# Degree of unsaturation

For other uses, see Degree of saturation.

The degree of unsaturation (also known as the index of hydrogen deficiency (IHD) or rings plus double bonds[1]) formula is used in organic chemistry to help draw chemical structures. The formula lets the user determine how many rings, double bonds, and triple bonds are present in the compound to be drawn. It does not give the exact number of rings or double or triple bonds, but rather the sum of the number of rings and double bonds plus twice the number of triple bonds. The final structure is verified with use of NMR, mass spectrometry and IR spectroscopy, as well as qualitative inspection.

## General formula

The formula for degree of unsaturation is:

${\displaystyle \mathrm {DU} =1+{\tfrac {1}{2}}\sum n_{i}(v_{i}-2)}$

where ni is the number of atoms with valence vi.[2]

That is, an atom that has a valence of x contributes a total of x − 2 to the degree of unsaturation. The result is then halved and increased by 1.

There is also another formula to determine the number of double bonds present in a hydrocarbon

${\displaystyle {\text{Double bond equivalent}}=(a+1)-{\frac {b-c+f}{2}}}$

where

a = number of carbon atoms in the compound
b = number of hydrogen atoms in the compound
c = number of nitrogen atoms in the compound
f = number of halogen atoms in the compound

## Rings plus pi bonds formulation

For molecules containing only carbon, hydrogen, monovalent halogens, nitrogen, and oxygen, the formula

${\displaystyle \mathrm {rings+\pi \ bonds} =C-{\frac {H}{2}}-{\frac {X}{2}}+{\frac {N}{2}}+1\,}$

where C = number of carbons, H = number of hydrogens, X = number of halogens and N = number of nitrogens,[3] gives an equivalent result. Oxygen and other divalent atoms do not contribute to the degree of unsaturation, as 2 − 2 = 0.

The degree of unsaturation is used to calculate the number of rings and pi bonds, where

• Rings count as 1 degree of unsaturation
• Double bonds count as one degree of unsaturation
• Triple bonds count as two degrees of unsaturation

Note: Benzene rings count as four degrees of unsaturation, since they consist of one ring and three pi bonds.