Chemical Equation Balancer

Formula

Each element gives one linear equation: the atoms it contributes on the left minus the atoms on the right must be zero. For coefficient vector $\mathbf{x}$ and matrix $A$ of atom counts (products negative):

The tool solves this system exactly with fractions, takes the one-dimensional solution and scales it to the smallest whole numbers.

Worked example

Balance $\mathrm{C_3H_8 + O_2 \to CO_2 + H_2O}$.

• Carbon: $3a = c$. Hydrogen: $8a = 2d$. Oxygen: $2b = 2c + d$.
• Take $a = 1$: then $c = 3$, $d = 4$ and $2b = 6 + 4$, so $b = 5$.
• Result: $\mathrm{C_3H_8 + 5\,O_2 \to 3\,CO_2 + 4\,H_2O}$.

Check oxygen: $5 \times 2 = 10$ on the left and $3 \times 2 + 4 = 10$ on the right.

Common mistakes

• Changing a subscript instead of a coefficient. Subscripts define the substance; only coefficients may change.
• Typing formulas in the wrong case, such as co2 or CL2. Each element starts with a capital letter.
• Omitting a product or reactant, which makes the equation impossible to balance.
• Forgetting the charges in ionic equations. Check that charge is balanced as well as atoms.