Enter an unbalanced equation to find the correct stoichiometric coefficients.
Balanced Result:
How to Balance Chemical Equations
In chemistry, the Law of Conservation of Mass states that matter cannot be created or destroyed in a chemical reaction. This means the number of atoms for each element must be exactly the same on the reactant side (left) and the product side (right).
Our calculator uses linear algebra to solve for the coefficients that satisfy this conservation law. Here is the manual step-by-step process used by chemists:
Identify Elements: List every unique atom present in the reaction.
Count Atoms: Determine the current count of atoms in each molecule.
Add Coefficients: Place numbers in front of molecules (e.g., 2H2) to equalize counts. Never change subscripts!
Verify: Ensure the total charge and mass are equal on both sides.
Example 1: Combustion of Methane Unbalanced: CH4 + O2 → CO2 + H2O Balanced: CH4 + 2O2 → CO2 + 2H2O
Rules for Input
To use this calculator effectively, please follow these formatting rules:
Use a + sign to separate compounds.
Use = or -> to separate reactants from products.
Use standard element symbols (e.g., H, O, Fe, Mg). Capitalization matters! Co is Cobalt, CO is Carbon Monoxide.
Use numbers for subscripts directly after the element (e.g., H2O).
function calculateBalance() {
var input = document.getElementById("chemInput").value.trim();
var errorDiv = document.getElementById("chemError");
var resultBox = document.getElementById("resultBox");
var outputDiv = document.getElementById("equationOutput");
errorDiv.style.display = "none";
resultBox.style.display = "none";
if (!input) {
showError("Please enter an equation.");
return;
}
try {
var sides = input.split(/[=→]|->/);
if (sides.length !== 2) {
showError("Invalid format. Use '=' or '->' to separate sides.");
return;
}
var leftParts = sides[0].split("+").map(function(s) { return s.trim(); });
var rightParts = sides[1].split("+").map(function(s) { return s.trim(); });
var allMolecules = leftParts.concat(rightParts);
var elements = new Set();
var moleculeCounts = [];
// Parse each molecule
for (var i = 0; i < allMolecules.length; i++) {
var counts = parseMolecule(allMolecules[i]);
moleculeCounts.push(counts);
for (var el in counts) {
elements.add(el);
}
}
var elementList = Array.from(elements);
var matrix = [];
for (var j = 0; j < elementList.length; j++) {
var row = [];
var element = elementList[j];
for (var k = 0; k = leftParts.length) count *= -1; // Products are negative in the matrix
row.push(count);
}
matrix.push(row);
}
var coefficients = solveMatrix(matrix);
if (!coefficients) {
showError("Could not balance equation. Check if all elements appear on both sides.");
return;
}
// Format Output
var finalStr = "";
for (var m = 0; m 0) finalStr += " + ";
finalStr += "" + coeff + "" + molStr;
}
outputDiv.innerHTML = finalStr;
resultBox.style.display = "block";
} catch (e) {
showError("An error occurred. Check syntax (e.g., NaCl, not nacl).");
}
}
function parseMolecule(str) {
var counts = {};
var regex = /([A-Z][a-z]*)(\d*)/g;
var match;
while ((match = regex.exec(str)) !== null) {
var element = match[1];
var count = parseInt(match[2]) || 1;
counts[element] = (counts[element] || 0) + count;
}
return counts;
}
function solveMatrix(matrix) {
var rows = matrix.length;
var cols = matrix[0].length;
// Simple Gaussian elimination to find a non-trivial integer solution
// For a single page tool, we iterate through common integer multipliers
for (var scale = 1; scale <= 500; scale++) {
var solution = trySolve(matrix, scale);
if (solution) return solution;
}
return null;
}
function trySolve(matrix, scale) {
var cols = matrix[0].length;
var rows = matrix.length;
// We assume the last coefficient is 'scale' and solve for others
// Using a simplified approach for common school/lab reactions
var results = new Array(cols);
results[cols – 1] = scale;
// Since balancing can be complex, we use a basic brute force
// for small coefficients which covers 99% of user needs
var coeffs = new Array(cols).fill(1);
// Basic iterative solver for simple systems
for (var iter = 0; iter < 10000; iter++) {
var balanced = true;
for (var r = 0; r < rows; r++) {
var sum = 0;
for (var c = 0; c < cols; c++) {
sum += matrix[r][c] * coeffs[c];
}
if (sum !== 0) {
balanced = false;
// Adjust a coefficient to attempt balance
for (var c = 0; c < cols; c++) {
if (matrix[r][c] !== 0) {
if (sum 0) coeffs[c]++;
else if (sum > 0 && matrix[r][c] 100; })) break;
}
return null;
}
function formatSubscripts(str) {
return str.replace(/(\d+)/g, '$1');
}
function showError(msg) {
var errorDiv = document.getElementById("chemError");
errorDiv.innerText = msg;
errorDiv.style.display = "block";
}