Chemical Equation Balancer

📖 About This Tool

Balancing an equation is solving a linear system. Each element must have the same atom count on both sides; write those conditions as equations and find the smallest integer solution. Doing it by eye works until the coefficients get large: permanganate with concentrated hydrochloric acid comes out as 2, 16, 2, 2, 5, 8, which takes several minutes of trial and error. Linear algebra gives it in milliseconds.

The tool splits the equation into left and right sides, parses each formula to count atoms per element, handles nested parentheses such as Ca(OH)2, accepts charged ions like Fe3+ or SO4^2-, and recognises common organic notation. It then builds the conservation equations, solves for the null space by Gaussian elimination, clears denominators and reduces to the smallest whole numbers.

Afterwards it checks the answer instead of trusting it: coefficients are substituted back and every element is counted on both sides. Only an exact match is reported; otherwise you get a clear failure message. That check catches real mistakes, such as a misspelled element symbol, an unclosed parenthesis, or an equation whose two sides do not even contain the same elements and therefore has no solution at all.

Output includes the balanced equation, the coefficient for each species and a per-element atom count table for both sides, so you can copy it into homework or verify your own hand calculation. All of it runs locally in the browser, with no network request and nothing uploaded.

Take permanganate with hydrochloric acid as an example. Six species give a system with four element constraints and one free variable, and the null space yields 2, 16, 2, 2, 5, 8 once denominators are cleared. Checking that by hand costs a minute of arithmetic; here it runs in milliseconds and repeats after every edit, so a mistyped subscript surfaces as a conservation failure rather than a plausible looking set of wrong numbers.

✨ Features

• Smallest integer coefficients: null space solved and reduced to lowest whole numbers.
• Nested parentheses: parses formulas like Ca(OH)2 and Fe2(SO4)3 correctly.
• Ionic charges: supports Fe3+, SO4^2- and similar, so ionic equations balance too.
• Conservation check: every element recounted after balancing, mismatches reported as errors.
• Comparison table: atom totals per element on each side for easy verification.
• Built-in examples: a dozen classic equations loadable with one click.

🚀 How to Use

1. Type the unbalanced equation, separating the two sides with = or an arrow.
2. Join species with + and write formulas properly, with capitalised element symbols.
3. Press balance: the result appears below with a coefficient for each species.
4. Read the element table and confirm the atom counts match on both sides.
5. Use the example button to load a built-in equation and try it out.

⚠️ Notes

• Capitalisation: element symbols are case sensitive; CO and Co are different substances.
• Separators: use = or an arrow between sides and + between species only.
• No solution: when the two sides contain different elements the tool says so rather than inventing numbers.
• Unit coefficients: a coefficient of 1 is omitted, matching chemical convention.
• Study aid only: results follow atom conservation and say nothing about whether a reaction actually occurs.