Degree of Unsaturation Calculator

What Is Degree of Unsaturation?

Degree of unsaturation (DoU), also called the index of hydrogen deficiency (IHD) or double bond equivalent (DBE), counts how many rings and pi bonds are present in an organic molecule. Each double bond or ring contributes 1. Each triple bond contributes 2. The value does not tell you which combination you have, only the total count.

Organic chemists use DoU when proposing structures from a molecular formula before NMR or IR data arrive. Pair this tool with the Combustion Analysis Calculator to move from combustion data to a formula, then estimate unsaturation. Bond-level insight is available in the Bond Order Calculator.

Degree of Unsaturation Formula

$$\mathrm{DoU} = \frac{1}{2}\left(2 + 2C - H + N - X\right)$$

where $C$, $H$, $N$, and $X$ are counts of carbon, hydrogen, nitrogen, and halogen atoms. Oxygen and other divalent atoms do not appear because they do not change the hydrogen deficiency count.

How to Interpret the Result

• DoU = 0: saturated (alkanes with no rings)
• DoU = 1: one double bond or one ring
• DoU = 2: two double bonds, one triple bond, two rings, or one ring plus one double bond
• DoU = 4: common for benzene (three double bonds + one ring)

Worked Example

For benzene, $\mathrm{C}_6\mathrm{H}_6$:

$$\mathrm{DoU} = \frac{1}{2}(2 + 2\times 6 - 6 + 0 - 0) = 4$$

For pyridine, $\mathrm{C}_5\mathrm{H}_5\mathrm{N}$:

$$\mathrm{DoU} = \frac{1}{2}(2 + 2\times 5 - 5 + 1 - 0) = 4$$

How to Use This Calculator

1. Enter carbon, hydrogen, nitrogen, and halogen atom counts from the molecular formula.
2. Ignore oxygen unless you need it for another calculation; it does not affect DoU.
3. Read DoU and the interpretation panel as you edit counts.

For molar mass checks on the same formula, use the Molar Mass Calculator.