Degree of Unsaturation Calculator Formula

Understand the math behind the degree of unsaturation calculator. Each variable explained with a worked example.

Formulas Used

Degrees of Unsaturation

dou = (2 * carbons + 2 + nitrogens - hydrogens - halogens) / 2

Variables

VariableDescriptionDefault
carbonsNumber of Carbons (C)6
hydrogensNumber of Hydrogens (H)6
nitrogensNumber of Nitrogens (N)0
halogensNumber of Halogens (F, Cl, Br, I)0

How It Works

Degree of Unsaturation (Index of Hydrogen Deficiency)

The degree of unsaturation tells how many rings and/or double bonds are in a molecule. Each ring or double bond reduces the hydrogen count by 2 relative to the fully saturated formula.

Formula

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

where C = carbons, H = hydrogens, N = nitrogens, X = halogens. Oxygen and sulfur are not included because they do not change the hydrogen count. A DoU of 4 for a C6 compound suggests a benzene ring.

Worked Example

Calculate the degree of unsaturation for benzene (C6H6).

carbons = 6hydrogens = 6nitrogens = 0halogens = 0
  1. 01DoU = (2 × 6 + 2 + 0 - 6 - 0) / 2
  2. 02DoU = (12 + 2 - 6) / 2 = 8 / 2 = 4
  3. 03Benzene has 3 double bonds + 1 ring = 4 DoU

Frequently Asked Questions

What does each degree of unsaturation represent?

Each degree represents either one double bond or one ring. A triple bond counts as two degrees. A benzene ring (3 double bonds + 1 ring) counts as four degrees of unsaturation.

Why are oxygen atoms not in the formula?

Adding an oxygen atom (as -OH, =O, or ether -O-) does not change the hydrogen count. A saturated alcohol C₃H₈O has the same H count as propane C₃H₈ with an oxygen inserted. So oxygen does not affect unsaturation.

Can the degree of unsaturation be a fraction?

For valid molecular formulas, the result is always a whole number or zero. A fractional result indicates an invalid formula (odd number of hydrogens without nitrogen, for example).