Chemistry Calculators

#1 Free Chemical Equation Balancer / Calculator 2025

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Chemical Equation Balancer

Balanced Equation:

Balancing chemical equations is a fundamental concept in chemistry based on the Law of Conservation of Mass. This law states that matter cannot be created or destroyed in a chemical reaction. Therefore, the total number of atoms of each element must be the same on both the reactant (starting materials) and product (substances formed) sides of the equation.

To balance an equation, we adjust the stoichiometric coefficients – the numbers placed in front of chemical formulas. These coefficients represent the relative number of moles of each substance involved in the reaction. You cannot change the subscripts within a chemical formula, as that would change the identity of the substance itself.

For example, in H₂O, the subscript '2' on hydrogen means there are two hydrogen atoms in one molecule of water. Changing it would make it a different compound. However, writing 2H₂O means two molecules of water.

Balancing is often done by inspection for simple equations, or by more systematic algebraic or matrix methods for complex ones. This calculator uses an algebraic (matrix-based) method to find the smallest integer coefficients that satisfy the conservation of atoms for all elements.

This calculator balances equations using the following process:

  1. Parsing the Input: The entered equation string is parsed to identify individual chemical formulas (species) on the reactant and product sides. It also breaks down each formula into its constituent elements and their counts (e.g., H₂O becomes H:2, O:1).
  2. Identifying Elements: A unique list of all elements present in the reaction is created.
  3. Setting up Linear Equations: For each element, an equation is formed based on the principle of atom conservation. If a reaction is aA + bB → cC + dD, then for an element X:
    (atoms of X in A)*a + (atoms of X in B)*b = (atoms of X in C)*c + (atoms of X in D)*d
    This can be rewritten as:
    (atoms of X in A)*a + (atoms of X in B)*b - (atoms of X in C)*c - (atoms of X in D)*d = 0
  4. Matrix Representation: This system of linear equations is represented as a matrix equation Mx = 0, where M is a matrix of atomic counts, and x is a vector of the unknown stoichiometric coefficients (a, b, c, d...).
  5. Solving the System: The calculator uses Gaussian elimination to solve this system of equations for the coefficients. Since there's typically one degree of freedom (we can scale all coefficients), one coefficient is usually set to a base value (like 1), and others are solved relative to it.
  6. Normalizing Coefficients: The solved coefficients might be fractions. They are then converted to the smallest possible set of positive integers by:
    • Multiplying by the least common multiple (LCM) of any denominators to make them all integers.
    • Dividing all coefficients by their greatest common divisor (GCD) to simplify them to the smallest ratio.
  7. Displaying the Result: The final balanced equation with the integer coefficients is displayed, along with a step-by-step breakdown of the process.

1. Enter the Equation:

  • Type the unbalanced chemical equation into the input field.
  • Use standard chemical formulas (e.g., H2O, CO2, Al2(SO4)3). Elements are case-sensitive (e.g., 'Co' for Cobalt, 'CO' for Carbon Monoxide).
  • Separate reactants from products using an arrow: -> or an equals sign: =.
  • Separate multiple reactants or products with a plus sign: +.
  • Spaces are optional around symbols like '+', '->', and chemical formulas. Example: H2+O2->H2O is the same as H2 + O2 -> H2O.
  • Coefficients already present in the input will be ignored for balancing, as the tool calculates new ones.

Example Inputs:

  • H2 + O2 -> H2O
  • Fe2O3 + C = Fe + CO2
  • C6H12O6 + O2 -> CO2 + H2O
  • KMnO4 + HCl -> KCl + MnCl2 + H2O + Cl2
  • Ca(OH)2 + H3PO4 -> Ca3(PO4)2 + H2O

2. Balance:

  • Click the "Balance Equation" button.

3. View Results:

  • The balanced equation will appear below, with the calculated stoichiometric coefficients. Coefficients of '1' are typically shown for clarity.
  • A step-by-step explanation of how the equation was balanced will also be displayed.
  • If there's an error in your input (e.g., invalid formula, unbalanced elements that cannot be balanced), an error message will guide you.

4. Reset:

  • Click the "Reset" button to clear the input field and results, allowing you to balance a new equation.

5. Explore Information:

  • Click on the "Theory," "How It Works," or "Instructions" bars to expand or collapse detailed information.
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