Half-Life Decay
Also known as radioactive decay · carbon dating
Worked example: C-14: 100 units after 11460 yr (2 half-lives) → 25 remain — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Half-life →
Grade 11Grade 11 Math — Functions & Applications
The half-life clock →
Grade 12Grade 12 Chemistry
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Half-Life Decay explained
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 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 < : 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 formula
- = Remaining quantity
- = Initial quantity
- = Elapsed time (s)
- = Half-life (s)