☢️

Radioactive Decay Calculator

Calculate remaining activity, percent remaining, and number of half-lives elapsed for any radioactive isotope using the exponential decay law.

Initial activity or quantity (Bq, Ci, grams, or any unit).
Half-life in the same time unit as time elapsed (years for C-14, days for I-131).
Time elapsed in the same unit as the half-life.

Results

Remaining Activity250.0,000 remaining
Percent Remaining25.000%
Half-lives Elapsed2.00 half-lives elapsed

📖What is it?

Radioactive decay follows the exponential law N(t) = N0 * e^(-lambda * t), where lambda = ln(2) / t_half is the decay constant. After each half-life, exactly half of the remaining atoms have decayed. This is first-order kinetics.

🎯How to use

Enter the initial activity or amount, the half-life (in any time unit), and the elapsed time in the same unit. The calculator returns the remaining quantity, percentage remaining, and how many half-lives have passed.

💡Example scenario

Carbon-14 dating (half-life 5,730 years): a sample with 1,000 initial C-14 atoms after 11,460 years (2 half-lives) = 250 atoms remaining (25%). I-131 for thyroid therapy (half-life 8.02 days): after 24 days (3 half-lives) = 12.5% of initial dose remains. U-235 (703 million year half-life): after 1 billion years = 37% remains.

🏆Pro tip

After 10 half-lives, only 0.098% of the original activity remains -- effectively negligible for most purposes. In nuclear medicine, 5-7 half-lives is used for radioactive waste disposal clearance. For carbon dating, the practical range is up to about 50,000 years (about 8-9 half-lives of C-14), beyond which the remaining signal becomes too small to measure accurately.