Molar Mass & Composition Calculator

Molar mass with uncertainty, mass % per element and the empirical formula from percentages.

Try an example: Water · Copper(II) sulfate pentahydrate · Several formulas: complex salt, phosphate, labelled CO₂ · Ions: permanganate and sulfate · Glucose from its elemental analysis · Iron oxide from 69.94 % iron

More about this tool

How it works

Type a chemical formula — with nested brackets, hydrate water, charges or isotopes — and get its molar mass from the current IUPAC standard atomic weights with the combined uncertainty, the formula in Hill order and the mass and atom percentage of every element. Up to ten formulas at once. The second mode turns mass percentages from an elemental analysis into the empirical formula and, with a molar mass, the molecular formula. Part of the Proofline math notebook.

The formula is read by Proofline’s own parser: element symbols, counts, nested ( ) and [ ] groups, hydrate parts after · * or a dot (5H2O counts five times), a trailing charge, isotopes written ^13C (D and T for ²H and ³H) and state symbols, which are dropped.
Molar mass M = Σ nᵢ·Aᵢ with the CIAAW abridged standard atomic weights Aᵢ (five significant figures where nature allows). Its uncertainty is √Σ(nᵢ·Uᵢ)²: atoms of one element share the same weight (fully correlated), different elements are independent. The value is rounded to the first significant digit of that uncertainty, as CIAAW does.
Ions subtract z electron masses (0.000549 g/mol each). Isotopes use AME2020 nuclide masses for common nuclides, otherwise the mass number with a warning. Elements without stable isotopes (Tc, Pm, Po … ) have no standard atomic weight and must be written as a specific isotope.
Empirical formula: moles per 100 g are mass % ÷ Aᵢ, divided by the smallest; the smallest multiplier from 1 to 12 that brings every ratio within 0.1 of a whole number gives the counts. With a molar mass, the molecular formula is the nearest whole multiple of the empirical formula.

Standard atomic weights describe normal terrestrial materials; isotopically enriched or unusual geological samples can differ beyond the stated uncertainty. Nothing here is advice on handling chemicals safely.

Sources

CIAAW / IUPAC: Abridged Standard Atomic Weights (latest table, incl. the 2021 revisions) (IUPAC Commission on Isotopic Abundances and Atomic Weights)
T. Prohaska et al.: Standard atomic weights of the elements 2021 (IUPAC Technical Report), Pure Appl. Chem. 94 (2022) (IUPAC / De Gruyter)
M. Wang et al.: The AME 2020 atomic mass evaluation (II), Chinese Physics C 45 (2021) 030003 (IOP Publishing)
CODATA recommended values of the fundamental physical constants (Avogadro and molar gas constants, electron mass) (NIST)

Part of Proofline

Proofline Math notebook

Solve, graph, test and visualise in one notebook — with data, findings and a report.

Open Proofline

Related tools

Chemical Equation Balancer & Stoichiometry – Balance any reaction or redox equation exactly, then find the limiting reagent and yields.
Solution, Gas Law & pH Calculator – Molarity, dilution, mass ↔ moles ↔ particles, ideal gas with partial pressures, pH and buffers.
Step-by-Step Equation Solver – Solve linear, quadratic, rational and radical equations or linear systems with every step shown.
Math Workbench – Simplify, factor, differentiate, integrate, solve, take limits, series and plots in one box.

How to calculate molar mass, composition and empirical formulas

Get the molar mass of any formula with its IUPAC uncertainty and the mass percentage of every element, or work out an empirical formula from an analysis.

What it is for

Most chemistry calculations start with a molar mass. This calculator reads a formula the way you would write it on paper — nested brackets such as K4[Fe(CN)6], hydrate water such as CuSO4·5H2O (a * or a dot works too), charges such as SO4^2- or Fe+3, and isotopes such as ^13C, D or T — and returns the molar mass, the formula in Hill order and how much of the mass each element contributes. You can enter up to ten formulas, one per line.

