What this calculator does
Activity is the number of decays per second, which is the decay constant multiplied by the number of atoms present. A millimole of carbon-14 has an activity of about 2.31 billion becquerels, or 0.062 curies.
Activity and half-life run in opposite directions, which is worth internalising. A short half-life means a high decay constant and therefore intense activity from a small sample. The same millimole with an eight-day half-life gives 1.65 trillion becquerels, over seven hundred times as much, because those atoms are decaying far faster.
The formula
The number of atoms is the amount in moles multiplied by the Avogadro constant. The decay constant is the natural log of 2 divided by the half-life converted to seconds. Activity is their product, in becquerels, where one becquerel is one decay per second. The curie figure uses the defined conversion of 3.7×10¹⁰ becquerels.
| Term | Meaning |
|---|---|
| Activity | Decays per second. Not the same as dose, which depends on the radiation type and absorption. |
| Becquerel (Bq) | One decay per second. A very small unit, so real figures are large. |
| Curie (Ci) | An older unit, 3.7×10¹⁰ Bq by definition, roughly the activity of a gram of radium. |
| Decay constant λ | ln2 over the half-life, the decay probability per nucleus per second. |
The inputs explained
| Field | What to enter |
|---|---|
| Amount of substance (mol) | Amount of the radioactive substance in moles. |
| Half-life (years) | Half-life in years. Convert shorter half-lives accordingly. |
When to use it
Assessing a source
Activity is the standard specification for a radioactive source, quoted in becquerels or curies.
Planning medical isotope use
Short-lived isotopes have high activity for their quantity, which is what makes small doses effective.
Understanding why long-lived waste is less intense
A long half-life means low activity per atom, though for a far longer time.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does half-life affect activity?
The same quantity with different half-lives.
| Half-life | Activity | Decay constant λ | Number of atoms N |
|---|---|---|---|
| 0.1 years | 132,273,363,300,000 Bq | 2.1965e-7 /s | 602,214,076,000,000,000,000 |
| 8 years | 1,653,417,041,000 Bq | 2.7456e-9 /s | 602,214,076,000,000,000,000 |
| 30 years | 440,911,210,900 Bq | 7.3215e-10 /s | 602,214,076,000,000,000,000 |
| 5730 years | 2,308,435,659 Bq | 3.8332e-12 /s | 602,214,076,000,000,000,000 |
Questions
Why does a shorter half-life mean higher activity?
Because activity is the rate of decay, and a short half-life means each atom is more likely to decay in any given second. The same number of atoms decaying faster produces more decays per second. Intensity and longevity are inversely related.
What is the difference between becquerels and curies?
Both measure activity. A becquerel is one decay per second, which is tiny. A curie is 3.7×10¹⁰ becquerels, originally defined as roughly the activity of a gram of radium. The becquerel is the SI unit; the curie persists in some fields.
Does activity tell me how dangerous something is?
Only partly. Activity counts decays, but the hazard also depends on the type of radiation emitted, its energy, whether the source is inside or outside the body, and the half-life. An alpha emitter outside the body is largely harmless and seriously dangerous if inhaled.
Why are the numbers so large?
Because a mole contains 6.02×10²³ atoms and a becquerel is a single decay per second. Even a very slow decay across that many atoms produces an enormous count. This is why the curie, or prefixed units like megabecquerels, are used in practice.
For how much remains over time, see the half-life calculator. For dating applications, see the radiocarbon dating calculator.