Chemical Equation Balancer

Balance chemical equations quickly with this tool.


Form compounds by adding elements like H, He, Li, etc., followed by the number of atoms of that element in each compound or no number if there is only one atom. Then group different reactants or products with the + symbol. Finally, to complete the equation, add the reactants, an = symbol, and the products. Example: H2 + O2 = H2O

To balance the chemical equation, simply click the Balance button, and the result will appear formatted in LaTeX.

How it works

Instead of using the trial-and-error method, this tool creates a system of equations and solves it to obtain the coefficients that balance the equation.

To make it clear, let's do an example with the following chemical equation:

  1. First, let's assign coefficients to each molecule of the equation like this:
  2. Identify the elements in the chemical formula:
  3. Build the vector equation, one for each molecule of the equation. In the i-th position of the vector, we store the number of atoms of that element in the i-th molecule found in the previous step. For example, the first vector is [3, 8, 0], representing that the first molecule is composed of 3 carbon atoms and 8 hydrogen atoms, so it is C3H8.
  4. Solve one side of the equation, leaving a vector of zeros on that side:
  5. Break it down into a matrix representing the chemical equation multiplied by a vector of coefficients:
  6. Represent the system of equations as an augmented matrix:
  7. Reduce the augmented matrix to its reduced row-echelon form:
  8. As you can see, the matrix has more unknowns than equations, leaving the variable x4 free. Parametrizing the variables in terms of t, we get:
  9. To eliminate fractions, choose a value for t that corresponds to the least common multiple of the denominators, in this case, 3. The coefficients become:
  10. Substituting the coefficients into the equation from step 1, we get the solution:

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