Radioactive Element Half-Life Decay Calculator

Enter Calculation

Radioactive element Custom (enter half-life) Carbon-14 Potassium-40 Cobalt-56 Cobalt-60 Strontium-90 Zirconium-93 Technetium-99 Iodine-129 Iodine-131 Iodine-134 Cesium-134 Cesium-135 Cesium-137 Promethium-147 Radon-220 Radon-222 Radium-226 Uranium-234 Uranium-235 Uranium-238 Plutonium-239 Plutonium-241 Plutonium-244

Half-life

Half-life unit seconds minutes hours days years

Calculation period (elapsed time)

Elapsed time unit seconds minutes hours days years

Initial quantity (any unit: Bq, g, %)

Formula

Show calculation steps (2)

1. Percent Remaining

   

   Fraction of the original sample still present, independent of the initial quantity.

2. Decay Constant

   

   Decay constant lambda from the half-life (in seconds).

Results

Remaining quantity

7.493458

same unit as the initial quantity

Percent remaining	7.4935 %
Number of half-lives elapsed	3.738225
Decay constant (per second)	0.000000999668

What this calculator does

This tool applies the radioactive decay law to find how much of a radioactive element is left after a given amount of time has passed. You supply the element's half-life, how much time has elapsed, and the initial quantity, and it returns the remaining quantity together with the percent remaining and the number of half-lives that have gone by. The physics is universal: it works the same way everywhere, whether you measure the substance in becquerels, grams, atoms, or percent.

How to use it

Pick a nuclide from the dropdown to auto-fill a standard literature half-life and its time unit, or choose "Custom" and type your own. Enter the calculation period (elapsed time) with its own unit, then the initial quantity. The half-life and elapsed time can use different units; the calculator converts both to seconds internally before taking the ratio, so the answer is always correct.

The formula explained

The amount remaining follows $$N(t) = N_0 \times \left(\frac{1}{2}\right)^{t / T_{1/2}}$$ The exponent \(t/T_{1/2}\) is simply the number of half-lives that have elapsed; every whole half-life multiplies the amount by one-half. An equivalent exponential form is \(N(t) = N_0 \times e^{-\lambda t}\), where the decay constant \(\lambda = \ln(2) / T_{1/2}\). Percent remaining is just \(N(t)/N_0 \times 100\).

Each half-life period reduces the remaining quantity by half: \(N_0\), \(N_0/2\), \(N_0/4\), \(N_0/8\).

Worked example (Iodine-131)

Iodine-131 has a half-life of 8.0252 days. After 30 days with an initial 100 units: \(t/T_{1/2} = 30 / 8.0252 = 3.7382\) half-lives. $$N(t) = 100 \times 2^{-3.7382} = 100 \times 0.07491 \approx 7.49 \text{ units}$$ i.e. about 7.49% remaining.

Iodine-131 sample halving over successive 8-day half-life intervals.

FAQ

Can elapsed time and half-life use different units? Yes. The calculator converts both to seconds, so days vs. years (etc.) are handled automatically.

Does the amount ever reach zero? No. Exponential decay approaches zero but never reaches it exactly; it just keeps halving.

What if I enter a negative elapsed time? The math still works and gives a value larger than the initial quantity, which represents a back-calculation to an earlier moment.