About this tool
The Half-Life / Radioactive Decay Calculator is a free, in-browser tool that models exponential decay with N = N₀·(½)^(t/T½). Leave one of the four boxes — initial amount, remaining amount, half-life, or elapsed time — blank and it is solved from the others, and the tool also reports the decay constant λ = ln2/T½ and the mean lifetime τ = 1/λ = T½/ln2.
Every calculation runs locally in your browser with no data sent anywhere, so the amounts and times you enter stay on your device. A small SVG curve illustrates the fraction remaining across several half-lives, and the results update live as you type.
The amounts N and N₀ can be in any consistent unit (grams, atoms, becquerels, or a percentage) as long as both use the same one. The half-life and elapsed time must share a single time unit (seconds, years, and so on); the decay constant is then per that time unit and the mean lifetime is in that same unit.
Frequently asked questions
What units should I use?
N and N₀ can be any consistent amount unit (grams, atoms, %, Bq) as long as both match. Half-life and elapsed time must use the same time unit; the decay constant λ comes out per that unit and mean lifetime in that unit.
How does it solve for half-life or elapsed time?
From N = N₀·(½)^(t/T) it inverts using logarithms: T½ = t·ln2 ÷ ln(N₀/N) and t = T½·ln(N₀/N) ÷ ln2. Both require N and N₀ positive with N smaller than N₀.
What are the decay constant and mean lifetime?
The decay constant is λ = ln2 ÷ T½ and describes the instantaneous decay rate; the mean lifetime τ = 1/λ = T½ ÷ ln2 ≈ 1.4427·T½ is the average time an individual nucleus survives.
Why do I get an error solving for half-life?
Finding the half-life or elapsed time needs a genuine decay: N₀ and N must both be positive with N less than N₀ and a positive elapsed time, otherwise ln(N₀/N) is undefined or non-positive and no finite answer exists.
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