By Allan Robinson | Updated August 30, 2022

Image courtesy of SDI Productions/E+/GettyImages

Step 1

Begin with the general formula for the degree of unsaturation (DU):

DU = 1 + \displaystyle\sum\frac{n_i(v_i-2)}{2}

where n_i is the number of atoms of type i and v_i is its valence. This expression works for any molecular formula.

Step 2

Identify the valence for the common elements: Carbon (4), Nitrogen (3), Oxygen (2), Hydrogen and halogens (1). These values are standard in organic chemistry.

Step 3

Substitute the valences into the formula and simplify each term:

• Carbon: n₄(4–2)/2 = n₄
• Nitrogen: n₃(3–2)/2 = n₃/2
• Oxygen: n₂(2–2)/2 = 0
• Hydrogen/halogens: n₁(1–2)/2 = –n₁/2

Step 4

Insert the simplified terms back into the overall expression:

DU = 1 + (–n₁/2) + 0 + (n₃/2) + n₄  = 1 – n₁/2 + n₃/2 + n₄

Here, n₁ counts hydrogen and halogens, n₃ counts nitrogen, and n₄ counts carbon.

Step 5

Re‑express the formula in a more convenient form for molecules containing only these elements:

DU = 1 + C + (N – X)/2

where C, N, and X are the numbers of carbon, nitrogen, and halogen/hydrogen atoms, respectively. This compact equation allows quick calculation of unsaturation for most organic compounds.

Using this method, chemists can predict structural features—rings, double bonds, and triple bonds—before confirming them with spectroscopic techniques.