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) / 2Variables
| Variable | Description | Default |
|---|---|---|
carbons | Number of Carbons (C) | 6 |
hydrogens | Number of Hydrogens (H) | 6 |
nitrogens | Number of Nitrogens (N) | 0 |
halogens | Number 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).
- 01DoU = (2 × 6 + 2 + 0 - 6 - 0) / 2
- 02DoU = (12 + 2 - 6) / 2 = 8 / 2 = 4
- 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).
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