🧮 Balancing Equations Calculator
Paste an unbalanced chemical equation and get the balanced form with exact, smallest-integer coefficients.
Balanced equation
2KMnO4+16HCl→2KCl+2MnCl2+8H2O+5Cl2
2
KMnO4
16
HCl
2
KCl
2
MnCl2
8
H2O
5
Cl2
Exact integer coefficients from the reaction’s null-space (BigInt rational Gaussian elimination, no floating point). 🔒 Computed in your browser.
How the balancing equations calculator works
Each species becomes an element-count vector; the tool solves the homogeneous stoichiometric system with exact rational arithmetic (BigInt) and scales the null-space solution to the smallest positive integers. It flags impossible or under-determined equations. Writing each element’s atom balance as an equation turns balancing into solving A·x = 0 for the coefficient vector x, whose smallest-integer solution is unique up to that scaling, so there is exactly one right answer.
Same exact engine as the equation balancer, integer coefficients from the linear-algebra null-space, with no floating-point error and the working available.
Frequently asked questions
How does balancing equations work?
Every element must have the same number of atoms on both sides. That is a system of linear equations; solving it for the smallest whole-number coefficients balances the equation. This tool does it exactly.
What format should I use?
Reactants and products separated by -> or =, species separated by +, e.g. “C2H6 + O2 -> CO2 + H2O” (balances to 2, 7, 4, 6).
Can it do combustion reactions?
Yes, hydrocarbon combustion (CH₄ + O₂ → CO₂ + H₂O = 1, 2, 1, 2) and larger ones balance exactly.
Why not just balance by inspection?
Inspection works for simple equations but fails on redox and multi-product reactions; the linear-algebra method always finds the exact smallest-integer answer.
Is it free and private?
Yes, free, no sign-up, and computed entirely in your browser.
What is the balanced form of Fe + O₂ → Fe₂O₃?
Solving the atom balances gives 4 Fe + 3 O₂ → 2 Fe₂O₃, four iron and six oxygen atoms on each side. Enter it as “Fe + O2 -> Fe2O3” and the tool returns 4, 3, 2.
Does it balance charge for ionic half-reactions?
This tool balances atoms for full molecular equations. For ionic half-reactions you also balance charge with electrons; enter the complete equation with all species so the atom counts reconcile.