About

Every element on the periodic table lists a single atomic mass value, yet no individual atom of that element actually weighs that amount. The published value is a weighted average across all naturally occurring isotopes, each contributing proportionally to its abundance. Errors in isotope fractionation measurements propagate directly into stoichiometric calculations, affecting molar mass determinations, reaction yield predictions, and mass spectrometry calibrations. This calculator computes the average atomic mass M_avg from user-supplied isotopic masses m_i (in amu) and their corresponding natural abundances f_i (in %). It validates that abundances sum to 100% within a ±0.1% tolerance to catch data entry mistakes before they corrupt downstream analysis.

The tool approximates atomic mass under the assumption that terrestrial isotope ratios are constant. In practice, natural variation exists: m(¹²C) is defined exactly as 12 amu, but lighter elements like lithium and boron show measurable geographic variation in isotope ratios. For high-precision work (IUPAC 2021 intervals), consult the Commission on Isotopic Abundances and Atomic Weights directly. Pro tip: mass spectrometry data often reports relative abundances that must be normalized to 100% before use here.

Formulas

The average atomic mass is computed as the weighted sum of each isotope's mass, where the weight is the fractional natural abundance.

M_avg = n∑i=1 f_i × m_i

where f_i = A_i100 is the fractional abundance derived from percentage abundance A_i.

Validation constraint: n∑i=1 A_i = 100% ± 0.1%

Variable legend:

M_avg = weighted average atomic mass in amu (atomic mass units).

m_i = isotopic mass of the i-th isotope in amu.

A_i = natural abundance of the i-th isotope in %.

f_i = fractional abundance (dimensionless, range 0 to 1).

n = total number of isotopes.

Reference Data

Element	Symbol	Isotope	Isotopic Mass (amu)	Abundance (%)	Avg. Atomic Mass (amu)
Hydrogen	H	¹H / ²H	1.00783 / 2.01410	99.9885 / 0.0115	1.008
Helium	He	³He / ⁴He	3.01603 / 4.00260	0.0001 / 99.9999	4.003
Lithium	Li	⁶Li / ⁷Li	6.01512 / 7.01601	7.59 / 92.41	6.941
Boron	B	¹⁰B / ¹¹B	10.01294 / 11.00931	19.9 / 80.1	10.81
Carbon	C	¹²C / ¹³C	12.00000 / 13.00335	98.93 / 1.07	12.011
Nitrogen	N	¹⁴N / ¹⁵N	14.00307 / 15.00011	99.636 / 0.364	14.007
Oxygen	O	¹⁶O / ¹⁷O / ¹⁸O	15.99491 / 16.99913 / 17.99916	99.757 / 0.038 / 0.205	15.999
Neon	Ne	²⁰Ne / ²¹Ne / ²²Ne	19.99244 / 20.99385 / 21.99138	90.48 / 0.27 / 9.25	20.180
Magnesium	Mg	²⁴Mg / ²⁵Mg / ²⁶Mg	23.98504 / 24.98584 / 25.98259	78.99 / 10.00 / 11.01	24.305
Silicon	Si	²⁸Si / ²⁹Si / ³⁰Si	27.97693 / 28.97649 / 29.97377	92.223 / 4.685 / 3.092	28.086
Sulfur	S	³²S / ³³S / ³⁴S / ³⁶S	31.97207 / 32.97146 / 33.96787 / 35.96708	94.99 / 0.75 / 4.25 / 0.01	32.06
Chlorine	Cl	³⁵Cl / ³⁷Cl	34.96885 / 36.96590	75.76 / 24.24	35.45
Argon	Ar	³⁶Ar / ³⁸Ar / ⁴⁰Ar	35.96755 / 37.96273 / 39.96238	0.3336 / 0.0629 / 99.6035	39.948
Potassium	K	³⁹K / ⁴⁰K / ⁴¹K	38.96371 / 39.96400 / 40.96183	93.2581 / 0.0117 / 6.7302	39.098
Calcium	Ca	⁴⁰Ca / ⁴²Ca / ⁴⁴Ca	39.96259 / 41.95862 / 43.95548	96.941 / 0.647 / 2.086	40.078
Iron	Fe	⁵⁴Fe / ⁵⁶Fe / ⁵⁷Fe / ⁵⁸Fe	53.93961 / 55.93494 / 56.93540 / 57.93328	5.845 / 91.754 / 2.119 / 0.282	55.845
Copper	Cu	⁶³Cu / ⁶⁵Cu	62.92960 / 64.92779	69.17 / 30.83	63.546
Zinc	Zn	⁶⁴Zn / ⁶⁶Zn / ⁶⁷Zn / ⁶⁸Zn / ⁷⁰Zn	63.92914 / 65.92603 / 66.92713 / 67.92485 / 69.92532	49.17 / 27.73 / 4.04 / 18.45 / 0.61	65.38
Bromine	Br	⁷⁹Br / ⁸¹Br	78.91834 / 80.91629	50.69 / 49.31	79.904
Silver	Ag	¹⁰⁷Ag / ¹⁰⁹Ag	106.90509 / 108.90476	51.839 / 48.161	107.868
Tin	Sn	¹²⁰Sn (dominant)	119.90220	32.58	118.710
Barium	Ba	¹³⁸Ba (dominant)	137.90525	71.698	137.327
Europium	Eu	¹⁵¹Eu / ¹⁵³Eu	150.91986 / 152.92124	47.81 / 52.19	151.964
Thallium	Tl	²⁰³Tl / ²⁰⁵Tl	202.97234 / 204.97443	29.52 / 70.48	204.383
Lead	Pb	²⁰⁴Pb / ²⁰⁶Pb / ²⁰⁷Pb / ²⁰⁸Pb	203.97304 / 205.97447 / 206.97590 / 207.97665	1.4 / 24.1 / 22.1 / 52.4	207.2
Uranium	U	²³⁴U / ²³⁵U / ²³⁸U	234.04095 / 235.04393 / 238.05079	0.0054 / 0.7204 / 99.2742	238.029

