Radioactive Decay Activity Calculator
Determine the remaining radioactive activity of a nuclear isotope after a given time has elapsed. Useful for radiation safety planning, medical isotope scheduling, and nuclear waste management.
About this calculator
Radioactive decay follows first-order kinetics: the activity of a sample decreases exponentially over time. The governing formula is A(t) = A₀ × (0.5)^(t / t½), where A₀ is the initial activity in becquerels (Bq), t is the elapsed time, and t½ is the half-life of the isotope. Each half-life period cuts the remaining activity in half. The decay constant λ is related to half-life by λ = ln(2) / t½ ≈ 0.693 / t½. This relationship means short-lived isotopes decay rapidly while long-lived ones remain active for centuries or millennia. Understanding activity over time is critical for safe handling, storage, and disposal of radioactive materials.
How to use
Suppose you have a sample of Iodine-131 with an initial activity of 1,000,000 Bq and a half-life of 8 days, and you want to know its activity after 24 days. Plug into A(t) = A₀ × (0.5)^(t / t½): A(24) = 1,000,000 × (0.5)^(24 / 8) = 1,000,000 × (0.5)³ = 1,000,000 × 0.125 = 125,000 Bq. After 24 days — exactly three half-lives — the activity has dropped to 12.5% of its original value. Enter initial activity, half-life, and elapsed time to get your result instantly.
Frequently asked questions
What is the difference between radioactive activity and dose rate?
Activity (measured in becquerels) describes how many nuclear decay events occur per second in a sample — it is a property of the source itself. Dose rate (measured in sieverts per hour) describes the radiation energy absorbed by a person or object near the source and depends on distance, shielding, and the type of radiation emitted. A highly active source far away or behind thick shielding may produce a low dose rate. You need both values for complete radiation safety assessment.
How does half-life affect long-term nuclear waste storage planning?
The half-life of an isotope directly determines how long it remains hazardously radioactive. Isotopes with very short half-lives (hours to days) decay quickly but are intensely active initially. Isotopes with long half-lives (thousands to millions of years), like plutonium-239 at 24,100 years, remain active for geological timescales and require deep geological repositories. Regulatory frameworks typically require isolation for at least 10 half-lives to reduce activity to negligible levels, so a longer half-life means a far more demanding storage commitment.
Why is the becquerel used as the unit of radioactive activity?
The becquerel (Bq) is the SI unit of radioactivity, defined as one nuclear disintegration per second. It replaced the older curie (Ci), which was defined as 3.7 × 10¹⁰ disintegrations per second — equal to the activity of one gram of radium-226. The becquerel was adopted for its straightforward physical definition and compatibility with SI units. In practice, medical and industrial contexts often use kilobecquerels (kBq) or megabecquerels (MBq) since a single becquerel represents an extremely small level of activity.