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Average Atomic Mass Calculator

Ready to calculate
M = Σ (abundance × mass).
2-8 isotopes.
% or fraction input.
100% Free.
No Data Stored.

How it Works

01Pick the Number of Isotopes

2-8 isotopes. Most elements have 1-3 stable isotopes; tin (Sn) has the most at 10.

02Enter Abundance + Mass

Natural abundance as % (or fraction) and atomic mass in amu (= u = Da) per isotope.

03Apply M = Σ (a × m)

Weighted average: multiply each isotope's mass by its fractional abundance and sum.

04Get Avg Mass + Per-Isotope Contribution

Output: weighted-average atomic mass (= the periodic-table value) plus each isotope's contribution.

What is an Average Atomic Mass Calculator?

Average atomic mass is the weighted-mean mass of an element's naturally-occurring stable isotopes — and it's the value that appears under each element symbol on the periodic table. It is NOT the simple arithmetic mean of isotope masses; it is weighted by the natural abundance of each isotope. Chlorine (Cl) is the textbook example: ³⁵Cl (mass 34.969 amu, 75.78% natural abundance) and ³⁷Cl (mass 36.966 amu, 24.22% abundance) give average atomic mass = 0.7578 × 34.969 + 0.2422 × 36.966 = 35.45 amu, the value tabulated in every periodic table.

Our Average Atomic Mass Calculator implements the standard identity M_avg = Σ (fractional abundance × isotope mass), summed across up to 8 isotopes (most elements have 1-3 stable isotopes; tin Sn has the most at 10). The calculator accepts abundance as either percentage (%) or fraction (0-1) — auto-converted — and atomic masses in amu (= u = Da), the unified atomic mass unit defined as exactly 1/12 the mass of a ¹²C atom. Numerically, amu = g/mol for any species, so the average atomic mass equals the molar mass.

Output: the weighted-average atomic mass plus a per-isotope contribution panel showing each isotope's mass × abundance, contribution amount, and percentage of the total — with a visual bar for each isotope. Smart warnings flag cases where the entered abundances don't sum to 100% (signals incomplete data) and unphysical isotope masses (outside the 1-300 amu range covering all known stable isotopes). Designed for general-chemistry students learning isotopes and the periodic table, AP/IB Chemistry coursework, instructors generating problem sets, mass-spec analysts working with isotopic compositions, and anyone needing a fast weighted-mean atomic mass calculation — runs entirely in your browser, no account, no data stored.

Pro Tip: Pair this with our Mole Calculator for stoichiometry, our Mass Percent Calculator for percent composition, our Grams to Moles Calculator for forward conversions, or our Molarity Calculator for solution preparation.

How to Use the Average Atomic Mass Calculator?

Pick the Number of Isotopes (2-8): match your problem's isotope count. Most elements have 1-3 stable isotopes (H 2, He 2, Li 2, C 2, N 2, O 3, S 4, Ca 6, Sn 10 — the maximum). For a problem covering only the major isotopes, use the smaller subset; for high-precision work include all stable isotopes.
Enter Abundance for Each Isotope: as either percent (%) or fraction (0-1) — pick the unit per isotope row. Both work: 75.78% and 0.7578 are equivalent. The calculator auto-converts. Source: IUPAC CIAAW (Commission on Isotopic Abundances and Atomic Weights), CRC Handbook, NIST Atomic Weights Database.
Enter Mass for Each Isotope: in amu (atomic mass units). amu = u (unified atomic mass unit) = Da (dalton). Defined as exactly 1/12 the mass of a ¹²C atom. Source: AME2020 (Atomic Mass Evaluation), NIST Nuclear Data Sheets, CRC Handbook of Chemistry and Physics.
Apply M_avg = Σ (a × m): the calculator multiplies each isotope's mass by its fractional abundance (= percentage / 100) and sums. Worked example for chlorine: 0.7578 × 34.969 + 0.2422 × 36.966 = 26.50 + 8.953 = 35.45 amu — matches the periodic-table value.
Verify Abundances Sum to 100%: the calculator displays Σ abundances; if it deviates from 100% by more than 0.5%, you're likely missing an isotope or have a transcription error. Re-check.
Read the Per-Isotope Contribution Panel: each isotope's contribution (abundance × mass) and its share of the total. Useful for understanding why the average is closer to the most-abundant isotope mass than to the simple arithmetic mean.
Compare to the Periodic Table: for a known element (Cl, Ne, Mg, Cu, etc.), the result should match the periodic-table value within 0.01-0.1 amu. Discrepancies indicate either incomplete isotope set, wrong abundance values, or wrong masses (especially for elements with isotopic-composition variation like H, Li, B, C, N, O — IUPAC reports interval values).

