Chemical Equation Balancer
Balance chemical reactions via linear algebra
About this calculator
The Chemical Equation Balancer finds the smallest whole-number coefficients that balance a reaction by solving the homogeneous stoichiometry matrix A·c = 0 with exact arithmetic. It accepts element symbols, nested parentheses and brackets, hydrate dots, and state labels like (aq), then shows the balanced equation, an element-by-element atom audit, and the underlying matrix. Reactions with an element on only one side, or with no positive integer solution, are clearly flagged.
How to use the Chemical Equation Balancer calculator
- Enter the quantities you know, using the units shown on each field.
- Read the computed results — they update instantly as you type.
- Use the visual explanation to see how the quantities relate.
- Copy the page URL to share the exact calculation.
Common examples
- CH4 + O2 -> CO2 + H2O → CH₄ + 2O₂ → CO₂ + 2H₂O
- Fe + O2 -> Fe2O3 → 4Fe + 3O₂ → 2Fe₂O₃
- Al + HCl -> AlCl3 + H2 → 2Al + 6HCl → 2AlCl₃ + 3H₂
- Photosynthesis: CO2 + H2O -> C6H12O6 + O2 → 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
- KMnO4 + HCl -> KCl + MnCl2 + H2O + Cl2 → 2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 8H₂O + 5Cl₂
Frequently asked questions
How does the Chemical Equation Balancer calculator work?
Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.
When would I use the Chemical Equation Balancer calculator?
It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.
How accurate are the results?
The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.