Radioactive Decay Calculator

Find the activity of a radioactive sample from its mass and half-life.

Sixteen radioactivity units, nine time scales, and reverse solves for mass, molar mass or half-life.

Updated October 17, 2026

CreatorFrank Zhao

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Introduction

Activity is the number of atomic nuclei in a sample that fall apart every second. It is the quantity radiation instruments are calibrated against, the quantity shipping papers and inventory records are written in, and the quantity this page works out.

You do not have to count decays to know the figure. If you know what the substance is and how much of it you have, the activity follows from two numbers you can look up: the isotope’s molar mass and its half-life. That is the calculation here, and it runs in both directions. Give the page a mass, a molar mass and a half-life and it returns the activity and the specific activity. Leave one of those three open and it solves for whatever is missing instead — and if you have already counted an activity, type it into that box and the page works back to the half-life or the molar mass from it.

Half-life is the anchor of the whole thing. The US EPA defines it as the time required for half of the radioactive atoms present to decay, and notes that radionuclides span a range from seconds to billions of years. Because every nucleus in a sample decays independently, that one number fixes the fraction of the sample that decays per second, and that fraction multiplied by the count of nuclei is the activity.

What you get out of it

Two results, and they answer different questions. Activity is a property of your sample — cut the sample in half and it halves. Specific activity is a property of the isotope — it is the activity of one kilogram of the pure material, whatever size your sample happens to be. Both boxes are editable, so either of them can also be the number you start from.

A 6.2 kg lump and a 1 g speck of the same plutonium isotope differ enormously in activity but share exactly the same specific activity. If you are comparing two materials, or checking a certificate, specific activity is usually the number you want.

How to use it

Three boxes are enough for the common case. Walk through it once with a real isotope and the other paths become obvious.

Weigh the radioisotope you actually have

Enter the mass of the radioactive substance, not the mass of the object or the compound it sits in. Choose the scale you weighed in; it is normalised before the arithmetic runs.

Enter the isotope's molar mass

One mole of the nuclide, in grams per mole. For a pure isotope this sits within a fraction of a percent of its mass number, so plutonium-239 is close to 239 g/mol and carbon-14 close to 14 g/mol. Use the specific isotope’s value from a reference table rather than the element’s average, because the average is a mixture of isotopes with different half-lives.

Enter the half-life on the matching scale

The menu opens on seconds and offers eight further scales up to billions of years. Match it to the value you read, and check that the two agree — a half-life typed in years while the menu still says seconds is the single most common way to get an answer that is wrong by orders of magnitude. Every example below therefore names both the number and the scale.

Read the two results

Activity appears in becquerels, with fifteen further scales on its menu — kilobytes up to petabecquerels, the three curie sizes, and the rutherfords. Specific activity appears beside it on the identical set of scales, with a per-kilogram denominator.

A worked first pass

Take one gram of uranium-238, molar mass 238.03 g/mol and half-life 4.468 billion years. Enter those three values and the page returns:

Activity

12,437.34 Bq

about 0.336 microcuries

Specific activity

12,437,339.25 Bq/kg

about 12.44 kBq per gram

Both numbers describe the same gram of metal. The second is simply the first divided by the mass you entered — and it is the one that stays true if you later weigh out a different amount of the same uranium.

a = \frac{A}{m}

=

\frac{12437.34\ \mathrm{Bq}}{0.001\ \mathrm{kg}}

=

1.244\times 10^{7}\ \mathrm{Bq/kg}

Calculation method

One physical statement stands behind every direction the page can solve. The rest is algebra rearranged around it, and each step below is a card you can read on its own.

Activity from a mass and a decay rate

The number of nuclei in the sample is the mass divided by the molar mass, multiplied by Avogadro’s number. Each of those nuclei has the same small probability of decaying per second, set by the half-life.

A = \frac{m}{M}\times N_{\mathrm{A}}\times \frac{\ln 2}{t_{1/2}}

A

Activity of the sample, in decays per second (becquerels)

m

Mass of the radioisotope, in kilograms after normalisation

M

Molar mass of the isotope, in kilograms per mole

N_A

Avogadro’s number, the count of particles in one mole

t_{1/2}

Half-life of the isotope, in seconds after normalisation

The decay constant behind that fraction

The factor $\ln 2 / t_{1/2}$ is the decay constant $\lambda$ — the probability per second that any one nucleus decays. Because it is a probability, a shorter half-life means a larger $\lambda$ and a more active sample of the same size.

