What is the index of hydrogen deficiency?

The index of hydrogen deficiency (IHD), also called the degree of unsaturation or double bond equivalents (DBE), counts the total number of rings plus pi bonds in a neutral organic molecule. A fully saturated acyclic hydrocarbon has IHD = 0; each double bond, ring, or half of each triple bond adds 1 to the IHD.

What is the IHD formula?

IHD = (2C + 2 + N − H − X) / 2, where C = number of carbon atoms, N = number of nitrogen atoms (trivalent), H = number of hydrogen atoms, and X = total halogen atoms (F + Cl + Br + I). Oxygen and sulfur cancel out because they are divalent and substituting them for a CH2 group does not change the hydrogen count.

Why does oxygen not appear in the IHD formula?

Oxygen (and sulfur) are divalent atoms. Replacing a CH2 group with an oxygen atom removes 2 hydrogens but also removes the carbon, leaving the IHD unchanged. Because their effect cancels, they do not appear in the formula. Including them in your formula is harmless — the calculator simply ignores them in the arithmetic.

What does an IHD of 4 mean?

An IHD of 4 is consistent with a benzene ring (1 ring + 3 pi bonds = 4). It could also represent other combinations such as two rings plus two double bonds, or one triple bond plus two rings. Always combine the IHD with spectral data to narrow down the actual structure.

What causes a non-integer or negative IHD?

A non-integer result means the molecular formula is invalid — the combination of atoms violates standard organic valence rules. A negative value means the formula cannot correspond to a real neutral organic molecule. Both outcomes indicate a typo or unsupported element in the input.

Can I use this for molecules with phosphorus or sulfur?

Sulfur (divalent, like oxygen) is safely ignored in the formula and is supported. Phosphorus is pentavalent like nitrogen in some compounds but the IHD formula was derived for standard organic valences. For phosphorus-containing compounds, treat each P as contributing like N (add 1 to the numerator per P) — but verify manually, as phosphorus can adopt multiple valences.

Index of Hydrogen Deficiency Calculator

Name: Index of Hydrogen Deficiency Calculator
Availability: InStock
Author: Nham Vu

Enter a molecular formula and instantly get the IHD value showing how many rings and pi bonds the molecule contains.

Molecular Formula

Supported elements: C, H, N, O, S, F, Cl, Br, I. Subscript numbers follow each symbol (e.g. C6H12O6).

Formula

IHD Formula

IHD = (2C + 2 + N − H − X) / 2

C — carbon atoms
N — nitrogen atoms (trivalent)
H — hydrogen atoms
X — total halogens (F + Cl + Br + I)
O, S — not in formula (cancel out)

Examples

Enter a molecular formula to calculate the IHD

Summary

Enter a molecular formula and instantly get the IHD value showing how many rings and pi bonds the molecule contains.

How it works

Enter the molecular formula using standard element symbols (e.g. C6H6 or C8H10N4O2).
The parser extracts each element symbol and its subscript count from the formula string.
The IHD formula is applied: IHD = (2C + 2 + N − H − X) / 2, where X is the total number of halogen atoms.
Oxygen and sulfur are divalent and do not change the hydrogen count, so they cancel from the formula.
The result panel shows the numeric IHD, a plain-English interpretation, and the step-by-step substitution.
Click any example molecule to load its formula and see the calculation immediately.

Use cases

Determine the number of rings and pi bonds in a compound identified by mass spectrometry.
Check whether a proposed structural formula is consistent with a given molecular formula.
Assess whether a molecule is potentially aromatic before running NMR analysis.
Solve organic chemistry homework problems involving structure elucidation.
Confirm the saturation level of pharmaceutical candidates during drug design.
Distinguish saturated (IHD = 0) from polyunsaturated natural products.
Verify synthesis targets contain the expected number of double bonds or rings.
Support structure proposals when combined with IR and NMR spectral data.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu