VSEPR Molecular Geometry Calculator
Enter the number of bonded atoms and lone pairs on the central atom to get the AXE notation, electron-domain geometry, molecular shape and approximate bond angles using VSEPR theory.
Predict a Molecule's Shape from Bonds and Lone Pairs
VSEPR Molecular Geometry Formula
Where:
- \(X\) — number of atoms bonded to the central atom (a double or triple bond counts as one)
- \(E\) — number of lone pairs on the central atom
- \(S\) — total electron domains, which fixes the electron-domain geometry
- \(\mathrm{AX}_X\mathrm{E}_E\) — the AXE notation; the subscript E is omitted when there are no lone pairs
The total number of electron domains \(S\) determines the arrangement of all domains around the central atom, and the number of lone pairs \(E\) then determines which of those positions are empty of atoms — giving the final molecular shape.
VSEPR Molecular Geometry – Calculation Example
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Example: a water molecule, H2O. The central oxygen atom is bonded to 2 hydrogen atoms and carries 2 lone pairs.
\[ S = X + E = 2 + 2 = 4 \ \text{domains (tetrahedral electron-domain geometry)} \]
\[ \mathrm{AXE} = \mathrm{AX}_2\mathrm{E}_2 \]
Two of the four tetrahedral positions are lone pairs, leaving only two bonded atoms.
Result: AX2E2 — bent molecular shape with bond angles of ≈104.5°.
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How to Use the Calculator
- Draw or picture the molecule and identify the central atom — usually the least electronegative atom, or the one with the most bonds.
- Enter the number of Bonded Atoms (X). Count each attached atom once; a double or triple bond to the same atom still counts as one bonded atom.
- Enter the number of Lone Pairs on Central Atom (E) from your Lewis structure. If you need help finding lone pairs or checking electron bookkeeping, the Formal Charge calculator can help validate your structure.
- Read the results: AXE Notation, Electron-Domain Geometry, Molecular Shape, Approximate Bond Angles, and a details block with repulsion notes and typical example molecules.
What Is VSEPR Theory?
VSEPR (Valence Shell Electron Pair Repulsion) theory predicts the three-dimensional shape of a molecule from a simple principle: electron pairs around a central atom repel each other and settle as far apart as possible. Each electron pair — whether a bonding pair or a lone pair — occupies a region of space called an electron domain. Counting the domains fixes the electron-domain geometry: 2 domains give a line, 3 a trigonal plane, 4 a tetrahedron, 5 a trigonal bipyramid, and 6 an octahedron.
The molecular shape describes only the positions of the atoms, not the lone pairs. When lone pairs are present, they "hide" positions from the shape but still repel, which is why a molecule with four domains and two lone pairs (water) is bent rather than tetrahedral, and why ammonia with one lone pair is trigonal pyramidal.
The key to interpreting your result is the repulsion hierarchy: lone-pair–lone-pair repulsion is strongest, followed by lone-pair–bonding, then bonding–bonding. Lone pairs are attracted to only one nucleus, so they spread out more and push the bonding pairs closer together. This compresses bond angles below their ideal values — 104.5° in water instead of the ideal 109.5°, and about 107° in ammonia.
Molecular shape matters far beyond geometry exercises. It determines whether a molecule is polar, how it hydrogen-bonds, how enzymes recognise substrates, and how drugs bind to receptors. Before applying VSEPR, make sure your Lewis structure is correct — the Degree of Unsaturation calculator can help you sanity-check the bonding framework of an organic molecule.
Quick Reference: Common AXE Cases
| AXE | Domains | Electron-Domain Geometry | Molecular Shape | Bond Angle | Example |
|---|---|---|---|---|---|
| AX2 | 2 | Linear | Linear | 180° | CO2 |
| AX3 | 3 | Trigonal planar | Trigonal planar | 120° | BF3 |
| AX2E | 3 | Trigonal planar | Bent | ≈119° | SO2 |
| AX4 | 4 | Tetrahedral | Tetrahedral | 109.5° | CH4 |
| AX3E | 4 | Tetrahedral | Trigonal pyramidal | ≈107° | NH3 |
| AX2E2 | 4 | Tetrahedral | Bent | ≈104.5° | H2O |
| AX5 | 5 | Trigonal bipyramidal | Trigonal bipyramidal | 90°, 120° | PCl5 |
| AX4E | 5 | Trigonal bipyramidal | Seesaw | ≈90°, <120° | SF4 |
| AX3E2 | 5 | Trigonal bipyramidal | T-shaped | <90° | ClF3 |
| AX2E3 | 5 | Trigonal bipyramidal | Linear | 180° | XeF2 |
| AX6 | 6 | Octahedral | Octahedral | 90° | SF6 |
| AX5E | 6 | Octahedral | Square pyramidal | <90° | BrF5 |
| AX4E2 | 6 | Octahedral | Square planar | 90° | XeF4 |
Assumptions and Limitations
- A correct Lewis structure is required. VSEPR predictions are only as good as your count of bonded atoms and lone pairs. Formal charges and resonance do not change the domain count as long as the number of bonded atoms stays the same.
