How this instrument works
Activity is the rate at which a radioactive sample is decaying, measured in becquerels (Bq), where 1 Bq equals one nuclear disintegration per second. For a given mass of a pure radioisotope, activity depends on two things: how many atoms are actually present (from the mass and the isotope's molar mass) and how fast each individual atom is likely to decay (from its half-life, the time it takes for half of any population of that isotope to decay). A shorter half-life means faster decay, so for the same mass, a short-half-life isotope like iodine-131 (about 8 days) is enormously more radioactive than a long-half-life isotope like plutonium-239 (about 24,100 years).
The formula chains those two pieces together: convert mass to a number of atoms (mass / molar mass, then multiplied by Avogadro's number), then multiply by the decay constant — ln(2) divided by the half-life — which gives the fraction of those atoms decaying per unit time. The result is activity in becquerels: how many disintegrations that specific mass of that specific isotope produces every second, right now.
This calculator answers 'how radioactive is this much material,' not 'how much of this material will be left after some elapsed time' — that second question (radioactive decay over an elapsed period) is a separate calculation built around the exponential decay law, N(t) = N0 x (1/2)^(t / half-life). This tool computes a snapshot activity from a present-day mass and a known half-life; it does not project how that mass or its activity will change going forward.
- Enter the sample's mass in grams into Sample mass (g).
- Enter the isotope's molar mass in g/mol into Molar mass (g/mol).
- Enter the isotope's half-life in years into Half-life (years) — convert from days or another time unit if needed (for example, 8.02 days is about 0.021958 years).
- Read Activity, A (Bq) for the total activity of the whole sample, and Specific activity (Bq/g) for the activity per gram, independent of how much sample you have.
Worked example — 6.19 kg of plutonium-239
Enter 6190 into Sample mass (g), 239.05 into Molar mass (g/mol), and 24100 into Half-life (years) — the real historical mass of plutonium-239 used in the Fat Man bomb's core, with Pu-239's real molar mass and half-life. Activity, A (Bq) reads about 1.421 x 10^13 Bq — a little over 14 terabecquerels — and Specific activity (Bq/g) reads about 2.296 x 10^9 Bq/g.
That 14+ TBq figure is trillions of disintegrations happening every single second, driven entirely by the sheer number of Pu-239 atoms in 6.19 kilograms combined with even that isotope's comparatively slow, 24,100-year decay rate — a useful illustration of just how many atoms are packed into an everyday-scale mass, since even an extremely slow per-atom decay rate adds up to enormous total activity across that many atoms.
Questions
What's the difference between activity and specific activity?
Activity is the total decay rate of your whole sample, in becquerels, and scales directly with how much of the isotope you have. Specific activity is activity per gram — a fixed property of the isotope itself, independent of sample size — so it lets you compare how 'hot' different isotopes are per unit mass without needing to fix the mass first. Multiplying specific activity by sample mass gives total activity back.
Why does a shorter half-life mean higher activity for the same mass?
Because activity measures decays per second, and a shorter half-life means each individual atom has a higher probability of decaying in any given second — the decay constant (ln2 / half-life) that drives activity is inversely proportional to half-life. Iodine-131's roughly 8-day half-life versus plutonium-239's roughly 24,100-year half-life is a factor of over a million; for equal masses, that translates into iodine-131 being millions of times more active per gram.
Does this calculate how much radioactive material is left after a certain time?
No — this calculates the activity of a sample of a given mass right now, not how that mass or activity changes going forward. Projecting decay forward in time uses a different formula, the exponential decay law N(t) = N0 x (1/2)^(t / half-life), which needs an elapsed time as an input that this calculator doesn't take.
My half-life is given in days or hours, not years — what do I do?
Convert it to years before entering it, since Half-life (years) expects that unit specifically. Divide days by 365.25 (iodine-131's 8.02-day half-life becomes about 0.021958 years), or convert hours to days first and then to years. Getting the half-life unit right matters enormously here, since activity is inversely proportional to half-life.
Why does the formula need molar mass, not just the raw mass?
Because activity depends on the number of individual atoms present, not the mass by itself — and converting a mass into an atom count requires knowing that isotope's molar mass (mass per mole) to first find how many moles the sample represents, then Avogadro's number to convert moles into an actual atom count. Two different isotopes with the same mass in grams generally have different atom counts, since their molar masses differ.