\lambda = \frac{\ln 2}{t_{1/2}}

Specific activity, with the mass divided out

Divide the activity by the mass and the sample size cancels. What is left depends only on the isotope.

a = \frac{A}{m} = \frac{N_{\mathrm{A}}}{M}\times \frac{\ln 2}{t_{1/2}}

This is why the page reports specific activity next to the activity rather than instead of it. Synthesis targets, calibration sources and shipping classifications are usually written as activity per unit mass, so that the figure holds however much material is on hand.

Solving back to whichever box you left open

Because the three input boxes are related by one equation, the page is not limited to the forward direction. Leave a box empty and it fills from the other two.

m

Mass

from the activity, the molar mass and the half-life.

M

Molar mass

from the activity, the mass and the half-life.

t_{1/2}

Half-life

from the activity, the mass and the molar mass.

m = \frac{A\,M\,t_{1/2}}{N_{\mathrm{A}}\ln 2}

\qquad

M = \frac{N_{\mathrm{A}}\,m\ln 2}{A\,t_{1/2}}

\qquad

t_{1/2} = \frac{N_{\mathrm{A}}\,m\ln 2}{A\,M}

In practice the page chains these steps for you: a measured activity is first turned into a specific activity using the sample mass, and the half-life or molar mass is then recovered from that. It also accepts a specific activity directly, which is useful when a certificate quotes activity per gram rather than a total.

What the model assumes

The sample is the pure radioisotope. The mass you enter is the mass of the radioactive atoms themselves. If your material is a compound, a mixture, or a natural element with several isotopes, apply the abundance or the mass fraction before you enter it.
One radionuclide, decaying by one route. A nuclide that branches between two decay modes has a total half-life that already accounts for both; the page does not split the activity between the branches.
Avogadro’s number is fixed at $6.02214\times 10^{23}$ particles per mole. It sits in its own collapsed group so you can see the value the arithmetic uses, and you can replace it if a reference you are matching quotes a different one. It is never solved back, so it cannot silently absorb a wrong mass scale.

Decay chains are outside this model

Some radionuclides decay through a series of steps rather than once, and each daughter is itself radioactive. The EPA describes these as series radionuclides. The number this page returns is the activity of the parent you entered, at the moment you describe it. It says nothing about daughters, and nothing about whether the chain has reached the state where a parent and daughter are decaying at equal rates.

Worked examples

Three samples, three different reasons for wanting the number. Every reading below is what this page shows for those entries.

A legacy source: what is 6.19 kg of plutonium-239 emitting?

A sealed source of known isotopic purity has been weighed, and the inventory needs its activity.

What you enter

Mass6.19 kg
Molar mass239.05 g/mol
Half-life24,100on the years scale

What the page returns

Activity
14,212,065,485,899 Bq
about 14.2 TBq, roughly 384 curies
Specific activity
2.30 × 10^12 Bq/kg

This is the kind of figure that belongs on a source inventory. It is also a reminder of scale: the same isotope in a one-milligram speck would read about 2.3 GBq.

Everyday material: the potassium-40 in a banana

A large banana holds roughly 0.5 g of potassium, and about 0.012% of natural potassium is the radioactive isotope potassium-40.

The abundance step comes first: 0.012% of 0.5 g is 0.00006 g of potassium-40, and that is the mass to enter. It is the step people skip.

What you enter

Mass of the isotope0.00006 g0.012% of the 0.5 g of potassium
Molar mass39.96 g/mol
Half-life1.248on the billion years scale

What the page returns

Activity
15.91 Bq
a little over fifteen decays per second
Specific activity
2.65 × 10^8 Bq/kg

Enter the full 0.5 g instead and the answer becomes about 132 kBq — more than eight thousand times too high, because the potassium you weighed is almost entirely potassium-39 and potassium-41, neither of which is radioactive.

Working backwards: identifying an isotope from a measured activity

A counter reads 12,437.34 Bq from a 1 g sample, and the certificate gives a molar mass of 238.03 g/mol but no half-life.

What you enter

Mass1 g
Molar mass238.03 g/mol
Activity12,437.34 Bqtyped into the Activity box

What the page returns

Specific activity
12,437,340 Bq/kg
derived from the activity and the mass
Half-life
4.4679997291242011208
on the billion years scale

The half-life box closes at 140,999,348,251,809,889.29 s while the time scale reads seconds. Switch that scale to billion years and the same number reads 4.468 — uranium-238, recovered from a mass and a count without ever looking up its half-life.

