Solve radioactive decay and exponential decay problems.
N(t) = N₀ × (½)^(t ÷ T½). Carbon-14 (half-life 5,730 years): 100 g left after 11,460 years is 25 g — two half-lives.
A half-life is the time it takes for a quantity to fall to half its value. Choose what to find — the remaining quantity N(t), the initial quantity N₀, the half-life T½ or the elapsed time t — enter the other three and the calculator solves it, adding the decay constant λ, the mean lifetime τ, the fraction remaining and a table of the quantity after each of the first ten half-lives.
The formula is exponential decay — see the Exponent Calculator and Log Calculator for the maths behind it. Related: Scientific Calculator, Percentage Calculator and Compound Interest Calculator (growth is the reverse of decay).
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Initial quantity N₀ | 100 |
| Remaining quantity N(t) | 25 |
| Half-life T½ | 5730 |
| Elapsed time t | 11460 |
| Number of half-lives (t ÷ T½) | 2 |
| Fraction remaining | 0.25 |
| Decay constant λ = ln 2 ÷ T½ | 0.00012096809 |
| Mean lifetime τ = T½ ÷ ln 2 | 8266.6426 |
| Half-lives | Time | Remaining | Percent |
|---|---|---|---|
| 1 | 5730 | 50 | 50% |
| 2 | 11460 | 25 | 25% |
| 3 | 17190 | 12.5 | 12.5% |
| 4 | 22920 | 6.25 | 6.25% |
| 5 | 28650 | 3.125 | 3.125% |
| 6 | 34380 | 1.5625 | 1.5625% |
| 7 | 40110 | 0.78125 | 0.78125% |
| 8 | 45840 | 0.390625 | 0.390625% |
| 9 | 51570 | 0.1953125 | 0.195313% |
| 10 | 57300 | 0.09765625 | 0.097656% |
| Elapsed time | Remaining (g) |
|---|---|
| After 1 half-life (5,730 y) | 50 |
| After 2 half-lives | 25 |
| After 3 half-lives | 12.5 |
| After 5 half-lives | 3.125 |
| After 10 half-lives | 0.09765625 |
| Isotope | Half-life |
|---|---|
| Carbon-14 | 5,730 years |
| Cobalt-60 | 5.27 years |
| Cesium-137 | 30.2 years |
| Iodine-131 | 8.02 days |
| Technetium-99m | 6.01 hours |
| Uranium-238 | 4.47 billion years |
The time required for half of a radioactive substance (or any exponentially decaying quantity) to decay.
Multiply the starting amount by one half raised to the number of half-lives elapsed: N₀ × 0.5^(t ÷ T½).
About 5,730 years, which is why it is used to date organic material up to roughly 50,000 years old.
λ = ln 2 ÷ T½ — the fraction decaying per unit time in the continuous model.
The average time an atom survives before decaying: τ = T½ ÷ ln 2, about 1.44 half-lives.
Yes — to medicine concentrations in the body, to cooling, and to anything that decays by a constant percentage.
It uses the standard method: N(t) = N₀ × (½)^(t ÷ T½) λ = ln 2 ÷ T½ The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