How is average atomic mass calculated?

The average atomic mass formula is one of the cleanest applications of weighted averaging — the periodic-table value is the weighted mean of isotope masses, with weights equal to natural abundances. The math is trivial; the conceptual point (weighted vs arithmetic mean) is what general-chemistry courses are really testing.

References: IUPAC CIAAW (Commission on Isotopic Abundances and Atomic Weights), 2021 standard atomic weights; AME2020 Atomic Mass Evaluation (Wang et al.); NIST Atomic Weights and Isotopic Compositions Database.

Core Formula

M_avg = Σ (fractional abundance_i × isotope mass_i)

Where the sum is over all naturally-occurring stable isotopes. Fractional abundance = percentage / 100 (so 75.78% → 0.7578). All isotope masses must be in the same unit (amu/u/Da are all equivalent and interchangeable).

Worked Example — Chlorine (Cl)

Two stable isotopes: ³⁵Cl and ³⁷Cl.

  • ³⁵Cl: mass = 34.96885 amu, abundance = 75.78%.
  • ³⁷Cl: mass = 36.96590 amu, abundance = 24.22%.
  • M_avg = 0.7578 × 34.96885 + 0.2422 × 36.96590 = 26.503 + 8.953 = 35.45 amu.
  • Periodic-table value: 35.45 ✓ exact match.
  • Note the average is closer to ³⁵Cl mass (75% weight) than to the arithmetic mean of 35.97 — weighted averaging matters.

Worked Example — Magnesium (Mg)

Three stable isotopes: ²⁴Mg, ²⁵Mg, ²⁶Mg.

  • ²⁴Mg: 23.985 amu, 78.99% — most abundant.
  • ²⁵Mg: 24.986 amu, 10.00%.
  • ²⁶Mg: 25.983 amu, 11.01%.
  • M_avg = 0.7899 × 23.985 + 0.1000 × 24.986 + 0.1101 × 25.983 = 18.946 + 2.499 + 2.861 = 24.305 amu.
  • Periodic-table value: 24.305 ✓.

Worked Example — Copper (Cu)

Two stable isotopes: ⁶³Cu and ⁶⁵Cu.

  • ⁶³Cu: 62.9296 amu, 69.17%.
  • ⁶⁵Cu: 64.9278 amu, 30.83%.
  • M_avg = 0.6917 × 62.9296 + 0.3083 × 64.9278 = 43.529 + 20.018 = 63.546 amu.
  • Periodic-table value: 63.546 ✓.

Stable Isotope Counts for Common Elements

  • Monoisotopic (1 stable isotope, 21 elements): Be, F, Na, Al, P, Sc, Mn, Co, As, Y, Nb, Rh, I, Cs, Pr, Tb, Ho, Tm, Au, Bi (the last has only one observed but technically radioactive at long T₁/₂).
  • 2 stable isotopes (15 elements): H, He, Li, B, C, N, Cl, V, Cu, Ga, Br, Ag, Sb, La, Lu.
  • 3 stable isotopes (8 elements): O, Ne, Mg, Si, K, Ar, Cr, Ce.
  • 4 stable isotopes (8 elements): S, Ca, Fe, Sr, Pd, Eu, Hf, W.
  • 5+ stable isotopes: Ti (5), Cr (4 main), Ni (5), Zn (5), Ge (5), Se (6), Mo (7), Ru (7), Cd (8), Te (8), Ba (7), Nd (7), Sm (7), Gd (7), Dy (7), Yb (7), Os (7), Pt (6), Hg (7).
  • Most stable isotopes: Tin (Sn) with 10 stable isotopes — the record.

