Atomic Mass Calculator

Calculate average atomic mass from isotope masses and abundances

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Atomic Mass Calculator

Isotope 1

Isotope 2

Quick Reference

  • Carbon-12: 98.93% at 12.000000 amu
  • Carbon-13: 1.07% at 13.003355 amu
  • Carbon avg: 12.011 amu
  • • Abundances must sum to 100%

ℹ️What It Does

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.

📐Formula

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 %)

Variables:

M= Average atomic mass (amu)
mᵢ= Mass of isotope i (amu)
aᵢ= Abundance of isotope i (%)

📝Step-by-Step Example: Carbon

1

Given Information

¹²C: 98.93% at 12.000000 amu

¹³C: 1.07% at 13.003355 amu

2

Apply Formula

M = (98.93 × 12.000000 + 1.07 × 13.003355) / 100

3

Calculate

M = (1187.16 + 13.914) / 100 = 1201.074 / 100

4

Result

Average atomic mass = 12.01074 amu ≈ 12.011 amu

⚠️Common Mistakes

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

Related Calculators

Frequently Asked Questions

What is average atomic mass?

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.

Why isn't atomic mass a whole number?

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.

What's the difference between atomic mass and mass number?

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.

How do I find isotope data?

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.

What if abundances are given as decimals?

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.

Can I use this for radioactive elements?

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.

Why is the unit "amu"?

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.

Where It's Used

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Education

Teaching isotopes and atomic structure

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Mass Spectrometry

Analyzing isotope ratios

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Nuclear Chemistry

Isotope abundance calculations

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Geochemistry

Dating samples with isotope ratios