and halogen atoms in the molecular formula, or type the formula directly, to see the total number of rings and pi bonds along with full step by step working.

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Reviewed 2026 Standard IUPAC degree of unsaturation (index of hydrogen deficiency) formula.

1. Enter Molecular Formula

Molecular formula e.g. C6H12O6

Type a standard molecular formula using element symbols and numbers (C, H, N, O, F, Cl, Br, I). Leave a number off an element to mean one atom (for example "Cl" means one chlorine). The count updates automatically as you type.

2. Or Enter Atom Counts Directly

Carbon atoms (C)

Hydrogen atoms (H)

Nitrogen atoms (N)

Halogen atoms (F, Cl, Br, I combined)

Oxygen and sulfur atoms do not affect the result, so they are not needed here. These fields update automatically whenever you change the formula above.

Degree of Unsaturation

Degree of Unsaturation
-
Rings + pi bonds

Carbon (C)

Atoms counted

Hydrogen + Halogens

H + X atoms counted

Nitrogen (N)

Atoms counted

Step by Step Working

Formula parsed-

C (carbon)-

H (hydrogen)-

X (halogens)-

N (nitrogen)-

Formula used-

Degree of unsaturation-

What the Value Means

0Fully saturated, no rings, acyclic

1One ring OR one double bond

2Two double bonds, or one ring + one double bond, or two rings

3One triple bond, or three combined rings/double bonds

4Typical for one benzene ring (1 ring + 3 pi bonds)

Result: Enter a molecular formula above.

What Is Degree of Unsaturation?

The degree of unsaturation (DoU), also known as the index of hydrogen deficiency (IHD) or degree of unsaturation index, tells you the total number of rings and pi bonds (double and triple bonds) in a molecule based only on its molecular formula. It is one of the first things chemists calculate when working out a structure from a formula, since it immediately narrows down the possibilities before any spectroscopy is considered.

The Degree of Unsaturation Formula

For a molecule with the general formula C_cH_hN_nO_oX_x (where X represents any halogen: F, Cl, Br or I), the degree of unsaturation is:

DoU = C - (H + X)/2 + N/2 + 1

Oxygen and sulfur are left out of the formula entirely. This is because they are divalent (they form two bonds) and inserting one into a carbon chain does not change the number of hydrogens required for the chain to be fully saturated. Halogens are treated the same as hydrogen because they are monovalent and each one replaces exactly one hydrogen atom. Nitrogen is trivalent, so each nitrogen atom allows one extra hydrogen atom compared to carbon, which is why it is added rather than subtracted.

Worked Example

Take glucose, C₆H₁₂O₆. There are 6 carbon atoms, 12 hydrogen atoms, no nitrogen and no halogens. Oxygen is ignored.

DoU = 6 - (12 + 0)/2 + 0/2 + 1 = 6 - 6 + 0 + 1 = 1

A degree of unsaturation of 1 tells you that glucose has exactly one ring or one double bond in its structure. This matches the cyclic (ring) form of glucose that predominates in solution, or the single carbonyl (C=O) double bond in its open chain form.

How to Use the Result

Calculate the degree of unsaturation from the molecular formula.
Use the number to work out how many rings and pi bonds must be present in total.
Combine this with other evidence, such as infrared (IR) spectroscopy (showing whether a carbonyl, alkene or aromatic ring is present) or nuclear magnetic resonance (NMR) spectroscopy (showing the environment of each hydrogen and carbon), to decide on the exact arrangement.
Remember that a benzene ring alone typically accounts for 4 degrees of unsaturation (1 ring plus 3 double bonds), so a DoU of 4 or more is a strong hint that an aromatic ring may be present.

Common Mistakes to Avoid

Forgetting to include halogens with hydrogen in the (H + X) term, since halogens replace hydrogen atoms one for one.
Including oxygen or sulfur in the formula, when they should be ignored completely.
Using the atomic count of one specific isomer instead of the overall molecular formula.
Forgetting to add 1 at the end of the formula, which accounts for the reference saturated acyclic alkane (CnH2n+2).

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Sources: Standard IUPAC organic chemistry nomenclature and the degree of unsaturation (index of hydrogen deficiency) formula as taught in university-level organic chemistry courses.

This calculator provides the standard degree of unsaturation from a molecular formula. It tells you the total number of rings and pi bonds but not their exact arrangement. Use spectroscopic evidence (IR, NMR, mass spectrometry) alongside this result to confirm the actual structure.