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Formula Hydrogen Deficiency & Unsaturation

Calculate the hydrogen-deficiency index from carbon, hydrogen, nitrogen and halogen atom counts.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For C₆H₆, the index is (2 + 2×6 − 6)/2 = 4. This can represent a ring plus three double bonds, but does not uniquely determine structure.

Index = (2 + 2C + N − H − X) / 2

Worked example

Enter these known values and leave the other values blank.

Carbon atoms
6
Hydrogen atoms
6
Nitrogen atoms
0
Total F, Cl, Br and I atoms
0
Hydrogen-deficiency index
4

Assumptions and limitations

  • Atom counts are nonnegative whole numbers and the retained result is nonnegative. Include explicit zeros for absent elements.
  • The usual rings-and-pi-bonds interpretation assumes an appropriate neutral, closed-shell formula with conventional valences. A half-integer result indicates that this interpretation needs review, such as for radicals, ions or an incorrect formula.
  • Divalent oxygen does not change this count; treat other elements and nonstandard valences separately. One ring or double bond contributes one, and a triple bond contributes two.

Common questions

Does an index of four prove a benzene ring?

No. It constrains the total ring and pi-bond count under the stated assumptions, but many structures can share that index.

Why are oxygen atoms absent from the inputs?

Ordinary divalent oxygen does not change the hydrogen-deficiency formula. That simplification does not cover every possible element, charge or bonding state.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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