Chemical Equation Balancer
Balance any chemical equation with the smallest whole-number coefficients.
What is Equation Balancer?
Balancing an equation means finding whole-number coefficients that put the same number of atoms of each element on both sides of the arrow — matter is not created in a reaction. For most equations the answer is unique, and this tool computes it exactly rather than by trial and error.
How it works
The element counts of every species form a matrix, and a balanced equation is a positive integer vector in its null space. The solver does Gauss-Jordan elimination over exact big-integer fractions, scales the result to the smallest integers and divides by their common factor, so `Fe + O2 -> Fe2O3` comes out as `4Fe + 3O2 → 2Fe2O3` rather than as something rounded. Two honest failure modes are reported rather than papered over: an equation whose two sides have different elements, and one with more than one independent balance (such as `C + O2 -> CO + CO2`), which has no single answer.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What does the balancer do with coefficients I type?
It ignores them and balances from scratch. Echoing an unbalanced input back would be worse than useless, so the coefficients in the answer are always derived.
Why does it say my equation has more than one balance?
Because it genuinely does. Some inputs are really two reactions at once — `C + O2 -> CO + CO2` conserves everything for a whole family of coefficient sets — and there is no single correct answer to give.
How do I write an equation?
Species separated by +, and the two sides separated by -> (or →). So `Fe + O2 -> Fe2O3`. Charges and states such as (aq) are not needed for balancing the atoms.