Academics · Study Skills

Balance it, then see why it balances.

Type an equation the way you would write it in your notes. The balancer shows the coefficients, counts every atom on both sides, and writes out the algebra it used. Then practice on fifteen equations with feedback element by element.

Balance an equationWhat you get

The balancer

Write formulas with capital letters for elements, ^ for charges (Fe^3+, SO4^2-) and a dot for hydrates. Nothing you type leaves this browser.

Loading the balancer. If nothing appears, turn on JavaScript.

What you get

Academics · Study SkillsFree

What you finish with
A balanced equation with the smallest whole-number coefficients, the atom count for each element on both sides, the system of equations behind it, a mass check, and practice progress on fifteen equations; a printable worksheet with an answer key.
Who it is for
Middle and high school chemistry and physical science students, students reviewing for a chemistry test, and the teachers and tutors who want a worksheet or a quick check.
Format
Browser tool with a practice set. Works on a phone or computer. Print a result or a worksheet with its answer key, save a .csv of your history, and move progress between devices with a file.
Access
Free. No account and no sign-in. Equations and progress stay in this browser; nothing is sent to Caveat.
Where it lives
The Study Skills space in Caveat Academics.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Type the reactants, an arrow (-> or =), and the products, with a plus sign between formulas. The pad under the box adds the arrow, a hydrate dot or a charge sign.
  2. Press Balance. Read the coefficients, then check the atom count: every element has the same number on both sides.
  3. Open "How it was solved" to see the one equation per element and the smallest whole numbers that satisfy them all.
  4. Switch to Practice. Type coefficients and press Check; each element turns blue when it matches. Hints come in three steps.
  5. Print a worksheet with the answer key for homework or a quiz.

Balance an equation

How the balancer works

The algebra method chemists use for hard equations, done with exact fractions so nothing is rounded.

From formulas to coefficients

  • Each formula is read into an atom count. Parentheses and brackets multiply what is inside; a hydrate dot adds the water (CuSO4·5H2O has 9 oxygen atoms).
  • Each unknown coefficient gets a letter. For every element, the atoms on the left must equal the atoms on the right, which gives one equation per element. For ions, the total charge must match too.
  • The system is solved exactly with whole-number fractions, then scaled to the smallest whole numbers. If there is no positive solution, or more than one independent one, the page says why instead of guessing.
  • State symbols such as (aq) or (g) are allowed and ignored. Numbers typed in front of formulas are set aside.

What balancing does not tell you

  • A balanced equation is not proof the reaction happens. The balancer checks atoms and charge, not chemistry: it will balance a reaction that never occurs.
  • Subscripts are part of the substance; only coefficients change. Changing H2O to H2O2 makes a different chemical.
  • For redox in acid or base, chemists often balance half-reactions with electrons first. The balancer solves the whole system at once, which gives the same result when a unique answer exists.

Checked when the page is built: a separate Python balancer, using exact fractions, solves every practice equation and example and must agree with the answer key. Burning propane comes out as C3H8 + 5O2 → 3CO2 + 4H2O, and with standard atomic weights both sides weigh 204.09 g for those amounts in moles. The dichromate half-reaction balances as Cr2O72− + 14H+ + 6e− → 2Cr3+ + 7H2O, with a net charge of +6 on both sides.

Sources

  1. OpenStax, Chemistry 2e (Rice University, 2019), section 4.1, "Writing and Balancing Chemical Equations", and section 17.1, "Review of Redox Chemistry", for half-reactions in acidic and basic solution (openstax.org, CC BY 4.0).
  2. IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), standard atomic weights, abridged to five significant figures, with conventional values for elements whose weight is given as an interval (ciaaw.org).
  3. Linear-algebra method for balancing equations: the coefficients form the null space of the element-by-species matrix. See, for example, the treatment in introductory linear algebra texts such as David C. Lay, Linear Algebra and Its Applications, section 1.6, "Applications of Linear Systems".

The balancer checks that atoms and charge are conserved; it does not predict whether a reaction takes place or what its products are. Practice equations are written by Caveat Academic Services and may be copied for class. Support: team@caveatacademic.com.