Chemical Equation Balancer
Type an unbalanced chemical equation such as Fe + O2 -> Fe2O3 to get the
smallest whole-number coefficients. Ionic equations with charges and electrons work too. The page
also shows the atom count on each side, the algebra behind the answer and a mass check.
Equation
Coefficients in the order typed:
Atom count
Enter an equation that can be balanced to see the atom count.
| Element | Left side | Right side | Equal? |
|---|
How it was solved
Enter a valid equation to see the algebra.
Mass check
Enter an equation that can be balanced to see the masses.
| Species | Coefficient | Molar mass (g/mol) | Coefficient × molar mass (g) |
|---|
Molar masses use conventional standard atomic weights. Masses are in grams when each coefficient is read as a number of moles.
Everything is calculated in your browser. Nothing you type is sent anywhere.
How to use the chemical equation balancer
- Type the unbalanced equation or tap an example. Separate the substances with
+and the two sides with->,=or→. - Write formulas with the correct capital letters. Brackets and hydrates work:
Ca(OH)2,CuSO4·5H2O. - Write a charge after a caret:
Fe^3+,SO4^2-,H^+. The electron ise^-ore-. State symbols such as(aq)are kept. - Read the balanced equation. Coefficients you typed are ignored and a coefficient of 1 is not written.
- Check the atom count, the solving steps and the mass table, then copy the result.
Why equations must balance
In a chemical reaction atoms are rearranged, but none are created or destroyed. Every element must therefore have the same number of atoms on both sides of the arrow. Because each atom keeps its mass, the total mass of the products equals the total mass of the reactants. This is the law of conservation of mass. Electric charge is conserved as well, so in an equation with ions the total charge on the left equals the total charge on the right. The coefficients make all these counts agree and give the mole ratio in which the substances react.
How it works
The tool uses the algebraic method. Every substance gets an unknown coefficient, and every element
gives one linear equation: atoms on the left equal atoms on the right. For
Fe + O2 -> Fe2O3 the unknowns are a Fe + b O2 → c Fe2O3, and the equations
are:
Fe: a = 2cO: 2b = 3c
There are three unknowns and two equations, so one unknown can be chosen freely: multiplying a
balanced equation by any number keeps it balanced. With c = 1 the equations
give a = 2 and b = 3/2. Multiplying everything by 2, the least common multiple
of the denominators, gives the smallest whole numbers a = 4, b = 3,
c = 2, so the result is 4 Fe + 3 O2 -> 2 Fe2O3.
The tool writes these numbers into a matrix, one row per element and one column per substance, and solves it by Gaussian elimination with exact fractions, so no rounding error can occur. The mass table multiplies each coefficient by the molar mass and rounds to three decimals.
Balancing by inspection
Small equations are usually balanced by hand, one element at a time. Take
C3H8 + O2 -> CO2 + H2O:
- Start with the most complex formula, C3H8, and give it the coefficient 1.
- Carbon: 3 C on the left, so write 3 CO2.
- Hydrogen: 8 H on the left, so write 4 H2O.
- Oxygen last: the right side now has 3 × 2 + 4 = 10 O, so write 5 O2.
The result is C3H8 + 5 O2 -> 3 CO2 + 4 H2O. The usual tips: leave elements
that occur in several substances, usually O and H, for last, and finish with a substance made of one
element, because its coefficient changes nothing else. Treat a polyatomic ion that stays intact, such
as SO4 or PO4, as one unit. If a fraction appears, such as 7/2 O2 for ethane, double everything:
2 C2H6 + 7 O2 -> 4 CO2 + 6 H2O.
Examples
Example 1: a metal and an acid. Al + HCl -> AlCl3 + H2 becomes
2 Al + 6 HCl -> 2 AlCl3 + 3 H2. Each side has 2 Al, 6 H and 6 Cl, and a mass of
272.712 g.
Example 2: neutralisation. Ca(OH)2 + H3PO4 -> Ca3(PO4)2 + H2O becomes
3 Ca(OH)2 + 2 H3PO4 -> Ca3(PO4)2 + 6 H2O. With PO4 as a unit: two on the right need 2 H3PO4,
three Ca need 3 Ca(OH)2, and the 12 H on the left make 6 H2O. Each side has a mass of 418.264 g.
Example 3: an ionic redox equation.
MnO4^- + Fe^2+ + H^+ -> Mn^2+ + Fe^3+ + H2O becomes
MnO4^- + 5 Fe^2+ + 8 H^+ -> Mn^2+ + 5 Fe^3+ + 4 H2O. The charge is
−1 + 10 + 8 = +17 on the left and 2 + 15 = +17 on the right.
Subscripts and coefficients
A subscript is part of a formula: it tells how many atoms of an element one unit of the substance contains. A coefficient stands in front of the formula and tells how many units take part. Balancing may change coefficients only, never subscripts. H2O is water and H2O2 is hydrogen peroxide, a different substance. A coefficient multiplies every atom in the formula, including atoms inside brackets: 3 Ca(OH)2 contains 3 Ca, 6 O and 6 H.
Ionic equations and charge balance
A net ionic equation shows only the ions and molecules that change and leaves out the spectator
ions. It must balance twice: in atoms and in charge. The tool adds one more equation, in which each
coefficient is multiplied by the charge of its ion. A half-reaction also contains
electrons: in MnO4^- + 8 H^+ + 5 e^- -> Mn^2+ + 4 H2O the charge is −1 + 8 − 5 = +2 on
both sides. Only the species you type are balanced, so for a redox reaction in acidic solution include
H^+ and H2O yourself, and in basic solution OH^- and H2O.
Why some equations have no unique answer
Usually the equations leave one unknown free, which gives one set of smallest whole numbers. Some
leave two or more. C + O2 -> CO + CO2 describes two independent reactions at once,
C + O2 → CO2 and 2 C + O2 → 2 CO, which can be mixed in any proportion. Both
3 C + 2 O2 → 2 CO + CO2 and 4 C + 3 O2 → 2 CO + 2 CO2 are balanced. The real proportion depends on
conditions such as the oxygen supply. The tool reports this and shows one example; write the
reactions as separate equations instead.
Common mistakes
- Changing a subscript to make the numbers fit. This turns the substance into a different one.
- Not reducing. 4 H2 + 2 O2 → 4 H2O is balanced, but the convention is the smallest whole numbers: 2 H2 + O2 → 2 H2O.
- Balancing atoms but not charge. Fe^3+ + Sn^2+ → Fe^2+ + Sn^4+ has equal atoms, but the charge is +5 on the left and +6 on the right. The correct equation is 2 Fe^3+ + Sn^2+ → 2 Fe^2+ + Sn^4+.
Frequently asked questions
Can it balance redox equations?
Yes. The algebraic method needs no oxidation numbers. Every reactant and product must be in the equation, including H2O, H^+, OH^- or e^- where they take part.
Can coefficients be fractions?
Fractions such as 1/2 O2 appear in thermochemistry, when an equation is written for one mole of a substance. This tool always gives the smallest whole numbers.
Does a balanced equation mean the reaction happens?
No. Balancing only checks atoms and charge, not whether the reaction takes place or which products form.
What do (s), (l), (g) and (aq) mean?
Solid, liquid, gas and aqueous, which means dissolved in water. They do not affect the balancing.
Is my data private?
Yes. The calculation runs in your browser and nothing is uploaded. Your last equation stays in your own browser storage.
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