Calculate average atomic mass from isotope masses and abundances
The atomic mass calculator determines the average atomic mass of an element by calculating the weighted average of all its naturally occurring isotopes. Each isotope's contribution is weighted by its natural abundance percentage, providing the value found on the periodic table.
Average Atomic Mass = Σ(abundanceᵢ × massᵢ) / 100
Expanded Form
M = (m₁×a₁ + m₂×a₂ + ...) / 100
Fractional Form
M = m₁×f₁ + m₂×f₂ + ...
(where f = fraction, not %)
Given Information
¹²C: 98.93% at 12.000000 amu
¹³C: 1.07% at 13.003355 amu
Apply Formula
M = (98.93 × 12.000000 + 1.07 × 13.003355) / 100
Calculate
M = (1187.16 + 13.914) / 100 = 1201.074 / 100
Result
Average atomic mass = 12.01074 amu ≈ 12.011 amu
Forgetting to divide by 100
Abundances are percentages, not decimals
Using simple average
Must weight by abundance, not just average masses
Abundances don't sum to 100%
Check that all abundances add up to 100%
Rounding too early
Keep full precision until final answer
Average atomic mass is the weighted average of the masses of all naturally occurring isotopes of an element. It accounts for both the mass and relative abundance of each isotope, giving the value shown on the periodic table.
Atomic mass isn't a whole number because it's a weighted average of isotopes with different masses. For example, chlorine has Cl-35 (75.76%) and Cl-37 (24.24%), giving an average of 35.45 amu, not 35 or 37.
Mass number is the total protons + neutrons in a specific isotope (always whole number). Atomic mass is the weighted average of all isotopes (usually decimal). Example: Carbon-12 has mass number 12, but carbon's atomic mass is 12.011 amu.
Isotope masses and abundances are available in chemistry reference books, the NIST database, or your chemistry textbook. Most elements have 2-3 naturally occurring isotopes, though some have more.
If abundances are given as decimals (0.9893 instead of 98.93%), don't divide by 100 in the formula. Just use M = Σ(abundanceᵢ × massᵢ) directly with the decimal values.
For radioactive elements with no stable isotopes (like technetium or promethium), the periodic table shows the mass number of the most stable isotope in brackets, not an average atomic mass.
amu stands for "atomic mass unit," defined as 1/12 the mass of a carbon-12 atom. It's also called "u" (unified atomic mass unit) or "Da" (dalton). 1 amu ≈ 1.66054 × 10⁻²⁷ kg.
Education
Teaching isotopes and atomic structure
Mass Spectrometry
Analyzing isotope ratios
Nuclear Chemistry
Isotope abundance calculations
Geochemistry
Dating samples with isotope ratios