molecalculator

Method, atomic weights and constants

The atomic weights, constants, unit factors and rounding behind every calculator, and how they are checked.

This page lists the data, constants, unit factors and rounding behind every calculator on molecalculator.com, so you know exactly what a number means and when it will differ from a value in your textbook or lab manual.

1. Atomic weights and molar mass

The molar mass calculator adds up the standard atomic weights of the atoms in a formula: M = Σ (number of atoms × atomic weight). The weights are the IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW) standard atomic weights in their abridged form, rounded to five significant figures (the 2021 table, with the 2024 revision of zirconium to 91.222). Some elements vary in isotopic composition in nature, so IUPAC gives their weight as an interval; for these (hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, argon, bromine, thallium and lead) the abridged single value is used, for example H 1.008, C 12.011, O 15.999, S 32.06 and Cl 35.45.

  • Elements without a characteristic terrestrial isotopic composition (Tc, Pm, Po, At, Rn, Fr, Ra, Ac and every element after uranium) have no standard atomic weight, so the calculator refuses them rather than guess an isotope. Bismuth, thorium, protactinium and uranium have no stable isotopes but do have standard atomic weights, and they are used.
  • D (deuterium, hydrogen-2) is accepted with the atomic mass of 2H, 2.0141 u.
  • Formulas: element symbols with whole-number counts, brackets ( ) [ ] { } with a count after them, and hydrate parts joined by · (or a dot or *) with an optional multiplier, as in CuSO4·5H2O or CaSO4·0.5H2O. A number in front of the whole formula multiplies it. Charges are left out: an electron adds only 0.00055 g/mol.
  • The molar mass is shown to three decimals and each element’s share to two; the last digit is not always significant, because many weights are known only to four or five figures.

2. Constants

  • Avogadro constant NA = 6.02214076 × 1023 mol−1 (exact in the SI since 2019).
  • Molar gas constant R = 8.31446261815324 J/(mol·K) (exact), equal to 0.0831446 L·bar/(mol·K) and 0.0820574 L·atm/(mol·K).
  • Planck constant h = 6.62607015 × 10−34 J·s, speed of light c = 299,792,458 m/s and elementary charge e = 1.602176634 × 10−19 C (all exact).
  • Unified atomic mass unit 1 u = 1.66053906892 × 10−27 kg (CODATA 2022).
  • Ion product of water Kw = 1.0 × 10−14 at 25 °C (pH + pOH = 14 at that temperature only).
  • Where a value depends on the substance or the conditions (a pKa, a specific heat, van der Waals a and b), the calculator makes it an input with a stated default, so you can enter the value from your own reference.

3. Units and conversion factors

  • Temperature: T(K) = t(°C) + 273.15.
  • Pressure: 1 atm = 101.325 kPa; 1 bar = 100 kPa; with R in J/(mol·K) and volume in litres, pressure comes out in kPa (1 J/L = 1 kPa).
  • Volume: 1 L = 1000 mL = 1 dm3; amount: 1 mol = 1000 mmol = 106 µmol; concentration: 1 M = 1 mol/L = 1000 mM = 106 µM.
  • Energy: 1 cal = 4.184 J (thermochemical calorie); 1 eV = 1.602176634 × 10−19 J.

4. Assumptions the pages name

  • Gases are ideal unless the page uses the van der Waals equation.
  • Strong acids and bases dissociate completely; buffer pH uses the Henderson–Hasselbalch equation with concentrations in place of activities, which is close only for dilute buffers.
  • Solution volumes are the final volume of the solution, not the volume of solvent added; volumes are not assumed to add exactly when liquids are mixed.
  • Reagents are pure unless a page asks for purity, and the formula you use must match the form you weigh (hydrate or anhydrous).

5. Rounding and number format

Each result states how it is rounded. Very large or very small values (above 109 or below 10−4) are written in scientific notation with four significant figures, for example 6.022 × 1023. When a fixed number of decimals would hide most of a value, more decimals are shown automatically. You can type numbers as 0.0025, 2.5e-3 or 2.5 × 10^-3.

6. How the calculators are checked

The molar mass tool runs the same rules in your browser and on the server, and both are tested against a third, separately written implementation on more than 60 formulas and invalid inputs, with the expected element counts written out by hand. The core calculators are each checked against an independent calculation of their worked example. Every newly published calculator is re-checked automatically; a page whose calculator does not reproduce its worked example has its calculator switched off until it is fixed. Report an error.

7. Safety and scope

The site is for study and lab planning. It gives no procedures for hazardous preparations, no medication or dosing calculations and no handling advice. Follow your method, the safety data sheet of each chemical and your supervisor. See the disclaimer.