Radioactive Decay Calculator

How to use this radioactive decay calculator

What this calculator does

This calculator estimates the instantaneous activity of a pure radionuclide sample from three physical quantities: its mass, its molar mass, and its half-life. It also reports specific activity, the number of radioactive atoms, the decay constant, and mean lifetime. The model uses the standard exponential-decay law, in which each nucleus has a constant probability of decaying per unit time. Activity is expressed in becquerels, where one becquerel means one nuclear transformation per second. The calculation is a physics estimate for an ideal single nuclide; it does not determine radiation dose, health risk, shielding needs, detector counts, or the behavior of a multi-step decay chain.

When to use it

Use it to check laboratory calculations for a known isotope, compare the intrinsic activity of equal masses of different radionuclides, estimate how activity falls after several half-lives, or create a reproducible workbook for teaching and documentation. For regulatory, medical, or safety work, pair the result with isotope-specific decay data, measurement uncertainty, instrument efficiency, and professional radiation-protection guidance.

How to calculate

1. The calculator opens with a complete demonstration based on a 1 g sample, a molar mass of 238.05 g/mol, and a half-life of 4.468 × 10⁹ years. Its XLSX export is immediately available.
2. Replace Sample mass with the amount of radionuclide and choose g, mg, or kg. Replace Molar mass of the substance with the isotope's molar mass and select g/mol or kg/mol. Enter Half-life and choose seconds, minutes, hours, days, or years.
3. Read Activity as expected decays per second. Use Specific activity to compare activity per gram. The remaining result cards show the atom count, decay constant, and mean lifetime.
4. Review the Decay checkpoints table to see the remaining fraction, mass, and activity after 0, 1, 2, 3, and 5 half-lives.
5. Select Download Excel to create a current-state workbook. Reset clears the demonstration values and results; export stays disabled until a complete valid state is entered again.

Input guide

Sample mass is required and must be a positive finite number. Accepted input uses a decimal point; plain scientific notation such as 1e-6 is accepted, while decimal commas are rejected to avoid ambiguity. A realistic example is 1 g. Increasing the mass increases both atom count and total activity in direct proportion, but it does not change specific activity. A common mistake is entering the total mass of a compound or solution when only part of it is the radionuclide.

Molar mass of the substance is required and must be positive. Enter the molar mass of the radionuclide itself, for example 238.05 g/mol. A larger molar mass means fewer atoms in the same sample mass, so calculated activity and specific activity fall when half-life is unchanged. Do not confuse atomic number or mass number with a measured molar mass value.

Half-life is required and must be positive. Choose the matching time unit. The startup value, 4.468 × 10⁹ years, is representative of uranium-238. A shorter half-life produces a larger decay constant and higher activity because more nuclei transform each second. A frequent error is entering years while leaving the unit set to seconds. The NIST overview of decay constants and exponential decay explains why a constant decay rate underpins radionuclide metrology.

Output guide

Activity is the expected number of decays per second, shown in Bq with an automatically selected SI prefix. It depends on all three inputs. Zero activity is not produced for a positive finite sample in this ideal model; extremely long half-lives can make the value very small. Specific activity is activity per gram and depends on molar mass and half-life, not on how many grams are entered. Number of atoms is the calculated population of radionuclide nuclei. Decay constant is λ in s⁻¹, equal to ln(2) divided by half-life in seconds. Mean lifetime is 1/λ, reported in the selected half-life unit. Each table row is an exact model checkpoint rather than a recommendation: remaining fraction equals 2 ^{– n}, and remaining mass and activity fall by that same factor after n half-lives.

Worked example

For the opening 1 g sample with molar mass 238.05 g/mol, the number of nuclei is (1 ÷ 238.05) × 6.02214076 × 10²³, or about 2.53 × 10²¹ atoms. Converting 4.468 × 10⁹ years to seconds and applying λ = ln(2)/t_1/2 gives approximately 4.92 × 10 ^{– 18} s⁻¹. Multiplying λ by the number of atoms gives about 1.24 × 10⁴ Bq, or 12.4 kBq. After one half-life, both the remaining mass and activity are one-half of their initial values; after five half-lives, 3.125% remains.

Learn more

The IAEA explanation of radiation in everyday life defines activity and half-life in practical terms. For the SI unit itself, see the BIPM overview of the International System of Units. For broader safety context, the U.S. EPA radiation basics distinguishes radioactivity from exposure and dose.