The skeletal formula, sometimes called line-angle formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of its bonding and some details of its molecular geometry. It is represented in two dimensions, as on a page of paper. It employs certain conventions to represent carbon and hydrogen atoms, which are the most common in organic chemistry.
The technique was developed by the organic chemist Friedrich August Kekulé von Stradonitz. Skeletal formulae have become ubiquitous in organic chemistry, partly because they are relatively quick and simple to draw. Carbon atoms are usually depicted as line ends or vertices with the assumption that all carbons have a valence of 4 and carbon-hydrogen bonds, usually not shown explicitly, are assumed to complete each C valence. A skeletal formula shows the skeletal structure or skeleton of a molecule, which is composed of the skeletal atoms that make up the molecule. 
The skeletal structure of an organic compound is the series of atoms bonded together that form the essential structure of the compound. The skeleton can consist of chains, branches and/or rings of bonded atoms. Skeletal atoms other than carbon or hydrogen are called "heteroatoms".
The skeleton has hydrogen and/or various substituents bonded to its atoms. Hydrogen is the most common non-carbon atom that is bonded to carbon and, for simplicity, is not explicitly drawn. In addition, carbon atoms are not generally labelled as such directly (i.e. with a "C"), whereas heteroatoms are always explicitly noted as such (i.e. using "N" for nitrogen, "O" for oxygen, etc.)
Heteroatoms and other groups of atoms that give rise to relatively high rates of chemical reactivity, or introduce specific and interesting characteristics in the spectra of compounds are called functional groups, as they give the molecule a function. Heteroatoms and functional groups are known collectively as "substituents", as they are considered to be a substitute for the hydrogen atom that would be present in the parent hydrocarbon of the organic compound in question.
Implicit carbon and hydrogen atoms
For example, in the image below, the skeletal formula of hexane is shown. The carbon atom labeled C1 appears to have only one bond, so there must also be three hydrogens bonded to it, in order to make its total number of bonds four. The carbon atom labelled C3 has two bonds to other carbons and is therefore bonded to two hydrogen atoms as well. A ball-and-stick model of the actual molecular structure of hexane, as determined by X-ray crystallography, is shown for comparison, in which carbon atoms are depicted as black balls and hydrogen atoms as white ones.
NOTE: It doesn't matter which end of the chain you start numbering from, as long as you're consistent when drawing diagrams. The condensed formula or the IUPAC name will confirm the orientation. Some molecules will become familiar regardless of the orientation.
Any hydrogen atoms bonded to non-carbon atoms are drawn explicitly. In ethanol, C2H5OH, for instance, the hydrogen atom bonded to oxygen is denoted by the symbol H, whereas the hydrogen atoms which are bonded to carbon atoms are not shown directly. Lines representing heteroatom-hydrogen bonds are usually omitted for clarity and compactness, so a functional group like the hydroxyl group is most often written −OH instead of −O−H. These bonds are sometimes drawn out in full in order to accentuate their presence when they participate in reaction mechanisms.
Shown below for comparison are a ball-and-stick model of the actual three-dimensional structure of the ethanol molecule in the gas phase (determined by microwave spectroscopy, left), the Lewis structure (centre) and the skeletal formula (right).
All atoms that are not carbon or hydrogen are signified by their chemical symbol, for instance Cl for chlorine, O for oxygen and Na for sodium. These atoms are commonly known as heteroatoms in the context of organic chemistry.
