How this atomic mass calculator works
"How do I calculate atomic mass" and "how do I calculate average atomic mass" are the same question approached from two directions, and this page answers both. The atomic mass printed on a periodic table is an average: each element's isotopes weighed by how common they are in a natural sample. So the first mode does the homework computation, a weighted average over the isotopes you enter, with every multiplication shown. The second mode goes the other way: name an element and get the finished answer, the IUPAC standard atomic weight, along with what that number actually means.
The averaging mode also checks your abundances. They have to describe a whole sample, so they must add to 100 percent. Within half a percent of 100 the gap reads as rounding and gets scaled away, with the scaling shown. Farther off than that, the page tells you what the gap usually means (a missing isotope, or fractions mixed with percents) instead of quietly fixing it. If you happen to enter fractional abundances that add to 1, the way many textbooks print them, it reads them as fractions and says so.
The formula
Each isotope's mass is measured in u, the unified atomic mass unit, and its fractional abundance is the share of the sample's atoms that are that isotope, so 75.76% becomes 0.7576. The fractions across all isotopes add to exactly 1. This is the same arithmetic as any weighted average: common isotopes pull the answer toward themselves, rare ones barely move it.
Worked example
Chlorine. Natural chlorine is two isotopes: chlorine-35 at 34.96885 u making up 75.76% of atoms, and chlorine-37 at 36.96590 u making up the other 24.24%.
Turn the percents into fractions and multiply: 34.96885 × 0.7576 = 26.4924, and 36.96590 × 0.2424 = 8.9605. Add them: 26.4924 + 8.9605 = 35.4529 u, which rounds to the 35.45 on every periodic table.
And because chlorine has exactly two isotopes, the computation runs backwards: given the average and the two masses, the abundance of chlorine-35 has to be (36.96590 - 35.4529) / (36.96590 - 34.96885) = 75.76%. One average, two masses, and the mix is pinned by algebra. The calculator shows this self-check whenever you enter two isotopes.
Why the table says 35.45 when no chlorine atom weighs that
This is the idea the whole page turns on. Every individual chlorine atom weighs either about 35 u or about 37 u. Not one of them weighs 35.45. The tabulated atomic mass is the average over the mixture, and an average describes the population, not any member of it: it is the census, not any citizen. The same thing happens with an "average household of 2.5 people," and nobody goes looking for the half person.
That is also why the number is so useful. When you weigh out a gram of chlorine you are weighing trillions of trillions of atoms in their natural mix, so the average is exactly the number that connects grams to atom counts. It feeds straight into molar mass, where the averages for each element in a formula are summed: our molar mass calculator does that next step, and our mole calculator carries it on to grams, moles and particle counts.
Mass number, atomic mass, and the carbon-12 ruler
Three numbers get tangled here, and separating them is most of the topic. The mass number is a count of protons plus neutrons: the 35 in chlorine-35, always a whole number, exact by definition. The isotope's atomic mass is a measurement: chlorine-35 actually weighs 34.96885 u, slightly less than 35 whole nucleons would suggest, because a bound nucleus gives up a little of its mass as binding energy, the price of holding itself together. And the element's atomic mass, the periodic table number, is the abundance-weighted average of those measured masses.
All of the measured masses lean on one anchor: a single atom of carbon-12 weighs exactly 12 u, by definition. It is the ruler every other mass is measured against, the way a meter stick is not itself a measurement of anything. Carbon's own table value of 12.011 is not a contradiction. Natural carbon carries about 1 percent carbon-13, and the census sits just above the ruler isotope.
Reading a periodic table cell, then: the whole number at the top is the atomic number (protons), and the decimal at the bottom is the average atomic mass. If your class reports a measured average against the accepted value, our percent error calculator handles the comparison, and our significant figures calculator will tell you how many digits of it you have earned.
One isotope, and fourteen elements that became ranges
Some elements need no averaging at all. Beryllium, fluorine, sodium, aluminum, phosphorus and gold each occur in nature as a single isotope, so their atomic mass is simply that isotope's measured mass, which is why their table values carry such clean digits: fluorine is 18.998 and there is no mixture to blur it.
At the other extreme, fourteen elements vary so much from one natural sample to another that IUPAC stopped publishing a single atomic weight for them and publishes an interval instead: hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, argon, bromine, thallium and lead. Lead is the spectacular case, [206.14, 207.94], a spread of nearly a whole mass unit. Lead sits at the end of three radioactive decay chains, so the isotope mix in an ore depends on how much uranium and thorium decayed next to it and for how long: a lead sample carries the history of its rock, and that history shows up in its mass. The lookup mode flags every one of the fourteen, and shows the conventional single value the world agreed to use when one number is needed.