# Chemical Equation Balancer - Redox & Ionic, With Checks

> Balance chemical equations by the algebraic method: smallest whole-number coefficients, brackets, hydrates, ionic charges, electrons, atom and charge checks.

- URL: https://qilingtools.com/en/math/chemical-equation
- Category: Chemistry Tools (https://qilingtools.com/en/chemistry)
- Tags: [Chemistry](https://qilingtools.com/en/tags/chemistry), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Balancing a chemical equation means finding a coefficient for every species so that each element has the same number of atoms on both sides. Inspection works for simple reactions, but redox reactions such as potassium permanganate with hydrochloric acid, copper with nitric acid or the oxidation of K₄[Fe(CN)₆] are easy to get wrong. This balancer uses the algebraic method: each species gets an unknown coefficient, every element (and, for ionic equations, the total charge) gives one linear equation, and exact fraction Gaussian elimination with BigInt finds the solution space, which is then scaled to the smallest positive integers. It also recognises the special cases: equations that cannot be balanced at all, equations whose only solution needs a zero or negative coefficient (a species on the wrong side or one that does not react), and equations with several independent balancings, for which it lists a basis and the smallest all-positive solution. Next to the answer you get an atom-count table for each element, molar masses and a mass-balance check, and the actual system of equations it solved.

## How to use

1. Type the equation with =, -> or → between reactants and products and + between species, or pick an example
2. Write ions as Fe^3+, SO4^2-, NH4+ or OH-, electrons as e-, and hydrates as CuSO4·5H2O or CuSO4*5H2O
3. Read the balanced equation, the atom and charge check and the linear system; copy the result with proper subscripts

## Features

- Algebraic balancing with exact BigInt fraction elimination — no rounding errors
- Coefficients reduced to the smallest whole numbers
- Nested (), [] and {} brackets such as K4[Fe(CN)6] and Ca3(PO4)2
- Hydrates (CuSO4·5H2O), charges (Fe^3+, SO4^2-, Fe+3, SO₄²⁻) and electrons (e-)
- State symbols (s), (l), (g), (aq) and ↑ ↓ are ignored
- Detects impossible equations, zero or negative coefficients and multiple independent solutions
- Atom, charge and mass conservation tables
- Formulas rendered with subscripts and superscripts; copy as Unicode text

## FAQ

### How does the algebraic method balance an equation?

Each species gets a coefficient, for example a KMnO₄ + b HCl = c KCl + d MnCl₂ + e H₂O + f Cl₂. Every element must balance: K gives a = c, Mn gives a = d, O gives 4a = e, H gives b = 2e and Cl gives b = c + 2d + 2f. That homogeneous linear system has a one-dimensional solution, which scaled to whole numbers is 2, 16, 2, 2, 8, 5. The calculator prints the system it built under the result.

### How do I enter ions and electrons?

Put the charge after ^, as in Fe^3+, SO4^2- or MnO4^-, or write Fe+3, NH4+ and OH-, or paste superscripts such as SO₄²⁻. Electrons are e-. For a single-atom ion like Fe3+ or Cu2+ the digit is read as the charge; for polyatomic ions use ^, e.g. SO4^2-. When charges are present an extra charge-balance equation is added.

### Why does it say there are several independent balancings?

If the equation really combines two or more independent reactions — for example H₂ + O₂ → H₂O + H₂O₂ — more than one ratio of coefficients conserves every atom, because the solution space has two or more dimensions. The actual proportions then depend on the reaction conditions. The calculator lists linearly independent basis solutions and suggests the all-positive solution with the smallest coefficients.

### What if it says the equation can’t be balanced?

“Cannot be balanced” means the only solution is all zeros, which usually points to a typo in a formula (case matters: Co is cobalt, CO is carbon monoxide) or a missing product. “Zero or negative coefficient” means there is a unique ratio, but one species has to move to the other side or does not take part in the reaction at all.

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