There are also symbols that appear to be chemical element symbols, but represent certain very common substituents or indicate an unspecified member of a group of elements. These are known as pseudoelement symbols or organic elements. The most widely used symbol is Ph, which represents the phenyl group. A list of pseudoelement symbols is shown below:
- R for any alkyl group or even any substituent at all
- Me for the methyl group
- Et for the ethyl group
- n-Pr for the propyl group
- i-Pr for the isopropyl group
- Bu for the butyl group
- i-Bu for the isobutyl group
- s-Bu for the secondary butyl group
- t-Bu for the tertiary butyl group
- Pn for the pentyl group
- Hx for the hexyl group
- Hp for the heptyl group
- Cy for the cyclohexyl group
- Ar for any aromatic substituent
- Bn for the benzyl group
- Bz for the benzoyl group
- Mes for the mesityl group
- Ph or Φ for the phenyl group
- Tol for the tolyl group
- Cp for the cyclopentadienyl group
- Cp* for the pentamethylcyclopentadienyl group
- Ac for the acetyl group (Ac is also the symbol for the element actinium. However, actinium is almost never encountered in organic chemistry, so the use of Ac to represent the acetyl group never causes confusion)
See the article leaving group for further information
Two atoms can be bonded by sharing more than one pair of electrons. The common bonds to carbon are single, double and triple bonds. Single bonds are most common and are represented by a single, solid line between two atoms in a skeletal formula. Double bonds are denoted by two parallel lines, and triple bonds are shown by three parallel lines.
In more advanced theories of bonding, non-integer values of bond order exist. In these cases, a combination of solid and dashed lines indicate the integer and non-integer parts of the bond order, respectively.
N.B. in the gallery above, double bonds have been shown in red and triple bonds in blue. This was added for clarity - multiple bonds are not normally coloured in skeletal formulae.
Benzene rings are common in organic compounds. To represent the delocalization of electrons over the six carbon atoms in the ring, a circle is drawn inside the hexagon of single bonds. This style is very common in introductory organic chemistry texts used in schools.
An alternative style that is more common in academia is the Kekulé structure. Although it could be considered inaccurate as it implies three single bonds and three double bonds (benzene would therefore be cyclohexa-1,3,5-triene), all qualified chemists are fully aware of the delocalization in benzene. Kekulé structures are useful for drawing reaction mechanisms clearly.
(R)-2-chloro-2-fluoropentane ball-and-stick model
The skeletal formula of amphetamine, a mixture of both R and S stereoisomers
The relevant chemical bonds can be depicted in several ways:
- Solid lines represent bonds in the plane of the paper or screen.
- Solid wedges represent bonds that point out of the plane of the paper or screen, towards the observer.
- Hashed wedges or dashed lines (thick or thin) represent bonds that point into the plane of the paper or screen, away from the observer.
- Wavy lines represent either unknown stereochemistry or a mixture of the two possible stereoisomers at that point.
An early use of this notation can be traced back to Richard Kuhn who in 1932 used solid thick lines and dotted lines in a publication. The modern wedges were popularised in the 1959 textbook "Organic Chemistry" by Donald J. Cram and George S. Hammond 
Skeletal formulae can depict cis and trans isomers of alkenes. Wavy single bonds are the standard way to represent unknown or unspecified stereochemistry or a mixture of isomers (as with tetrahedeal stereocenters). A crossed double-bond has been used sometimes; is no longer considered an acceptable style for general use, but may still be required by computer software.
Hydrogen bonds are generally denoted by dotted or dashed lines.
- General, Organic, and Biological Chemistry, H. Stephen Stoker 2012
- IUPAC Recommendations 1999, Revised Section F: Replacement of Skeletal Atoms
- Clayden, Jonathan; Greeves, Nick; Warren, Stuart; Wothers, Peter (2001). Organic Chemistry (1st ed.). Oxford University Press. p. 27. ISBN 978-0-19-850346-0.
- J. Brecher (2006). "Graphical representation of stereochemical configuration (IUPAC Recommendations 2006)". Pure Appl. Chem. 78 (10): 1897–1970. doi:10.1351/pac200678101897.
- The Historical Origins of Stereochemical Line and Wedge Symbolism William B. Jensen Journal of Chemical Education 2013 90 (5), 676-677 doi:10.1021/ed200177u
- Drawing organic molecules from chemguide.co.uk