Common Element Isotopic Compositions (CIAAW 2021)

  • H: ¹H 99.985%, ²H (D) 0.015% → 1.008 amu (interval value).
  • C: ¹²C 98.93%, ¹³C 1.07% → 12.011 amu (interval).
  • N: ¹⁴N 99.636%, ¹⁵N 0.364% → 14.007 amu.
  • O: ¹⁶O 99.757%, ¹⁷O 0.038%, ¹⁸O 0.205% → 15.999 amu (interval).
  • Cl: ³⁵Cl 75.78%, ³⁷Cl 24.22% → 35.45 amu.
  • Cu: ⁶³Cu 69.17%, ⁶⁵Cu 30.83% → 63.546 amu.
  • Br: ⁷⁹Br 50.69%, ⁸¹Br 49.31% → 79.904 amu (interval).
  • Sn: 10 stable isotopes (¹¹²Sn through ¹²⁴Sn) → 118.710 amu.
  • U: ²³⁸U 99.275%, ²³⁵U 0.7204%, ²³⁴U 0.0055% → 238.029 amu.
Real-World Example

Worked Example — Compute Average Atomic Mass of Boron

Question: Boron has two stable isotopes: ¹⁰B with mass 10.013 amu and natural abundance 19.9%, and ¹¹B with mass 11.009 amu and abundance 80.1%. Compute the average atomic mass of boron.

Step 1 — Convert Percentages to Fractions.

  • ¹⁰B: 19.9% → 0.199 fractional abundance.
  • ¹¹B: 80.1% → 0.801 fractional abundance.
  • Verify sum: 0.199 + 0.801 = 1.000 ✓ (= 100%).

Step 2 — Compute Each Isotope's Contribution.

  • ¹⁰B contribution: 0.199 × 10.013 = 1.993 amu.
  • ¹¹B contribution: 0.801 × 11.009 = 8.818 amu.

Step 3 — Sum to Get Average Atomic Mass.

  • M_avg = 1.993 + 8.818 = 10.81 amu.
  • Periodic-table value for boron: 10.81 ✓ exact match.

Step 4 — Sanity Check.

  • The average (10.81) lies between the two isotope masses (10.01 and 11.01) ✓.
  • The average is closer to ¹¹B (10.81 is 80% of the way from 10.01 to 11.01) ✓ — because ¹¹B is 80% abundant.
  • Simple arithmetic mean: (10.01 + 11.01) / 2 = 10.51 — this is WRONG; would be the value if both isotopes were equally abundant.

Step 5 — Practical Implications.

  • Stoichiometry: 1 mole of boron = 6.022 × 10²³ atoms with average mass 10.81 g (= 10.81 amu × 1 mol).
  • Mass spec: a boron sample shows two peaks at m/z = 10 and 11 with relative intensities ~20:80, allowing isotopic-ratio measurement.
  • Isotope variation: IUPAC reports the boron atomic weight as an INTERVAL [10.806, 10.821] because natural samples vary by source — boron-rich evaporite minerals are slightly enriched in ¹⁰B vs marine boron.
  • Isotopic enrichment: ¹⁰B is enriched (>95%) for nuclear reactor control rods (large neutron-capture cross-section); ¹¹B is depleted in those rods. This changes the effective average mass dramatically.

Who Should Use the Average Atomic Mass Calculator?