Why the reverse direction matters

Forward calculation tells you what a quantity of material will do. Reverse calculation tells you what the material is, because the specific activity is a fingerprint: two containers of the same mass reading the same activity are the same nuclide, and a container that disagrees is either a different isotope or a different mass.

One practical caveat: a specific activity measured this way is only as good as the mass you entered. A balance error of 1% moves the derived half-life by about 1%, so weigh carefully if the half-life is the number you actually care about.

Common mistakes

Almost every wrong answer from this page traces back to one of five input problems. All of them are visible in the numbers once you know what to look for.

Entering the compound, not the isotope

A salt, an alloy or a natural element is mostly not the radioisotope. Multiply by the mass fraction first. The banana above is the classic version of this error, and it inflates the answer by three to four orders of magnitude.

Using the element's average molar mass

Chlorine is 35.45 g/mol on average, but chlorine-36 is 35.97 g/mol. For a pure nuclide use the isotope’s value; the average blends isotopes with wildly different half-lives into a number that describes none of them.

Mismatching the half-life scale

The box offers nine time scales. A half-life of 5,730 years typed while the menu still reads seconds understates the materials’ activity by a factor of about 1.8 × 10¹¹. Check the unit shown next to the number, not the number alone.

Treating the result as a dose

Activity counts decays, not harm. The EPA notes that alpha, beta and gamma emissions differ greatly in how far they travel and how they affect tissue, so two samples with identical activity can pose very different hazards. Dose needs the radiation type, the energy, and how the source is shielded and handled.

Reading a rounded half-life as exact

Half-lives in tables are measured values with uncertainties. Uranium-238 is often printed as 4.468 billion years, which is precise enough for most work, but an activity computed from a half-life quoted to three figures is only good to about three figures.

Sanity-check the specific activity first

Specific activity is the fastest way to catch a scale error, because it depends only on the isotope. Look it up in a reference table for the nuclide you intended: if the page disagrees by orders of magnitude, the molar mass or the half-life is wrong, whatever the activity says.

A unit slip worth naming

Becquerels and curies are both offered, and they differ by a factor of $3.7\times 10^{10}$ . A source quoted as 10 µCi is 370 kBq, not 10 kBq. If a number looks implausibly large or small next to the certificate, check which of the two scales the menu is showing before you change any input.

Questions

Is the specific activity the same as the half-life?

They carry the same information in different forms, and you can move between them if you know the molar mass. Two samples of the same isotope always share a specific activity, no matter how much material is in either one. Half-life is written in time; specific activity is that time converted into decays per second per kilogram.

Why does the page ask for a molar mass if I only want activity?

Because activity is a count of nuclei, and a balance measures mass. The molar mass is the bridge between the two — it converts the grams you weighed into the number of atoms that could decay. There is no way around it: the same mass of two isotopes with the same half-life but different molar masses holds different numbers of atoms.

Do I need to account for the sample decaying while I work?

For half-lives of years or longer, no. For very short half-lives, yes — the activity you calculate is the activity at the moment you describe the mass. A 66-hour isotope loses about 10% of its activity in ten hours, so the timestamp matters as much as the number.

Can I use the result for a shipping or licensing declaration?

Use it as a cross-check rather than as the declaration itself. Regulated activity limits come from the transport or licensing regime that applies to you, and they depend on the specific radionuclide, its form, and the package. This page gives you the physical activity; the classification and the paperwork follow different rules.

Where the model stops

•The result is the activity of the parent nuclide you describe, computed from its mass, molar mass and half-life. It is not a dose, not a risk assessment, and not a count of the radiation that reaches any particular place.
•The calculation assumes a pure isotope with the abundance or mass fraction already applied, and it does not model decay chains, ingrowth, or radioactive equilibrium. If a daughter nuclide contributes to what an instrument reads, this page will not see it.
•Accuracy is bounded by your inputs. Tabulated half-lives and molar masses carry their own uncertainties, and the isotope tables at NIST’s atomic-weight database publish both the values and their uncertainties for exactly this reason.
•For radiation protection, dosimetry, waste classification or regulatory reporting, work from the applicable guidance and a measurement of the actual source. Use this page to understand and check the numbers, not to authorise handling of radioactive material.

Useful next steps

The activity of a sample at some later time, and how much of it is left, come from the same half-life you entered here — the half-life calculator works that side of the problem.

If the molar mass you need is for a compound rather than a single isotope, build it from its elements with the molar mass calculator, then come back and enter the isotope you actually care about. And when the mass you have is a count of atoms rather than grams, the molarity calculator converts between the two.

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