- Multiple bonds count once. A double or triple bond occupies roughly the same space as a single bond, so CO2 is AX2, not AX4.
- Angles are approximate. Real bond angles deviate from the ideal values depending on atom sizes, electronegativity differences, and multiple bonding. The calculator reports ideal or typical values.
- One central atom only. The model applies to a single central atom with the domains you enter; molecules with several centres (such as chains or rings) must be analysed one atom at a time.
- Positional rules for 5 and 6 domains. In trigonal bipyramids, lone pairs prefer equatorial positions; in octahedra, multiple lone pairs sit opposite each other — the calculator's details block notes this when it applies.
- VSEPR does not predict bond lengths or exact angles. For quantitative energetics or precise geometry, more advanced methods are needed.
If you are working through a full reaction problem after determining a structure, the Limiting Reactant calculator or the Equilibrium Constant calculator may be useful next steps.
Frequently Asked Questions
How do I find the number of lone pairs without drawing a full Lewis structure?
A quick shortcut works for many main-group central atoms: compare the valence electrons of the central atom with what it uses for bonding. Each lone pair needs 2 electrons. For example, oxygen has 6 valence electrons; in H2O it shares one electron with each of two hydrogens, leaving 4 electrons = 2 lone pairs. If the atom is a central atom with only single bonds, lone pairs \( E = \frac{V - X}{2} \) where \(V\) is valence electrons and \(X\) is the number of bonds. Be careful with charged species — an extra electron adds to \(V\), a positive charge subtracts one.
Does a double or triple bond count as more than one electron domain?
No — this is one of the most common mistakes. A double or triple bond to the same atom occupies roughly the same region of space as a single bond, so it counts as one electron domain and one bonded atom. That's why CO2 is AX2 (linear), not AX4, and why formaldehyde H2CO is AX3 (trigonal planar), not AX5. However, multiple bonds do repel slightly more strongly than single bonds, which is why angles next to a double bond are often a bit larger than the ideal value.
Why is the bond angle in water 104.5° instead of the ideal 109.5°?
Water has four electron domains arranged tetrahedrally, but two of them are lone pairs. A lone pair is attracted to only one nucleus, so its electron cloud spreads out wider than a bonding pair and repels neighboring pairs more strongly. With two lone pairs squeezing the two O–H bonds together, the ideal 109.5° tetrahedral angle compresses to about 104.5°. The same effect gives ammonia (one lone pair) about 107° instead of 109.5°.
What is the difference between electron-domain geometry and molecular shape?
Electron-domain geometry describes how all electron regions (bonding pairs and lone pairs) are arranged around the central atom. Molecular shape describes only the positions of the atoms — lone pairs are invisible in the shape name but still push atoms around. AX4, AX3E, and AX2E2 all have tetrahedral electron-domain geometry, yet their molecular shapes are tetrahedral, trigonal pyramidal, and bent respectively. Exams frequently test this distinction, so always state which one is being asked for.
How do I analyze a molecule with more than one central atom?
VSEPR applies to one atom at a time. Pick an atom, count only the groups directly attached to it plus its own lone pairs, and run the prediction for that atom alone; then repeat for the next atom. In ethanol, for example, the oxygen is AX2E2 (bent) while each carbon must be analyzed separately — both happen to be roughly tetrahedral. The overall 3D structure is the combination of all these local geometries joined by the bonds between them.
Do formal charges or resonance structures change the VSEPR result?
Usually no. As long as the number of bonded atoms and lone pairs on the central atom stays the same, resonance and formal charges don't alter the AXE notation or the shape. The nitrate ion NO3− has three equivalent resonance structures, but in every one of them nitrogen is bonded to three oxygens with no lone pairs — AX3, trigonal planar. What does matter is when different valid structures give different atom counts, such as choosing where a protonation or lone pair actually sits; then use the structure that best matches formal-charge rules.
Can VSEPR tell me whether a molecule is polar?
Not by itself, but the shape is the essential first step. A molecule is polar when its individual bond dipoles don't cancel. Symmetric shapes with identical substituents — linear AX2 like CO2, trigonal planar AX3 like BF3, tetrahedral AX4 like CH4, octahedral AX6 like SF6 — are nonpolar because the dipoles cancel. Bent (H2O), trigonal pyramidal (NH3), and seesaw (SF4) shapes leave an unsymmetrical dipole, making them polar. You also need to check that the bonds themselves are polar; CCl4 is tetrahedral but nonpolar only because its four identical C–Cl dipoles cancel.