Radioactive Decay Calculator
Model exponential decay with ease by entering either the decay constant or the isotope half-life.
Units cancel; use Bq, Ci, counts per minute, etc.
Must use same time unit as decay constant or half-life.
Optional. Leave blank to use half-life.
Optional if decay constant is supplied.
Decay constant
0.0231
Fraction remaining
0.3536
Remaining activity
353.5534
How to Use This Calculator
Enter initial activity
Use any convenient units; the calculation scales proportionally.
Provide decay data
Enter either the decay constant lambda or the half-life. The other can remain blank.
Specify elapsed time
Keep time units consistent with the decay data for accurate results.
Review decay summary
Results display the decay constant used, the remaining fraction, and the remaining activity.
Formula
A = A0 e^(-lambda t)
lambda = ln(2) / t1/2. Fraction remaining f = e^(-lambda t).
Example
With A0 = 1000 Bq, t1/2 = 30 days, t = 45 days: lambda = ln(2)/30 about 0.0231 day^-1, remaining activity = 1000 * e^(-0.0231 * 45) about 360 Bq.
Full Description
Radioactive decay follows first-order kinetics, meaning the probability of decay is constant in time and proportional to the amount present.
Using decay constants or half-life data allows you to forecast remaining activity for safety assessments, medical dosing, or tracer studies.
Frequently Asked Questions
Can I omit half-life and decay constant?
No. At least one must be provided to determine the decay rate.
What if both are supplied?
The calculator uses the decay constant field when present; otherwise it converts the half-life.
Does this account for daughter products?
No. It assumes a single-step decay chain without buildup of daughters.
How do I convert units?
Ensure time units for lambda and t match (for example both in days). Activity units can be any consistent measure.
Can I compute elapsed time from activity?
Yes by rearranging the formula: t = ln(A0 / A) / lambda.