1
Standard early-curriculum exercise on isotopes and the periodic table. The calculator handles arithmetic; students focus on the conceptual point that average atomic mass is a weighted (not arithmetic) mean.
2
Mass spec measures isotope-specific peaks; computing the average from peak intensities verifies isotopic composition. Useful for quality control and forensic isotopic-fingerprinting.
3
Isotopic compositions vary across geological / cosmological samples; computing average atomic mass from measured abundances is a standard step in dating and provenance studies.
4
Engineered isotope mixtures (²³⁵U enriched fuel, ⁶Li for tritium breeding, ¹⁰B for control rods) have non-natural M_avg values. The calculator computes the effective average mass for any custom mixture.
5
Generate problem sets with custom isotope abundances; demonstrate the difference between weighted and arithmetic means; teach the concept of fractional abundance.
6
NIST Standard Reference Materials (SRMs) for isotopic-composition measurement need accurate average masses computed from certified abundances.
7
For any element, enter the IUPAC CIAAW abundances and AME2020 isotope masses; the calculator should reproduce the periodic-table M_avg value within 0.01-0.1 amu.

Technical Reference

Atomic Mass Unit (amu / u / Da) — Definition. The unified atomic mass unit (u, also written amu or Da for dalton) is defined as exactly 1/12 the mass of a ¹²C atom in its electronic and nuclear ground state. Numerically: 1 u = 1.66053906892 × 10⁻²⁷ kg = 931.49410372 MeV/c² (mass-energy equivalent). Since the 2019 SI redefinition, the dalton is no longer formally an SI base unit but is accepted for use in chemistry, biochemistry, and atomic / nuclear physics. Numerical equivalence with g/mol: 1 u = 1 g/mol (exactly, by definition of Avogadro's number Nₐ = 6.02214076 × 10²³). So an element's average atomic mass in amu is numerically identical to its molar mass in g/mol.

IUPAC CIAAW Standard Atomic Weights. The Commission on Isotopic Abundances and Atomic Weights (CIAAW) of IUPAC publishes recommended atomic weights every two years. For elements with stable isotopic compositions (no significant natural variation), CIAAW publishes a single conventional value with uncertainty: e.g. F = 18.998 403 162(5). For elements with variable isotopic compositions across natural samples, CIAAW publishes an INTERVAL: e.g. C = [12.0096, 12.0116], with the conventional midpoint value 12.011 typically used in textbooks. Variable-composition elements are: H, Li, B, C, N, O, Mg, Si, S, Cl, Br, Tl — the variation is typically < 0.1% but can be larger for samples from biological, geographic, or industrial sources with non-natural isotopic processing.

AME (Atomic Mass Evaluation). The Atomic Mass Evaluation (AME) is the international standard for individual isotope masses, published roughly every 5-10 years (most recent: AME2020, Wang, Huang, Kondev, Audi, Naimi, Chinese Phys. C 45 030003). AME compiles all measured isotope masses (mass spec, nuclear reactions, decay energies) and produces a global least-squares evaluation. Typical uncertainty: ±0.01-1 keV/c² (= ±10⁻⁵ to 10⁻⁷ amu) for stable isotopes; larger for short-lived radioactive isotopes. The values used in this calculator and most textbooks are AME-derived.

Standard Atomic Weights and Conventional Values (CIAAW 2021, selected).

  • H: [1.00784, 1.00811] interval; conventional 1.008.
  • He: 4.002602(2).
  • Li: [6.938, 6.997] interval; conventional 6.94.
  • Be: 9.0121831(5).
  • B: [10.806, 10.821] interval; conventional 10.81.
  • C: [12.0096, 12.0116] interval; conventional 12.011.
  • N: [14.00643, 14.00728] interval; conventional 14.007.
  • O: [15.99903, 15.99977] interval; conventional 15.999.
  • F: 18.998403162(5).
  • Cl: [35.446, 35.457] interval; conventional 35.45.
  • Cu: 63.546(3).
  • Br: [79.901, 79.907] interval; conventional 79.904.
  • U: 238.02891(3).

Variation Sources for Interval Atomic Weights.

