Formula Calculators

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A formula in science is a symbolic representation of a substance, relationship, or process using letters, numbers, and mathematical operators. In chemistry, molecular formulas show the exact number and type of atoms in one molecule (C₆H₁₂O₆ for glucose). Empirical formulas show the simplest whole-number ratio of atoms (CH₂O for glucose). Structural formulas show bond arrangements. Mathematical formulas express quantitative relationships between variables (A = πr²; E = mc²). In biology, formulas describe processes (GTR = NAR × LAR; N̂ = MC/R). A formula is the compact, universal language of quantitative science.

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Types of Chemical Formulas

  • Molecular formula: Exact atom count per molecule (C₆H₁₂O₆ = glucose; H₂SO₄ = sulfuric acid)
  • Empirical formula: Simplest whole-number ratio of atoms (CH₂O for glucose; HO for H₂O₂)
  • Structural formula: Shows bonds between atoms (Lewis structure, skeletal formula)
  • Condensed structural formula: CH₃CH₂OH (ethanol) — shows bonding groups without full structural diagram

Calculating Molar Mass from Molecular Formula

Sum the atomic masses (g/mol) of all atoms in the formula. Example: H₂SO₄: 2(1.008) + 32.06 + 4(16.00) = 2.016 + 32.06 + 64.00 = 98.076 g/mol.

Empirical Formula from Percent Composition

Divide mass% by atomic mass → get moles ratio → divide by smallest → multiply to get whole numbers. Example: 40.0% C, 6.7% H, 53.3% O: C: 40.0/12.01 = 3.33; H: 6.7/1.008 = 6.65; O: 53.3/16.00 = 3.33. Divide by 3.33: C:H:O = 1:2:1 → CH₂O.

Glossary

Molecular Formula
Shows the exact number and type of atoms per molecule (e.g., C₆H₁₂O₆ for glucose); molar mass = sum of (atomic mass × count) for all atoms; distinct from empirical formula (simplest ratio).
Empirical Formula
The simplest whole-number atom ratio in a compound; determined from percent composition; CH₂O is the empirical formula of both glucose and acetic acid.
Molar Mass
The mass of one mole of a compound (g/mol); calculated from molecular formula as sum of (atomic mass × number) for all atoms; numerically equal to molecular mass in Daltons.

Frequently Asked Questions

Molecular formula: shows the exact number and type of atoms in one molecule. Empirical formula: shows the simplest whole-number ratio of atoms. Examples: glucose molecular formula C₆H₁₂O₆; empirical formula CH₂O (divide all subscripts by 6). Hydrogen peroxide molecular formula H₂O₂; empirical formula HO. Acetic acid molecular formula C₂H₄O₂; empirical formula CH₂O (same as glucose's empirical formula — different molecules can have the same empirical formula!). To find the molecular formula from empirical: determine the actual molar mass (from mass spectrometry); molar mass / empirical formula mass = integer n; multiply empirical formula subscripts by n.

Molar mass = sum of (atomic mass × number of atoms) for all elements. Example: Ca(OH)₂ = calcium hydroxide: Ca: 1 × 40.08 = 40.08. O: 2 × 16.00 = 32.00. H: 2 × 1.008 = 2.016. Molar mass = 40.08 + 32.00 + 2.016 = 74.10 g/mol. Note: parentheses mean the entire group inside is multiplied by the subscript outside. Ca(OH)₂ means 1 Ca, 2 O, and 2 H (not 1 Ca, 1 OH, and 2). Use periodic table atomic masses for accuracy; atomic masses are rounded differently in different sources.

Method: assume 100 g sample (so mass% becomes grams). Divide grams by atomic mass to get moles. Divide all moles by the smallest mole value to get ratio. If ratios are not whole numbers: multiply all by smallest integer to convert to whole numbers. Example: compound is 72.37% C, 10.84% H, 16.79% O: C: 72.37/12.01 = 6.026 mol; H: 10.84/1.008 = 10.754 mol; O: 16.79/16.00 = 1.049 mol. Divide by 1.049: C = 5.74; H = 10.25; O = 1.00. Multiply by 4: C = 23; H = 41; O = 4. Empirical formula: C₂₃H₄₁O₄.

Mathematical formulas express quantitative relationships between variables in compact, universal form: Physics: F = ma (Newton's second law); E = mc² (mass-energy equivalence); PV = nRT (ideal gas law). Chemistry: pH = −log[H⁺]; ΔG = ΔH − TΔS; Keq = [products]/[reactants]. Biology (ecology): N(t) = N₀e^(rt); N̂ = MC/R (mark-recapture); RGR = NAR × LAR. Biology (genetics): p² + 2pq + q² = 1 (HWE). Biology (physiology): GFR = Ucr × V / Pcr (kidney clearance). Mathematics: A = πr²; z = (X − μ)/σ. Each formula encodes a deep quantitative insight that would take paragraphs of words to describe.