What this calculator does
Bond order is half the difference between bonding and antibonding electrons. Eight bonding against two antibonding gives 3, the triple bond of nitrogen; against four it gives 2, the double bond of oxygen.
The molecular orbital picture explains things the simple dot-and-cross model cannot. Oxygen comes out with a bond order of 2 and two unpaired electrons, which is why liquid oxygen is attracted to a magnet. A Lewis structure gives the right bond order and the wrong magnetism.
The formula
Bonding electrons minus antibonding electrons, divided by two. Electrons in antibonding orbitals cancel the stabilisation of those in bonding orbitals, so each antibonding electron offsets one bonding electron. A bond order of zero means no bond forms at all, which is why helium exists as single atoms.
| Term | Meaning |
|---|---|
| Bond order | Half the net bonding electrons. Higher means a shorter, stronger bond. |
| Bonding orbital | A molecular orbital lower in energy than the atomic orbitals it came from. |
| Antibonding orbital | One higher in energy, which destabilises the molecule when occupied. |
| Fractional bond order | Possible for ions and radicals, where an odd number of electrons remains. |
The inputs explained
| Field | What to enter |
|---|---|
| Bonding electrons | Electrons occupying bonding molecular orbitals. |
| Antibonding electrons | Electrons occupying antibonding orbitals, conventionally marked with an asterisk. |
When to use it
Comparing bond strengths
Higher bond order means a shorter and stronger bond, which predicts bond length and dissociation energy trends.
Explaining why a molecule does not exist
A bond order of zero means no net bonding, which is why He₂ is not a stable molecule.
Working with ions and radicals
Adding or removing an electron changes the bond order by half, which is why fractional values appear.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What bond order does each electron count give?
The same bonding count against a range of antibonding electrons.
| Antibonding electrons | Bond order | Interpretation | Bonding electrons used |
|---|---|---|---|
| 2 antibonding | 3.00 | triple bond | 8 |
| 4 antibonding | 2.00 | double bond | 8 |
| 5 antibonding | 1.50 | bond order 1.50 | 8 |
| 6 antibonding | 1.00 | single bond | 8 |
Questions
Can bond order be a fraction?
Yes, whenever an odd number of net bonding electrons remains. The superoxide ion has a bond order of 1.5 and nitric oxide has 2.5. Fractional values are normal for radicals and ions and indicate a bond intermediate in strength between two whole orders.
What does a bond order of zero mean?
That no bond forms. Helium would have two bonding and two antibonding electrons in a hypothetical He₂ molecule, cancelling exactly, which is why helium exists as isolated atoms. The same reasoning explains why the noble gases are unreactive.
How does bond order relate to bond length?
Inversely. Higher bond order means the atoms are pulled closer, so the bond is shorter and stronger. Nitrogen at bond order 3 has a much shorter bond than fluorine at bond order 1, and a far higher dissociation energy.
Why does molecular orbital theory explain oxygen better?
Because it predicts two unpaired electrons in the antibonding orbitals alongside a bond order of 2. That explains why oxygen is paramagnetic and sticks to a magnet. A Lewis double bond structure pairs all the electrons and gets the magnetism wrong.
For the ionic end of the bonding spectrum, see the percent ionic character calculator. For electron shielding, see the effective nuclear charge calculator.