  • H: ²H/¹H ratio varies 130-160 ppm (atmospheric water cycle, glacial/oceanic gradient).
  • C: ¹³C/¹²C ratio varies ~10-30 ppm (biological fractionation; C₃ vs C₄ photosynthesis; petrogenic vs biogenic origin). Used in carbon-source forensics.
  • N: ¹⁵N/¹⁴N varies (atmospheric vs biological vs industrial fertilizer-derived).
  • O: ¹⁸O/¹⁶O varies dramatically — basis of paleoclimate proxies (ice cores, foraminifera shells).
  • S: ³⁴S/³²S varies (biological reduction, volcanic emissions).
  • Cl: ³⁷Cl/³⁵Cl varies in seawater vs evaporite vs industrial chlorine.

Synthetic and Engineered Isotope Mixtures. The CIAAW values are for natural-abundance samples. Engineered enrichment changes M_avg dramatically:

  • Reactor-grade ²³⁵U enriched 3-5% vs natural 0.72%: M_avg shifts by ~0.05 amu (small, but enough to require special accounting in fuel-mass calculations).
  • Weapons-grade ²³⁵U enriched 90%+: M_avg ≈ 235.6 (vs natural 238.03 — a 1% shift).
  • Deuterated solvents (D₂O, CDCl₃) have ¹H replaced with ²D: M_avg shifts from 1.008 to 2.014 (×2).
  • ¹³C-labeled compounds for NMR / metabolic tracing have selective ¹³C enrichment in specific positions.
  • ⁶Li enriched for tritium-breeding blankets in fusion: M_avg shifts from 6.94 to ~6.0.
  • ¹⁰B enriched for nuclear control rods: M_avg shifts from 10.81 to ~10.0.

Special Case: Elements with No Stable Isotopes. 11 elements have no stable isotopes — all isotopes are radioactive. For these, IUPAC reports the mass number of the longest-lived isotope (in square brackets): Tc , Pm , Po , At , Rn , Fr , Ra , Ac , Np , Pu , elements 95+ (Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr) and superheavy elements 104+. These cannot be assigned a meaningful "average atomic mass" because they don't exist in nature with stable isotopic compositions.

Mass Spectrometry Connection. Mass spec ionizes atoms and separates them by mass-to-charge ratio (m/z). For an element with multiple isotopes, the spectrum shows distinct peaks at each isotope mass with intensity proportional to abundance. Computing average atomic mass from a mass spectrum: identify the peaks, integrate intensities (proportional to abundance), normalize to 100%, then apply M_avg = Σ (abundance × mass). The calculator can be used in reverse — feeding measured intensities and known isotope masses to verify the computed average matches the known periodic-table value (a basic mass-spec calibration check). References: IUPAC CIAAW 2021 standard atomic weights; AME2020 Atomic Mass Evaluation; NIST Atomic Weights and Isotopic Compositions Database; CRC Handbook of Chemistry and Physics.

Conclusion

Average atomic mass is one of the foundational concepts in general chemistry — the weighted mean of an element's naturally-occurring stable isotopes, weighted by their fractional abundances. M_avg = Σ (fractional abundance × isotope mass). The single line of math hides the conceptual depth: the result is NOT the simple arithmetic mean; the abundance weights matter and shift the value toward the most common isotope.

Two key reminders: (1) Abundances must sum to 100% for a complete isotope set — if your inputs sum to 95%, you're missing isotopes or have wrong values. The calculator displays Σ abundance and warns if > 0.5% off. (2) The unit "amu" is identical to "u" and "Da" — all three are unified atomic mass units defined as 1/12 the mass of ¹²C. Numerically, amu = g/mol for any species, so the average atomic mass equals the molar mass. For elements with isotopic-composition variation (H, Li, B, C, N, O, Mg, Si, S, Cl, Br, Tl), IUPAC reports both conventional (single value) and interval (range) atomic weights — the conventional values are appropriate for general use, the interval values for high-precision analytical work.