Frequently Asked Questions

The fractional abundances represent a complete probability distribution across all naturally occurring isotopes. If they do not sum to 100%, either an isotope is missing from your data or there is a measurement error. This calculator enforces a ±0.1% tolerance to account for rounding in published data while still catching significant omissions.

Mass number (A) is a dimensionless integer equal to the count of protons plus neutrons. Isotopic mass (m) is measured in amu and reflects the actual nuclear binding energy via mass defect. For example, ¹²C has mass number 12 and isotopic mass exactly 12.00000 amu by definition, but ¹⁶O has mass number 16 and isotopic mass 15.99491 amu. Always use isotopic mass, not mass number, for this calculation.

Yes, but you must normalize them first. Mass spectrometry reports peak intensities relative to the base peak (tallest = 100). Convert each relative intensity to a percentage of the total summed intensities: A_i = I_i∑I × 100. Then enter these normalized values.

IUPAC periodically revises standard atomic weights based on updated isotope ratio measurements. Many elements now have interval-based weights (e.g., lithium: [6.938, 6.997]) reflecting natural geographic variation. Your result may also differ due to rounding in the isotopic masses you enter. For maximum accuracy, use IUPAC 2021 evaluated data with at least 5 decimal places for each isotopic mass.

The mass of a nucleus is less than the sum of its constituent proton and neutron masses. This difference, called mass defect (Δm), converts to binding energy via E = Δm × c². Iron-56 has the highest binding energy per nucleon (8.79 MeV), which is why its isotopic mass per nucleon is the lowest. This effect makes isotopic masses non-integer and is the physical basis for the entire calculation.

You can enter any isotope's mass and abundance. However, for radioactive isotopes with very short half-lives, the natural abundance approaches 0% and is often excluded from standard atomic weight calculations. For elements with no stable isotopes (e.g., technetium, promethium), IUPAC lists the mass number of the longest-lived isotope in brackets rather than a weighted average.