The second mode works the other way round. Enter the mass percentages from an elemental analysis and you get the empirical formula; add a measured molar mass and you also get the molecular formula.

Atomic weights are the abridged standard atomic weights of IUPAC's Commission on Isotopic Abundances and Atomic Weights. The calculator does not look up compound names: type the formula.

Worked example

Copper(II) sulfate pentahydrate is the classic blue crystal. Entering CuSO4·5H2O gives a molar mass of 249.68 ± 0.02 g/mol, Hill formula CuH10O9S and 21 atoms per formula unit. The composition table shows copper at 25.451 % of the mass, sulfur at 12.841 %, oxygen at 57.671 % and hydrogen at 4.037 %. Water alone, H2O, comes out as 18.015 ± 0.001 g/mol.

Three formulas at once — Ca3(PO4)2, K4[Fe(CN)6] and ^13CO2 — give 310.17, 368.35 and 45.001 g/mol. In the labelled carbon dioxide the ¹³C row uses the nuclide mass 13.0033548 instead of the standard weight of carbon.

For the empirical mode, an iron oxide with Fe 69.94, O 30.06 gives mole ratios of 1 : 1.50022. The smallest multiplier that makes both whole numbers is 2, so the formula is Fe2O3 (159.687 g/mol). Glucose's analysis C 40.0, H 6.71, O 53.29 gives CH2O, and with a molar mass of 180.16 g/mol the molecular formula C6H12O6.

How to read the result

The molar mass is rounded to the first significant digit of its uncertainty, the way IUPAC quotes atomic weights. The ± value combines the uncertainties of the atomic weights: atoms of the same element share one weight, so their uncertainties add up directly, while different elements are combined in quadrature. It reflects natural isotope variation, not the purity of your sample.

Mass % tells you which element dominates the weight; atom % counts atoms instead. For ions, the molar mass includes the tiny mass of the added or removed electrons, so it can differ from printed tables in the fourth decimal place.

In the empirical mode, the ratio table shows each step: moles in 100 g, the ratio to the smallest, and the ratio times the multiplier. Values close to whole numbers confirm the formula.

Tips and common mistakes

Element symbols are case sensitive: Co is cobalt, CO is carbon monoxide.
Write Fe^3+ or Fe+3 for the iron(III) ion. Fe3+ means three iron atoms with one positive charge, and the calculator warns you.
Do not type a leading coefficient such as 2H2O; a formula starts with an element or a bracket.
Technetium, promethium and the heavy radioactive elements have no standard atomic weight. Write a specific isotope such as ^99Tc.
If your percentages do not add up to about 100 %, an element (often oxygen) is probably missing from the list.

FAQ

Why is the molar mass of water 18.015 and not 18.02 or 18.0153?

It is given to the precision the atomic weights support. Hydrogen's standard weight is 1.0080 ± 0.0002 and oxygen's 15.999 ± 0.001, which limits water to three decimals.

Can I use it for ions?

Yes. Add the charge at the end, for example SO4^2-, NH4+ or MnO4-. The result lists the charge and corrects for the electron mass.

What if no multiplier gives whole numbers?

The calculator tries multipliers from 1 to 12 and warns you if none brings every ratio within 0.1 of a whole number. Rounding errors in the analysis are the usual cause.

Is this the same calculation as in Proofline?

Yes. The chemistry cell of the Proofline notebook runs the same engine in your browser, so the numbers are identical.

Guide last updated: November 2, 2026

For scripts and AI agents

JSON API: POST https://prooflinemolarmass.usefulweb.site/api/v1/calculate (same calculation as this page)
Interface description: OpenAPI 3.1 · AI guide: llms.txt
MCP server (Streamable HTTP): https://prooflinemolarmass.usefulweb.site/mcp · tool name proofline_molar_mass

Example request

curl -s -X POST https://prooflinemolarmass.usefulweb.site/api/v1/calculate \
  -H 'content-type: application/json' \
  -d '{"formulas":"H2O"}'

Feedback · ideas & bug reports welcome