Decay Correction Calculator

Calculator Input

This calculator supports forward correction, back-correction, target-time solving, and count-based activity estimation with detector parameters.

Calculation mode

Isotope or sample label

Activity unit

Reference activity

Measured activity

Target activity

Half-life

Half-life unit

Elapsed time

Elapsed time unit

Time-to-target output unit

Branching ratio

Detector efficiency

Total counts

Count time (seconds)

Graph span in half-lives

Plotly Graph

The chart traces projected activity decay from the current reference point across the selected number of half-lives.

Example Data Table

Sample values below show how activity falls with time for a source having a 6-hour half-life and an initial activity of 150 MBq.

Elapsed Time	Decay Factor	Activity	Percent Remaining
0 hours	1.000000	150.000 MBq	100%
6 hours	0.500000	75.000 MBq	50%
12 hours	0.250000	37.500 MBq	25%
18 hours	0.125000	18.750 MBq	12.5%
24 hours	0.062500	9.375 MBq	6.25%

Formula Used

Basic decay law: A(t) = A₀ × e^(-λt)

Decay constant: λ = ln(2) / T½

Back-correction: A₀ = A(t) × e^(λt)

Time to target: t = ln(A₀ / A) / λ

Counts-based activity: A = Counts / (time × branching ratio × efficiency)

Radioactive decay follows exponential behavior. The half-life gives the time required for activity to drop to half its current value. The decay constant converts half-life into a continuous rate model. A decay correction multiplies measured activity by the inverse decay factor when you need the activity at an earlier reference time.

How to Use This Calculator

Select a calculation mode based on your task.
Enter the sample half-life and choose its unit.
Provide reference, measured, or target activity values as needed.
Enter elapsed time between the reference and measurement moments.
For detector work, add counts, count time, branching ratio, and efficiency.
Click Calculate decay correction to display the result above the form.
Review the summary table and graph for validation.
Export the result using the CSV or PDF buttons.

FAQs

1. What is decay correction?

Decay correction adjusts radioactive activity to a different time point. It is used when sample preparation, transport, imaging, or measurement occurs after the original reference time.

2. Why is half-life important here?

Half-life controls how fast the source loses activity. A shorter half-life means faster decay and larger corrections over the same elapsed interval.

3. When should I back-correct activity?

Use back-correction when you measured a sample later but need its earlier activity. This is common in nuclear medicine, radiochemistry, and lab calibrations.

4. Can I use counts instead of direct activity?

Yes. If you know count time, detector efficiency, and branching ratio, the calculator estimates measured activity from counts and then applies decay correction.

5. What units can I use?

The calculator supports seconds through years for time and Bq, kBq, MBq, GBq, Ci, mCi, and uCi for activity.

6. What does the correction factor mean?

The correction factor equals e^(λt). It tells you how much larger the earlier activity was compared with the measured later activity.

7. Why does the graph start high and curve downward?

Exponential decay drops quickly at first in absolute terms, then gradually approaches zero. The graph visualizes how activity changes over several half-lives.

8. Can this be used for teaching and reports?

Yes. It includes formulas, a worked example table, a chart, and export tools, making it useful for classroom demonstrations, lab notes, and technical reports.