# Half-Life Activity Decay Calculator (A = A₀·e^(−λt)) Compute remaining radionuclide activity A(t) = A₀·2^(−t/T½) with λ = ln2/T½ in Bq/Ci/dpm units, for Tc-99m, F-18 and other isotopes. > Canonical page: https://elysiatools.com/en/tools/half-life-activity-decay - **Category:** Math & Numbers - **Keywords:** half life, radioactive decay, activity decay, remaining activity, decay constant, becquerel, curie, tc-99m, f-18, nuclear medicine ## Overview The Half-Life Activity Decay Calculator computes the remaining radioactivity of any radionuclide over time using standard decay equations. It supports units including Becquerel (Bq, kBq, MBq, GBq), Curie (Ci, mCi, µCi), and dpm, providing remaining activity, percentage remaining, and elapsed half-lives. ## Inputs - **Initial Activity A₀** (number): Activity at t = 0 in the selected activity unit. Must be non-negative. - **Activity Unit** (select): Unit of the initial (and remaining) activity. - **Half-life T½** (number): Physical half-life in the selected time unit. Must be greater than zero. - **Half-life T½** (select): Time unit of the half-life. - **Elapsed Time t** (number): Time since the initial activity measurement. Must be non-negative. - **Elapsed Time t** (select): Time unit of the elapsed time. - **Decimal Places** (number) ## When to use - Adjusting radiopharmaceutical dosage for patient administration delays in nuclear medicine. - Calculating residual activity in laboratory radiotracers and radioactive standard sources. - Estimating the radioactive decay of waste stored for decay-in-storage disposal. ## How it works - Enter the initial radionuclide activity (A₀) and select the corresponding activity unit. - Specify the isotope physical half-life (T½) and the elapsed decay duration (t) in seconds, minutes, hours, days, or years. - Set the desired decimal precision to calculate the remaining activity, decay constant (λ), and elapsed half-lives. ## Use cases - Nuclear medicine clinics verifying Tc-99m or F-18 activity prior to patient injection. - Research laboratories calibrating scintillation counting standards and assay reagents. - Radiation safety officers tracking short-lived radioactive isotope inventory decay. ## Frequently asked questions ### What mathematical formula does this calculator use? It applies the exponential decay law A(t) = A₀ · e^(−λt) or A(t) = A₀ · 2^(−t/T½), where λ = ln(2) / T½. ### Can I use different time units for half-life and elapsed time? Yes, you can independently select seconds, minutes, hours, days, or years for half-life and elapsed time. ### What activity units are supported? Supported units include Bq, kBq, MBq, GBq, Ci, mCi, µCi, and dpm (disintegrations per minute). ### Does the calculation depend on the isotope type? The calculation depends entirely on the numerical half-life value and unit you provide for your specific isotope. ### What is the relationship between elapsed half-lives and remaining percentage? 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