Introductory chemistry is a small number of relationships applied to a very large number of compounds, and the difficulty is almost never the algebra. It is the bookkeeping: whether the volume was in litres, whether the temperature was absolute, whether the subscript was meant to be a 2 or a 3, and whether the number you were given is a mass or a count. Almost every worked problem that goes wrong went wrong at a conversion, not at the chemistry. This guide covers the relationships in the order a problem uses them, explains the conventions that are usually left implicit in a textbook, and points at the calculator for each step. Every tool here runs in your browser against a bundled periodic table, so nothing you type is uploaded.
Moles are a count, and the number is only strange because of what it was chosen to do
A mole is a count the way a dozen is a count: 6.02214076 × 10²³ particles, which is Avogadro's number to its exact defined value. It is not a round number because it was not chosen to be one — it was chosen so that one mole of carbon-12 weighs exactly twelve grams. That single decision is what makes the mole useful, because it bridges the two things a chemist can actually do: weigh something on a balance, and reason about how many particles react. A balance gives grams, a reaction is governed by particles, and the mole is the exchange rate between them. Once that is clear, the three conversions that follow are all the same conversion written three ways — mass to moles, moles to particles, and back — which is what the Mole Calculator, the Grams to Moles Converter and the Molecules to Moles Converter are, in the order they are usually needed.
Molar mass is the conversion step everyone skips, and it is where the arithmetic lands
Molar mass is the mass of one mole of a substance in grams per mole, and for a formula it is just the sum of each element's standard atomic weight multiplied by how many atoms of that element the formula contains. Glucose is 6 × 12.011 (carbon) + 12 × 1.008 (hydrogen) + 6 × 15.999 (oxygen) = 180.156 g/mol. Read that sum again: every term is a count times a weight, so a wrong subscript moves the answer by a whole atomic mass. That is why the Molar Mass Calculator prints the breakdown term by term rather than only the total — a figure of 180.16 is checkable, and a figure of 160.2 is wrong in a way the table makes obvious. It is also the point at which significant figures become a judgement call rather than an afterthought: four decimal places is more precision than any textbook problem carries, so the number you finally write down should be rounded to the figures your data actually had, which is what the Significant Figures Calculator in Units & Numbers is for.
Read the formula before you trust any number computed from it
H2O and H2O2 are different compounds, and the difference is one digit. Written formulas also carry structure that a careless read loses: Cu(NO3)2 is one copper, two nitrogens and six oxygens because the subscript outside the bracket multiplies everything inside it; K4[Fe(CN)6] nests a bracket around a parenthesised group; and CaSO4·2H2O, a hydrate, means the water part is multiplied by two. The formula field on these pages shows its own parse as you type — element by element, with a hydrate marked as such — so a typo is visible before it reaches the arithmetic, and a symbol that is not an element is refused rather than silently counted as zero. This is the cheapest check in the category and the one most worth making.
Balancing an equation is linear algebra, not trial and error
A balanced equation is a set of whole numbers that makes the count of every element agree on both sides — which is exactly the statement that the coefficient vector lies in the null space of the element-count matrix. Solving that matrix rather than guessing at coefficients has a practical payoff: the tool cannot get stuck, it always finds the smallest whole-number solution (4Fe + 3O2 → 2Fe2O3, not 8Fe + 6O2 → 4Fe2O3), and it can tell you the two cases trial and error hides. An equation whose two sides contain different elements has no balance at all, because a balance is a conservation statement and there is nothing to conserve. And an equation like C + O2 → CO + CO2 has a whole family of balances, because it is really two reactions added together — there is no single answer to give, and the balancer says so instead of picking one. Coefficients you type into the box are ignored and re-derived: the tool's job is to find them, and printing back an unbalanced input as balanced would be a lie.
