Chemical Equation Balancer
Balance a chemical equation by solving the system of element conservation equations, with the working shown and the smallest whole-number coefficients found.
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Balancing is solving simultaneous equations
Every element must appear in equal numbers on both sides, and each element gives one equation relating the unknown coefficients. Balancing by inspection means solving that system by trial, which works for simple cases and becomes unreliable quickly. Setting it up as a matrix and solving properly always finds the answer if one exists, and finds it in one pass rather than by adjustment and re-checking.
The answer is a ratio, not a set of numbers
If a set of coefficients balances an equation, so does every multiple of it. The convention is the smallest set of whole numbers, found by dividing through by their greatest common divisor. This is why an equation can appear to have several correct answers: they are all the same ratio, and only the reduced form is conventional.
Some equations cannot be balanced
An equation whose products cannot be made from its reactants has no solution, and the system of equations is then inconsistent. A redox reaction split across two half-equations may also have a family of solutions rather than one, which happens when the reaction as written does not determine the electron transfer. In both cases the arithmetic reports the problem, which is more useful than adjusting coefficients indefinitely.
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Frequently Asked Questions
Why can I not balance my equation?
Usually because the products cannot be formed from the reactants as written, which makes the system of equations inconsistent. Check the formulae before assuming the balancing is at fault.
Why are there several valid answers?
Because any multiple of a balancing set also balances. The convention is the smallest whole numbers, obtained by dividing through by the greatest common divisor, so the alternatives are the same ratio scaled up.
Does this handle ionic charges?
It balances atoms, not charge. A redox half-equation also needs the charges to balance, which requires adding electrons, and that is a separate step this does not perform.
How should I write the formulae?
Element symbols with the usual capitalisation, subscripts as plain numbers, and brackets where needed, as in Ca(OH)2. Use an arrow or an equals sign between the two sides and plus signs between species.
Is balancing by inspection wrong?
No, and it is unreliable beyond simple cases. It is trial and error over the same system of equations this solves directly, so it gives the same answer when it works and no indication when the equation cannot be balanced at all.
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How to Use
Enter an unbalanced equation to find its coefficients.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.