Decay Constant Calculator

About this calculator

The decay constant λ describes how quickly a radioactive isotope decays: it's the probability per unit time that any given nucleus will decay, and it relates to the more commonly cited half-life through λ = ln(2)/half-life. This calculator also returns the mean lifetime τ = 1/λ, the average time a given nucleus survives before decaying, which is longer than the half-life since it's weighted by the exponential decay curve rather than the 50% mark.

Decay constants are fundamental in nuclear physics, radiometric dating and nuclear medicine. Geologists and archaeologists use known decay constants (for carbon-14, uranium-238 and other isotopes) to date rock and organic samples from measured remaining activity. In medicine, the decay constant of a radiopharmaceutical isotope like technetium-99m determines both how quickly a diagnostic tracer's signal fades and how soon a patient's radiation exposure drops to a safe level, directly shaping dosing and imaging-window decisions.