Degree of Unsaturation Calculator
Calculate the index of hydrogen deficiency (IHD) from your molecular formula
Enter using element symbols and numbers (e.g., C6H6 for benzene)
Quick Examples
Degree of Unsaturation
Molecular Formula
Possible Structural Features
Calculation Steps
Example Molecules with This DU
Understanding Degree of Unsaturation
The degree of unsaturation (DU), also known as the index of hydrogen deficiency (IHD) or double bond equivalent (DBE), is a calculation that determines the total number of rings and/or pi bonds in a molecule. This value is incredibly useful for structure determination in organic chemistry, especially when combined with spectroscopic data.
What Each Degree Represents
- One degree of unsaturation can represent:
- One ring (e.g., cyclopentane, cyclohexane)
- One double bond (e.g., C=C, C=O, C=N)
- Two degrees of unsaturation can represent:
- One triple bond (e.g., C≡C, C≡N)
- Two rings
- Two double bonds
- One ring + one double bond
- Four degrees of unsaturation often indicates a benzene ring (one ring + three double bonds)
The Formula
DU = (2C + 2 + N - H - X) / 2
Where:
- C = Number of carbon atoms
- N = Number of nitrogen atoms (and other trivalent atoms like P)
- H = Number of hydrogen atoms
- X = Number of halogen atoms (F, Cl, Br, I)
Important Notes
- Oxygen and sulfur are ignored - They don't affect the calculation (divalent atoms)
- Halogens count as hydrogens - They replace H atoms in the formula
- Nitrogen adds one - Each N increases the DU calculation by 1/2, which becomes 1 when doubled
- The result must be a whole number or half-integer - Fractional results indicate an error in the formula
Worked Examples
Example 1: Benzene (C₆H₆)
Given: C = 6, H = 6, N = 0, X = 0
DU = (2×6 + 2 + 0 - 6 - 0) / 2
DU = (12 + 2 - 6) / 2
DU = 8 / 2
DU = 4
Interpretation: Benzene has 4 degrees of unsaturation (1 ring + 3 double bonds = benzene ring)
Example 2: Acetone (C₃H₆O)
Given: C = 3, H = 6, O = 1 (ignored), N = 0, X = 0
DU = (2×3 + 2 + 0 - 6 - 0) / 2
DU = (6 + 2 - 6) / 2
DU = 2 / 2
DU = 1
Interpretation: Acetone has 1 degree of unsaturation (C=O double bond)
Example 3: Caffeine (C₈H₁₀N₄O₂)
Given: C = 8, H = 10, N = 4, O = 2 (ignored), X = 0
DU = (2×8 + 2 + 4 - 10 - 0) / 2
DU = (16 + 2 + 4 - 10) / 2
DU = 12 / 2
DU = 6
Interpretation: Caffeine has 6 degrees of unsaturation (two fused rings with multiple C=O and C=N bonds)
Example 4: Chloroform (CHCl₃)
Given: C = 1, H = 1, X = 3 (Cl), N = 0
DU = (2×1 + 2 + 0 - 1 - 3) / 2
DU = (2 + 2 - 1 - 3) / 2
DU = 0 / 2
DU = 0
Interpretation: Chloroform has 0 degrees of unsaturation (fully saturated, no rings or double bonds)
Common Degree of Unsaturation Values
| DU | Possible Structures | Examples |
|---|---|---|
| 0 | Alkanes, fully saturated molecules | Ethane (C₂H₆), Butane (C₄H₁₀) |
| 1 | One ring OR one double bond | Cyclopentane, Ethene, Acetone |
| 2 | Two rings, two double bonds, one triple bond, or one ring + one double bond | Bicyclo[2.2.1]heptane, 1,3-Butadiene, Acetylene |
| 3 | Various combinations of rings and pi bonds | Cyclopropene, Propadiene |
| 4 | Benzene ring, or other combinations | Benzene, Toluene, Phenol |
| 5 | Benzene + one additional ring/double bond | Indene, Benzaldehyde |
| 6+ | Multiple aromatic rings, complex structures | Naphthalene, Anthracene |
Applications in Structure Determination
1. Spectroscopy Analysis
Degree of unsaturation is often the first calculation performed when analyzing unknown compounds. Combined with NMR, IR, and mass spectrometry data, it helps narrow down possible structures dramatically.
2. Quality Control
In pharmaceutical and chemical industries, DU calculations verify that synthesized compounds match expected molecular formulas.
3. Natural Product Chemistry
When isolating new compounds from plants or microorganisms, the degree of unsaturation provides crucial information about the molecule's complexity and functional groups.
4. Reaction Mechanism Studies
Tracking changes in DU before and after reactions helps chemists understand whether rings are being formed/broken or double bonds are being added/removed.
References
The degree of unsaturation calculation and structural analysis principles are based on fundamental organic chemistry from reputable sources:
Note: This calculator provides the degree of unsaturation value based on the molecular formula. The actual structure can only be determined by combining this information with spectroscopic data (NMR, IR, MS) and chemical tests. Multiple isomers can have the same molecular formula and degree of unsaturation.
Recommended Calculator
Casio FX-991ES Plus
The professional-grade scientific calculator with 417 functions, natural display, and solar power. Perfect for students and professionals.
View on Amazon