Use this when the starting amount, elapsed time, and half-life are known.
Use this to reconstruct the quantity before decay began.
This logarithmic form estimates time from the remaining ratio.
Use this when the initial amount, final amount, and elapsed time are known.
These values describe the continuous exponential-decay model.
- Select the unknown quantity from the calculation modes.
- Choose an isotope preset or enter a custom half-life.
- Enter all values required by the selected question type.
- Choose matching units, precision, and display notation.
- Press calculate to view the result and complete working.
- Review the graph, milestone table, percentages, and interpretation.
- Use export tools to print, copy, or save your work.
What half-life means
Half-life measures how long half of a radioactive population remains. Every interval acts on the quantity still present. Therefore, decay follows an exponential pattern instead of a straight line.
A sample does not lose the same numerical amount each interval. It loses the same fraction during every half-life. This distinction explains the curved decay graph.
Amounts and activity
The same equation can model mass, atom counts, nuclei, activity, or detector count rates. The quantity unit must stay consistent between initial and remaining values. Activity is proportional to the number of undecayed nuclei in an ideal model.
Whole and fractional half-lives
Whole-number problems can often use repeated halving. Fractional values require powers or logarithms. The calculator automatically applies the suitable mathematical approach.
Radioactive dating
Dating compares the remaining quantity with an estimated original quantity. The ratio reveals how many half-lives have passed. Multiplying that count by the isotope half-life gives the estimated age.