Tool 02
Type an unbalanced equation to get the smallest whole-number coefficients, with an atom-by-atom and charge check. Ionic equations, electrons and redox reactions balance in one step because the coefficients are solved, not guessed.
Free, no account, and nothing you type leaves your browser.
Solved as a linear system over exact fractions, not by trial and error — so redox equations that resist inspection come out in one step.
Give each species an unknown coefficient:
aCH4 + bO2 → cCO2 + dH2O
Each element must have the same number of atoms on both sides:
The smallest whole numbers that satisfy every equation:
a = 1, b = 2, c = 1, d = 2
Balanced equation:
CH4 + 2O2 → CO2 + 2H2O
Open this example in the toolGive each species an unknown coefficient:
aFe + bO2 → cFe2O3
Each element must have the same number of atoms on both sides:
The smallest whole numbers that satisfy every equation:
a = 4, b = 3, c = 2
Balanced equation:
4Fe + 3O2 → 2Fe2O3
Open this example in the toolGive each species an unknown coefficient:
aFe2+ + bMnO4− + cH+ → dFe3+ + eMn2+ + fH2O
Each element must have the same number of atoms on both sides:
The total charge must also be the same on both sides:
2a − b + c = 3d + 2e
The smallest whole numbers that satisfy every equation:
a = 5, b = 1, c = 8, d = 5, e = 1, f = 4
Balanced equation:
5Fe2+ + MnO4− + 8H+ → 5Fe3+ + Mn2+ + 4H2O
Open this example in the toolConservation of each element becomes one linear equation: the total atoms of that element on the left must equal the total on the right. Stack those into a matrix, reduce it to row-echelon form using exact fractions rather than floating point, and read off the null-space vector — that vector is the set of coefficients. Clearing denominators and dividing by the greatest common divisor gives the smallest whole numbers. It never guesses, so it handles redox equations like permanganate and hydrochloric acid in the same single step as burning hydrogen.
Charges are read with the same rules as in the molar mass calculator, so Fe2+, MnO4- and SO4^2- all work, and e- stands for an electron. As soon as one species carries a charge, the solver adds a row for charge: the total charge of the reactants must equal the total charge of the products. A plus sign separates two species when it stands between spaces or is followed by the next formula, so Fe2+ + MnO4- and Fe2++MnO4- are read the same way.
When --> follows a formula without a space, as in H++OH-->H2O, the first minus is read as that species' charge if the equation balances that way; otherwise --> is read as an arrow. A space before the arrow, or ->, removes the doubt.
Grams per mole and percent composition for any formula, ion or common substance name.
OpenFull and noble-gas notation and an orbital diagram for all 118 elements, plus a trainer.
OpenTwo to four elements in one table, every bar scaled against all 118.
OpenTemperature, energy, pressure, moles and atomic lengths, with exact SI constants.
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