Frequently Asked Questions

What is the Average Atomic Mass Calculator?
It implements the standard weighted-mean atomic mass formula taught in every general-chemistry course: M_avg = Σ (fractional abundance × isotope mass). 2-8 isotopes supported; abundance entered as % or fraction (auto-converted); masses in amu (= u = Da). Output: weighted-average atomic mass plus per-isotope contribution panel with visual bars.

Pro Tip: Pair this with our Mole Calculator.

What is average atomic mass?
The weighted mean of an element's naturally-occurring stable isotopes' masses, weighted by their fractional abundances. The value tabulated under each element's symbol on the periodic table. Example chlorine: ³⁵Cl (75.78%) and ³⁷Cl (24.22%) → 0.7578 × 34.969 + 0.2422 × 36.966 = 35.45 amu. NOT the simple arithmetic mean (which would be 35.97); the weighted mean is closer to the most-abundant isotope.
What's the formula for average atomic mass?
M_avg = Σ (fractional abundance_i × isotope mass_i), summed over all isotopes. Fractional abundance = % / 100. Two-isotope shortcut: M_avg = a₁·m₁ + a₂·m₂ where a₁ + a₂ = 1. For chlorine: M_avg = 0.7578 × 34.969 + 0.2422 × 36.966 = 35.45 amu. For magnesium (3 isotopes): M_avg = 0.7899 × 23.985 + 0.1000 × 24.986 + 0.1101 × 25.983 = 24.305 amu.
What is amu?
Atomic mass unit (amu) is identical to u (unified atomic mass unit) and Da (dalton) — defined as exactly 1/12 the mass of a ¹²C atom. Numerically, 1 amu = 1.66053907 × 10⁻²⁷ kg = 931.494 MeV/c². Critical numerical equivalence: 1 amu = 1 g/mol (exactly, by definition of Avogadro's number). So an element's average atomic mass in amu is numerically the same as its molar mass in g/mol.
What's the average atomic mass of chlorine?
35.45 amu. Two stable isotopes: ³⁵Cl (mass 34.96885 amu, abundance 75.78%) and ³⁷Cl (mass 36.96590 amu, abundance 24.22%). Math: M_avg = 0.7578 × 34.96885 + 0.2422 × 36.96590 = 26.50 + 8.95 = 35.45 amu. The classic textbook example used to illustrate weighted averaging.
What's the average atomic mass of carbon?
12.011 amu (IUPAC interval value [12.0096, 12.0116]). Two stable isotopes: ¹²C (mass exactly 12 amu by definition, abundance 98.93%) and ¹³C (mass 13.00335 amu, abundance 1.07%). Math: M_avg = 0.9893 × 12 + 0.0107 × 13.00335 = 11.872 + 0.139 = 12.011 amu. Note: ¹⁴C exists but is radioactive (T₁/₂ 5730 yr) and trace abundance ~10⁻¹² — not included in the standard atomic weight (would shift M_avg by < 10⁻¹⁰ amu).
How do I calculate average atomic mass from percentages?
Three steps. (1) Convert percentages to fractions (divide by 100). 75.78% → 0.7578. (2) Multiply each fraction by the corresponding isotope mass. (3) Sum all the products. Example for chlorine: 75.78% × 34.969 / 100 + 24.22% × 36.966 / 100 = 26.50 + 8.95 = 35.45 amu. The calculator automates this for 2-8 isotopes.
Why isn't the periodic table value a whole number?
Because elements have multiple isotopes with different masses, and the weighted average isn't generally a whole number. Carbon would be exactly 12 if there were only ¹²C; chlorine would be exactly 35 if only ³⁵Cl. But chlorine has 24% ³⁷Cl, dragging the average up to 35.45. Hydrogen would be exactly 1 if only ¹H; tiny ²H abundance pulls it to 1.008. Even monoisotopic elements show tiny departures from integers because of nuclear binding energy: ¹⁹F mass = 18.998 amu (not exactly 19) due to the mass-defect from the binding energy holding the nucleus together.
Why do percentages need to sum to 100%?
