Half-Life Decay

Also known as radioactive decay · carbon dating

N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}

N =

N0 =

t =

t1/2 =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

Radioactive decay never runs out of sample all at once — it halves, and halves again, forever. Each half-life leaves exactly 50% of what entered it, so after two half-lives a quarter remains, after ten about a thousandth. Carbon-14, with its 5,730-year half-life, is the famous example: a bone whose C-14 content has fallen to one quarter of the living value has been dead roughly 11,460 years. N and N0 can be in any matching unit — grams, atom counts, or becquerels — since only their ratio matters.

Solving for time or half-life inverts the exponential with a base-2 logarithm, which demands 0 < N < N0: you cannot take the log of a zero ratio, and decay never leaves more than it started with. The same mathematics governs drug elimination in pharmacology and the six-hour half-life of technetium-99m, the workhorse isotope of medical imaging.

Half-Life Decay

N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}

Where

$N$ = Remaining quantity
$N_0$ = Initial quantity
$t$ = Elapsed time
$t_{1/2}$ = Half-life

Missing one of these? Work it out first, then come back

Remaining quantity — Radioactive Activity (A = λN), Bohr Model Energy Levels
Initial quantity — Radioactive Activity (A = λN), Bohr Model Energy Levels
Elapsed time — Zero-Order Integrated Rate Law, First-Order Integrated Rate Law
Half-life — Half-Life and Decay Constant, Half-Life of a Second-Order Reaction