Bond Order Calculator
Enter the number of bonding and antibonding electrons to get the bond order from molecular orbital (MO) theory, or switch to Lewis structure mode to count single, double, and triple bonds directly. A third resonance mode handles polyatomic ions such as nitrate or carbonate. The result updates instantly, with a full show-your-work panel, a bond-type interpretation, and a reference table of common diatomic molecules.
Formula
Worked example
For O2: from its MO diagram, Nb = 10 (sigma1s, sigma*1s, sigma2s, sigma*2s, sigma2p, two pi2p) and Na = 6 (sigma*1s, sigma*2s, two pi*2p). Bond order = (10 - 6) / 2 = 2, a double bond. For NO3- resonance: 4 total bond-order units (one double + two single) spread over 3 equivalent N-O positions gives 4/3 = 1.33.
What is bond order?
Bond order is a number that describes how many chemical bonds exist between two atoms. In the simplest case it is an integer: 1 for a single bond (H-F), 2 for a double bond (O=O), and 3 for a triple bond (N-N). When electrons are delocalized across several bonds, as in resonance structures or molecular orbital theory, the bond order can be a fraction such as 1.5 (benzene C-C) or 2.5 (O2+). A bond order of zero means no net bond forms between those atoms and the species is unstable (e.g. He2).
Three ways to calculate bond order
Molecular orbital (MO) theory counts electrons in bonding and antibonding orbitals and applies the formula BO = (Nb - Na) / 2. This is the most rigorous approach and works for any diatomic. Lewis structure counting simply totals the bond-order contributions of each bond type: single bonds count 1, double bonds count 2, triple bonds count 3. Resonance averaging applies when a molecule has delocalized electrons described by two or more resonance structures: sum all bond-order units across every resonance position, then divide by the number of equivalent positions. For nitrate (NO3-), one double and two single N-O bonds give 2 + 1 + 1 = 4 units over 3 positions, so each N-O bond order is 4/3 = 1.33.
Bond order, bond length, and bond energy
Bond order is directly related to two measurable properties. As bond order increases, bond length decreases: N2 (BO = 3, length ~110 pm) is much shorter than N2H4 N-N (BO = 1, length ~145 pm). Bond dissociation energy rises with bond order as well: a C-C single bond requires about 347 kJ/mol to break, a C=C double bond about 614 kJ/mol, and a C-C triple bond about 839 kJ/mol. These trends make bond order a fast predictor of molecular stability, reactivity, and spectroscopic properties such as stretching frequency.
Molecular orbital diagram and electron filling order
To apply the MO method, fill molecular orbitals from lowest to highest energy following the Aufbau principle. For period-2 homonuclear diatomics lighter than O2 (Li2 through N2), the pi2p orbitals lie below sigma2p, so the filling order is: sigma1s, sigma*1s, sigma2s, sigma*2s, pi2p (x and y), sigma2p, pi*2p (x and y), sigma*2p. For O2 and heavier molecules, sigma2p drops below pi2p. Count every electron in a bonding orbital as Nb and every electron in an antibonding orbital as Na, then apply the formula. The reference table above lists pre-calculated values for common diatomics so you can check your count.
Bond order of common homonuclear diatomic molecules (MO theory)
| Molecule | Bonding e- (Nb) | Antibonding e- (Na) | Bond order | Bond type |
|---|---|---|---|---|
| H2 | 2 | 0 | 1 | Single |
| H2+ | 1 | 0 | 0.5 | Half-bond |
| He2 | 2 | 2 | 0 | No bond |
| He2+ | 2 | 1 | 0.5 | Half-bond |
| Li2 | 4 | 2 | 1 | Single |
| Be2 | 4 | 4 | 0 | No bond |
| B2 | 6 | 4 | 1 | Single |
| C2 | 8 | 4 | 2 | Double |
| N2 | 10 | 4 | 3 | Triple |
| N2+ | 9 | 4 | 2.5 | Bond order 2.5 |
| O2 | 10 | 6 | 2 | Double |
| O2+ | 10 | 5 | 2.5 | Bond order 2.5 |
| O2- | 10 | 7 | 1.5 | Bond order 1.5 |
| F2 | 10 | 8 | 1 | Single |
| Ne2 | 10 | 10 | 0 | No bond |
Electron counts from the standard MO filling order for period 1 and 2 diatomics. Bond order = (Nb - Na) / 2.
Frequently asked questions
What does a bond order of zero mean?
A bond order of zero means the molecule has equal numbers of bonding and antibonding electrons, so the stabilizing effect of bonding orbitals is completely cancelled out. The molecule is not expected to exist as a stable species. He2, for example, has Nb = 2 and Na = 2, giving a bond order of zero, which is why helium does not form a diatomic molecule under normal conditions.
Can bond order be a fraction?
Yes. Fractional bond orders arise in three situations: an odd number of electrons in the MO diagram (e.g. H2+ has one bonding electron and BO = 0.5), resonance delocalization across equivalent positions (benzene C-C average BO = 1.5), or charged species that have gained or lost an electron relative to a neutral molecule (O2+ has BO = 2.5 compared with 2 for neutral O2).
How does bond order relate to bond length?
Higher bond order means a shorter bond. For carbon-carbon bonds: single (BO = 1) is about 154 pm, aromatic or partial double (BO = 1.5) is about 140 pm, double (BO = 2) is about 134 pm, and triple (BO = 3) is about 120 pm. The same trend holds across other atom pairs - the bond becomes shorter and harder to stretch as more electron density is concentrated between the nuclei.
How do I calculate the bond order of NO3-?
Use the resonance averaging method. Draw all three resonance structures of nitrate: each has one N=O double bond and two N-O single bonds. Total bond-order units = 2 + 1 + 1 = 4. Equivalent N-O positions = 3. Average bond order = 4 / 3 = 1.33. This matches experimental data showing that all three N-O bonds in nitrate are identical and intermediate in length between a pure single and a pure double bond.
What is the difference between MO theory and Lewis structure bond order?
Lewis structures give integer bond orders by counting shared electron pairs between atoms. MO theory assigns electrons to molecular orbitals that span the whole molecule and can give non-integer bond orders for species with an odd electron count or unusual electron configuration. For most stable diatomic molecules the two methods agree. Where they differ, MO theory is more accurate because it accounts for the actual quantum-mechanical distribution of electrons.
Does bond order predict magnetic properties?
Partially, yes. If filling the MO diagram leaves one or more electrons unpaired, the molecule is paramagnetic. O2 is a classic example: its two pi*2p orbitals each hold one electron (Hund's rule), making O2 paramagnetic with a bond order of 2. This prediction by MO theory confirmed by experiment was a major early success of the model. Lewis structures incorrectly showed O2 as diamagnetic.