Radioactive Decay Remaining Activity Calculator

Track decay precisely with flexible unit controls included. Switch between half-life or decay constant mode. Download reports, compare examples, and verify your steps always.

Calculator Inputs

Enter initial activity, elapsed time, and either half‑life or decay constant. Enable a target to estimate the time required to reach it.

λ = ln(2) / T1/2
Used when “Use Half-life” is selected.
Used when “Use Decay Constant” is selected.
Target uses your selected activity unit.

Formula Used

Exponential decay model:

This calculator converts your units internally to Bq and seconds, performs the decay calculation, then converts back to your selected display unit.

How to Use This Calculator

  1. Enter Initial Activity and choose its unit.
  2. Enter Time Elapsed and choose its unit.
  3. Select Use Half-life or Use Decay Constant.
  4. Provide the matching parameter (half‑life or λ).
  5. Optional: enable Target Activity to estimate required time.
  6. Press Calculate to show results above the form.
  7. Use Download CSV or Download PDF for reporting.

Example Data Table

Isotope Example Initial Activity Half-life Elapsed Time Remaining Activity
Fluorine‑18 (PET tracer) 250 MBq 109.8 min 3 h ~80.0 MBq
Iodine‑131 (therapy) 10 mCi 8.02 day 16 day ~2.5 mCi
Technetium‑99m (imaging) 740 MBq 6 h 12 h ~185 MBq

Values are approximate and rounded for demonstration.

Radioactive Decay Remaining Activity Guide

1) Why remaining activity matters

Remaining activity is the practical quantity used in labs, imaging suites, and waste handling. It helps you decide when a source is usable, when exposure rates become negligible, and when decay storage meets release criteria. Reporting activity with the correct unit avoids miscommunication across teams.

2) The exponential model behind the calculator

Most single‑nuclide decay processes follow an exponential law. The activity A(t) drops in proportion to how many unstable nuclei remain. The model uses the decay constant λ and elapsed time t, giving A(t)=A0e−λt.

3) Connecting half‑life and decay constant

Half‑life T1/2 is often tabulated because it is intuitive: after one half‑life, activity halves; after two, it becomes one quarter. The calculator converts between representations using λ = ln(2)/T1/2. If you input λ, it can also show the equivalent half‑life derived from the same relationship.

4) Unit conversions and common reporting formats

Activity is commonly reported in becquerel (Bq) and curie (Ci). The tool converts internally using 1 Ci = 3.7×1010 Bq, then returns results in your selected unit (Bq, kBq, MBq, GBq, Ci, mCi, or μCi).

5) Fraction, percent, and half‑lives elapsed

Beyond a single number, operational decisions often use ratios. The remaining fraction A/A0 shows what proportion is left, while percent remaining supports quick checks for logistics and safety documentation. Half‑lives elapsed n = t/T1/2 gives a clear sense of decay progress, even when you change time units.

6) Estimating time to reach a target activity

Decay‑in‑storage planning often starts with a target activity. When you enable the target option, the calculator rearranges the decay equation to solve for time: t = ln(A0/Atarget)/λ. This is especially useful when you need to determine the holding time before transport, disposal, or measurement at a lower count rate.

7) Practical sources of uncertainty

Real measurements include uncertainty from detector calibration, geometry, and sample handling. Some materials contain multiple radionuclides, making a single half‑life approximation imperfect. Use this calculator for dominant‑nuclide estimates and document assumptions for traceability.

8) Worked example with typical values

Suppose A0=740 MBq and T1/2=6 h. After 12 h, n=2 half‑lives, so the fraction remaining is 0.25 and A(t)≈185 MBq. If you start at 10 mCi with T1/2=8.02 days, after 16 days you expect about 2.5 mCi. These examples match the table above and help validate inputs.

FAQs

1) What is “activity” in radioactive decay?

Activity is the decay rate: the number of nuclear decays per second. It is measured in Bq, where 1 Bq equals one decay per second, and is often expressed in larger units for practical sources.

2) When should I use half‑life mode versus decay constant mode?

Use half‑life mode when your reference data lists T1/2. Use decay constant mode when λ is provided by a model, fit, or literature table. The calculator converts between them consistently using ln(2).

3) Why does the calculator show results in Bq and Ci?

Bq is the SI unit, while Ci is still common in medical and legacy documentation. Showing both helps you cross‑check reports and communicate across institutions that use different unit conventions.

4) Can this calculator handle multiple radionuclides?

It is designed for a single dominant radionuclide with one decay constant. For mixtures, you would compute each component separately and sum activities, or use a dedicated multi‑component decay model.

5) What does “half‑lives elapsed” mean operationally?

It is the number of half‑life intervals in your elapsed time. After n half‑lives, the remaining fraction is (1/2)n. It provides an intuitive check even when your time is entered in different units.

6) Why must the target activity be less than the initial activity?

In pure decay, activity decreases monotonically. If the target is greater than or equal to the initial activity, there is no positive time solution for reaching it through decay alone, so the tool blocks that case.

7) Are the example table values exact?

No. The examples are rounded to illustrate typical magnitudes and workflow checks. For compliance work, use certified half‑life data, measured initial activity, and document the exact time basis used.

Designed for quick checks, lab logs, and safety workflows.

Related Calculators

Wavelength Frequency Converter CalculatorWavenumber to Wavelength Converter CalculatorPlanck Constant Based Photon CalculatorRadiant Energy CalculatorRadiant Power CalculatorRadiant Flux CalculatorRadiant Intensity CalculatorRadiant Exitance CalculatorSolid Angle CalculatorInverse Square Law Intensity Calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.