The ratio chain: percent composition, empirical formula, molecular formula, stoichiometry, limiting reagent
These five tools are one argument in five steps, and doing them out of order is the usual source of confusion. Percentage composition by mass comes first: for each element, its mass contribution divided by the molar mass, so water is 11.19% hydrogen and 88.81% oxygen. Divide each percentage by that element's atomic mass and you have a mole ratio; divide every result by the smallest and round to whole numbers and you have the empirical formula — the simplest ratio, CH2O for a sugar analysis of 40.00% C, 6.71% H, 53.29% O. If you also know the compound's measured molar mass, dividing it by the empirical formula's mass gives the multiplier: 180.16 ÷ 30.03 is 6, so the molecular formula is C6H12O6. Stoichiometry then uses the balanced equation's coefficients as the exchange rate between species — 4 mol of H2 in 2H2 + O2 → 2H2O makes 4 mol of water — and the limiting reagent is whichever reactant runs out first. That one deserves its own sentence: the limiting reagent is the one with the smallest amount divided by its own coefficient, not the smallest amount. Two moles of nitrogen against three of hydrogen is hydrogen-limited, because the equation needs three hydrogens per nitrogen and the ratios are 2 and 1.
Solutions: concentration is per litre, and the units are where the marks go
Molarity is moles of solute per litre of solution, so it is the first place a problem can go wrong without any chemistry being wrong: 500 mL is 0.5 L, and 5.844 g of sodium chloride (M = 58.44 g/mol) made up to 500 mL is 0.2 mol/L. Dilution is the same relationship rearranged — M₁V₁ = M₂V₂, because the moles of solute do not change when you add solvent — and it takes exactly three of its four values, which is why the calculator asks you to leave precisely one field blank and tells you how many you have given. Beer–Lambert, A = εlc, is the spectroscopic cousin of the same idea: absorbance is proportional to concentration, and the constant of proportionality ε belongs to the dye rather than to your experiment, which is why its units (L·mol⁻¹·cm⁻¹) are printed next to the field. A cuvette is 1 cm, and almost every student who gets an absurd concentration has typed the path length in millimetres.
Acids and gases: two constants, and both of them have units
pH is the negative logarithm of the hydrogen-ion concentration, which is why the scale runs backwards — more hydrogen ions means a smaller number. From any one of pH, pOH, [H⁺] or [OH⁻] the other three follow, because pH + pOH = 14 and [H⁺][OH⁻] = 1 × 10⁻¹⁴. That constant is the one caveat worth knowing: it is measured at 25 °C and drifts with temperature, so neutrality is pH 7 in a laboratory and rather less than that in a hot solution. The gas laws have the same shape of trap. PV = nRT relates four quantities, and the value of R decides the units everything else must be in — 0.082057366 L·atm·mol⁻¹·K⁻¹ wants litres, atmospheres and kelvin, so 101.325 kPa has to be converted and 0 °C has to become 273.15 K before it is used. The unit selectors on the Ideal Gas Law Calculator exist for exactly that. Boyle's, Charles's and Gay-Lussac's laws are the combined law with one variable held constant, which is why they are presented as one selector rather than four pages: P₁V₁/T₁ = P₂V₂/T₂ covers all of them, and the field the law does not use is hidden rather than left there inviting a number that has nowhere to go.
Reporting the answer: the working matters more than the last digit
Every tool in this category shows the formula with your numbers already substituted — n = 25 g ÷ 18.015 g/mol, not only 1.3877 — for a reason that is pedagogically simple and practically useful. A number nobody can retrace cannot be checked, and in a subject where a single misplaced subscript propagates through five steps, being able to see which step went wrong is worth more than the answer. Rounding is the other half of reporting well: carry full precision through the calculation and round once, at the end, to the figures your data supports, rather than rounding at every step and accumulating the error. And sanity-check the magnitude before you believe the number, which is easier than it sounds because chemistry has landmarks — a molar mass is tens to hundreds of grams per mole, a molarity is usually between 0.001 and 1, and a pH outside 0–14 in ordinary aqueous solution means something upstream is wrong.