Because the fractional abundances must sum to 1 (or 100% in percent terms) for a complete probability distribution. The weighted average formula assumes you've covered ALL the natural isotopes — if the sum is 95%, you're missing 5% of the abundance and the result will be biased. The calculator displays Σ abundance and warns if > 0.5% off from 100% — usually signals a missing isotope or transcription error. Common mistake: forgetting low-abundance isotopes that still contribute to the average (e.g. for oxygen, ¹⁷O is only 0.038% but is required for the standard atomic weight calculation).
What's the difference between atomic mass and mass number?
Mass number (A) = total number of protons + neutrons in a single nucleus. Always an integer. ³⁵Cl has A = 35 (17 protons + 18 neutrons). Atomic mass (m) = actual mass of one atom in amu. Approximately equal to A but not exactly (due to nuclear binding-energy mass defect; electrons add ~0.0005 amu each). ³⁵Cl has actual mass = 34.96885 amu, NOT exactly 35. Average atomic mass (M_avg) = weighted mean of the actual atomic masses of all natural isotopes. The periodic-table value: chlorine 35.45 amu (between but not equal to either 35 or 37).
Can I use this for engineered or enriched isotope mixtures?
Yes — just enter your specific (non-natural) isotope abundances. Examples: (1) Enriched ²³⁵U for nuclear fuel — natural M_avg = 238.03; 5%-enriched M_avg ≈ 237.93; 90%-enriched (weapons-grade) ≈ 235.4. (2) Deuterated solvent D₂O — replace ¹H 99.985% / ²H 0.015% with 0% / 99.99% → effective M_avg of "hydrogen" becomes ~2.014 amu (D mass) instead of 1.008. (3) ¹³C-labeled compounds for NMR / metabolic studies — selective ¹³C enrichment at specific positions changes that atom's effective mass for spectral analysis. The calculator gives correct results for any isotope mixture you specify.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE chemistry team built this calculator to handle the standard <strong>average atomic mass</strong> computation taught in every general-chemistry course and used by every periodic-table lookup. The defining identity is <strong>M_avg = Σ (fractional abundance × isotope mass)</strong>, summed across all naturally-occurring stable isotopes of an element. The calculator supports <strong>2-8 isotopes</strong> (most elements have 1-3 stable isotopes; tin Sn has the most at 10), with abundance entered as % or fraction (auto-converted), masses in amu (= u = Da, the unified atomic mass unit defined as 1/12 the mass of ¹²C). Output: weighted-average atomic mass (= the periodic-table value), per-isotope contribution with visual percentage bars, and a complete transparent calculation breakdown. Smart warnings flag cases where abundances don't sum to 100% (signals incomplete data) and unphysical isotope masses (outside the 1-300 amu typical range).

IUPAC CIAAW (Commission on Isotopic Abundances and Atomic Weights), 2021 standard atomic weightsAME2020 (Atomic Mass Evaluation) — accurate isotope massesNIST Atomic Weights and Isotopic Compositions Database

Disclaimer

The average atomic mass formula M_avg = Σ (abundance × mass) assumes natural-abundance isotopic ratios for the standard periodic-table value. Isotopic abundances vary slightly across natural samples (geographic, biological, anthropogenic) — IUPAC CIAAW publishes both 'conventional' (single-value) and 'interval' (range) atomic weights for elements with significant variation: H, Li, B, C, N, O, Mg, Si, S, Cl, Br, Tl. For general chemistry use the conventional values; for high-precision analytical work use the interval values or measure isotopic composition directly. Synthetic / radioactive isotopes are not included in periodic-table averages. Engineered isotopic enrichment (²³⁵U, ⁶Li, deuterated solvents) gives M_avg values that differ from natural; the calculator accepts your specific abundances and computes the average correctly. References: IUPAC CIAAW 2021 standard atomic weights; AME2020 Atomic Mass Evaluation; NIST Atomic Weights and Isotopic Compositions Database.