Bond order is the number of chemical bonds between a pair of atoms. In MO theory it equals (bonding electrons − antibonding electrons) / 2. A value of 1 corresponds to a single bond, 2 to a double bond, 3 to a triple bond, and fractional values occur in species such as NO (bond order 2.5) or He₂⁺ (bond order 0.5).

What counts as a bonding or antibonding electron?

Electrons placed in bonding molecular orbitals (σ1s, σ2s, σ2p, π2p and their higher analogues) are bonding electrons. Electrons placed in antibonding orbitals (σ*1s, σ*2s, σ*2p, π*2p, etc.) are antibonding electrons. Non-bonding electrons neither add to nor subtract from bond order.

Can bond order be a fraction?

Yes. Molecular ions and radicals often have odd total electron counts that yield half-integer bond orders such as 0.5, 1.5, or 2.5. For example, O₂⁺ has bond order 2.5 and NO has bond order 2.5.

What does a bond order of 0 mean?

A bond order of zero means bonding and antibonding contributions cancel out. The species gains no stability from covalent bonding and will not exist as a bound molecule under normal conditions. He₂ is the classic example with bond order 0.

How does bond order relate to bond length and strength?

Higher bond order means a stronger bond with a shorter bond length. Triple bonds (order 3) are shorter and stronger than double bonds (order 2), which are in turn shorter and stronger than single bonds (order 1). This trend holds across similar atom pairs.

How do I determine paramagnetism from bond order?

Paramagnetism depends on unpaired electrons in the MO diagram, not directly on bond order. After filling orbitals with Hund's rule, count electrons without a partner in the same orbital. Any unpaired electron makes the species paramagnetic. O₂ is famously paramagnetic despite having bond order 2 because two electrons sit unpaired in degenerate π* orbitals.

Bond Order Calculator

Enter the number of bonding and antibonding electrons to calculate bond order, bond stability, and magnetic character using MO theory.

Electron Count Input

Count electrons in bonding and antibonding MOs from your orbital diagram.

Quick-fill a common molecule

Bonding electrons (in σ and π orbitals)

Antibonding electrons (in σ* and π* orbitals)

Enter electron counts and click Calculate to see results.

Common diatomic molecules — MO electron counts

Species	Total e⁻	Bonding e⁻	Antibonding e⁻	Bond Order	Magnetic
H₂	2	2	0	1	Diamagnetic
He₂⁺	3	2	1	0.5	Paramagnetic
He₂	4	2	2	0	Diamagnetic
N₂	14	8	2	3	Diamagnetic
O₂	16	8	4	2	Paramagnetic
O₂⁺	15	8	3	2.5	Paramagnetic
O₂⁻	17	8	5	1.5	Paramagnetic
F₂	18	8	6	1	Diamagnetic
NO	15	8	3	2.5	Paramagnetic

Bonding/antibonding counts reflect valence MOs only (1s core included for He). Click any molecule row to auto-fill the calculator.

Summary

The Bond Order Calculator applies molecular orbital (MO) theory to determine the bond order of a diatomic molecule or ion. Bond order equals half the difference between the number of electrons in bonding orbitals and the number in antibonding orbitals. A higher bond order means a stronger, shorter bond; a bond order of zero means the species is unstable and unlikely to exist as a bound molecule.

How it works

Fill the molecular orbital diagram for your molecule by distributing valence electrons into bonding and antibonding orbitals following the Aufbau principle.
Count the total electrons in bonding molecular orbitals (σ, π).
Count the total electrons in antibonding molecular orbitals (σ*, π*).
Apply the formula: Bond Order = (Bonding electrons − Antibonding electrons) / 2.
A result of 0 means the molecule is unstable; fractional results (0.5, 1.5) occur in species like He₂⁺ or NO.
Check for unpaired electrons in the MO diagram to determine if the species is paramagnetic (has unpaired e⁻) or diamagnetic.

Use cases

Calculate the bond order of diatomic molecules such as H₂, N₂, O₂, and F₂.
Determine bond order for molecular ions like O₂⁺, O₂⁻, and NO⁺.
Verify MO theory homework problems and exam practice.
Predict whether a species is stable based on bond order > 0.
Determine bond strength and approximate bond length from bond order.
Assess paramagnetism or diamagnetism of a diatomic species.
Compare bond orders across isoelectronic species.
Teach or learn the MO filling sequence for first- and second-row diatomics.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu